Package 'vcmeta'

Description

This function computes the Pearson correlation between paired measurements using a reported paired-samples t statistic and other sample information. This correlation estimate is needed in several functions that analyze mean differences and standardized mean differences in paired-samples studies.

Usage

cor.from.t(m1, m2, sd1, sd2, t, n)

Arguments

Value

Returns the sample Pearson correlation between the two paired measurements

Examples

cor.from.t(9.4, 9.8, 1.26, 1.40, 2.27, 30)

# Should return:
#                Estimate
# Correlation:  0.7415209

Description

Computes the estimate, standard error, and confidence interval for an average G-index of agreement from two or more studies. This function assumes that two raters each provide a dichotomous rating to a sample of objects. As a measure of agreement, the G-index is usually preferred to Cohen's kappa.

Usage

meta.ave.agree(alpha, f11, f12, f21, f22, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

f11 <- c(43, 56, 49)
f12 <- c(7, 2, 9)
f21 <- c(3, 5, 5)
f22 <- c(37, 54, 39)
meta.ave.agree(.05, f11, f12, f21, f22, bystudy = TRUE)

# Should return:
#          Estimate         SE        LL        UL
# Average 0.7843250 0.03540254 0.7149373 0.8537127
# Study 1 0.7446809 0.06883919 0.6097585 0.8796032
# Study 2 0.8512397 0.04770701 0.7577356 0.9447437
# Study 3 0.6981132 0.06954284 0.5618117 0.8344147

Description

Computes the estimate, standard error, and confidence interval for an average Pearson or partial correlation from two or more studies. The sample correlations must be all Pearson correlations or all partial correlations. Use the meta.ave.gen function to meta-analyze any combination of Pearson, partial, or Spearman correlations.

Usage

meta.ave.cor(alpha, n, cor, s, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Meta-analytic interval estimation for bivariate correlations.” Psychological Methods, 13(3), 173–181. ISSN 1939-1463, doi:10.1037/a0012868.

Examples

n <- c(55, 190, 65, 35)
cor <- c(.40, .65, .60, .45)
meta.ave.cor(.05, n, cor, 0, bystudy = TRUE)

# Should return:
#         Estimate         SE        LL        UL
# Average    0.525 0.05113361 0.4176678 0.6178816
# Study 1    0.400 0.11430952 0.1506943 0.6014699
# Study 2    0.650 0.04200694 0.5594086 0.7252465
# Study 3    0.600 0.08000000 0.4171458 0.7361686
# Study 4    0.450 0.13677012 0.1373507 0.6811071

Description

Computes the estimate, standard error, and confidence interval for an average correlation. Any type of correlation can be used (e.g., Pearson, Spearman, semipartial, factor correlation, Gamma coefficient, Somers d coefficient, tetrachoric, point-biserial, biserial, etc.).

Usage

meta.ave.cor.gen(alpha, cor, se, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Meta-analytic interval estimation for bivariate correlations.” Psychological Methods, 13(3), 173–181. ISSN 1939-1463, doi:10.1037/a0012868.

Examples

cor <- c(.396, .454, .409, .502, .350)
se <- c(.104, .064, .058, .107, .086)
meta.ave.cor.gen(.05, cor, se, bystudy = TRUE)

# Should return:
#         Estimate         SE        LL        UL
# Average   0.4222 0.03853362 0.3438560 0.4947070
# Study 1   0.3960 0.10400000 0.1753200 0.5787904
# Study 2   0.4540 0.06400000 0.3200675 0.5701415
# Study 3   0.4090 0.05800000 0.2893856 0.5160375
# Study 4   0.5020 0.10700000 0.2651183 0.6817343
# Study 5   0.3500 0.08600000 0.1716402 0.5061435

Description

Computes the estimate, standard error, and confidence interval for an average Cronbach reliability coefficient from two or more studies.

Usage

meta.ave.cronbach(alpha, n, rel, r, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2010). “Varying coefficient meta-analytic methods for alpha reliability.” Psychological Methods, 15(4), 368–385. ISSN 1939-1463, doi:10.1037/a0020142.

Examples

n <- c(583, 470, 546, 680)
rel <- c(.91, .89, .90, .89)
meta.ave.cronbach(.05, n, rel, 10, bystudy = TRUE)

# Should return:
#         Estimate          SE        LL        UL
# Average   0.8975 0.003256081 0.8911102 0.9038592
# Study 1   0.9100 0.005566064 0.8985763 0.9204108
# Study 2   0.8900 0.007579900 0.8743616 0.9041013
# Study 3   0.9000 0.006391375 0.8868623 0.9119356
# Study 4   0.8900 0.006297549 0.8771189 0.9018203

Description

This function should be used with the meta.ave.gen function when the effect size is a correlation. Use the estimated average correlation and its standard error from meta.ave.gen in this function to obtain a more accurate confidence interval for the population average correlation.

Usage

meta.ave.fisher(alpha, cor, se)

Arguments

Value

Returns a 1-row matrix. The columns are:

• Estimate - estimate of average correlation (from input)

• LL - lower limit of the confidence interval

• UL - lower limit of the confidence interval

Examples

meta.ave.fisher(0.05, 0.376, .054)

# Should return:
# Estimate        LL        UL
#    0.376 0.2656039 0.4766632

Description

Computes the estimate, standard error, and confidence interval for an average of any type of parameter from two or more studies.

Usage

meta.ave.gen(alpha, est, se, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen(.05, est, se, bystudy = TRUE)

# Should return:
#          Estimate        SE          LL        UL
# Average  0.393125 0.1561622  0.08705266 0.6991973
# Study 1  0.022000 0.1240000 -0.22103553 0.2650355
# Study 2  0.751000 0.4640000 -0.15842329 1.6604233
# Study 3  0.421000 0.1020000  0.22108367 0.6209163
# Study 4  0.287000 0.5920000 -0.87329868 1.4472987
# Study 5  0.052000 0.8640000 -1.64140888 1.7454089
# Study 6  0.146000 0.2410000 -0.32635132 0.6183513
# Study 7  0.562000 0.2520000  0.06808908 1.0559109
# Study 8  0.904000 0.3180000  0.28073145 1.5272685

Description

Computes the estimate, standard error, and confidence interval for a weighted average effect from two or more studies using the constant coefficient (fixed-effect) meta-analysis model.

Usage

meta.ave.gen.cc(alpha, est, se, bystudy = TRUE)

Arguments

Details

The weighted average estimate will be biased regardless of the number of studies or the sample size in each study. The actual confidence interval coverage probability can be much smaller than the specified confidence level when the population effect sizes are not identical across studies.

The constant coefficient model should be used with caution, and the varying coefficient methods in this package are the recommended alternatives. The varying coefficient methods do not require effect-size homogeneity across the selected studies. This constant coefficient meta-analysis function is included in the vcmeta package primarily for classroom demonstrations to illustrate the problematic characteristics of the constant coefficient meta-analysis model.

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

• Hedges LV, Olkin I (1985). Statistical methods for meta-analysis. Academic Press, New York. ISBN 01-233-63802.

• Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2009). Introduction to meta-analysis. Wiley, New York.

See Also

meta.ave.gen

Examples

est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen.cc(.05, est, se, bystudy = TRUE)

# Should return:
#             Estimate         SE          LL        UL
# Average    0.3127916 0.06854394  0.17844794 0.4471352
# Study 1    0.0220000 0.12400000 -0.22103553 0.2650355
# Study 2    0.7510000 0.46400000 -0.15842329 1.6604233
# Study 3    0.4210000 0.10200000  0.22108367 0.6209163
# Study 4    0.2870000 0.59200000 -0.87329868 1.4472987
# Study 5    0.0520000 0.86400000 -1.64140888 1.7454089
# Study 6    0.1460000 0.24100000 -0.32635132 0.6183513
# Study 7    0.5620000 0.25200000  0.06808908 1.0559109
# Study 8    0.9040000 0.31800000  0.28073145 1.5272685

Description

Computes the estimate, standard error, and confidence interval for a weighted average effect from multiple studies using the random coefficient (random-effects) meta-analysis model. An estimate of effect-size heterogeneity (tau-squared) is also computed.

Usage

meta.ave.gen.rc(alpha, est, se, bystudy = TRUE)

Arguments

Details

The random coefficient model assumes that the studies in the meta-analysis are a random sample from some definable superpopulation of studies. This assumption is very difficult to justify. The weighted average estimate will be biased regardless of the number of studies or the sample size in each study. The actual confidence interval coverage probability can much smaller than the specified confidence level if the effect sizes are correlated with the weights (which occurs frequently). The confidence interval for tau-squared assumes that the true effect sizes in the superpopulation of studies have a normal distribution. A large number of studies, each with a large sample size, is required to assess the superpopulation normality assumption and to accurately estimate tau-squared. The confidence interval for the population tau-squared is hypersensitive to very minor and difficult-to-detect violations of the superpopulation normality assumption.

The random coefficient model should be used with caution, and the varying coefficient methods in this package are the recommended alternatives. The varying coefficient methods allows the effect sizes to differ across studies but do not require the studies to be a random sample from a definable superpopoulation of studies. This random coefficient function is included in the vcmeta package primarily for classroom demonstrations to illustrate the problimatic characteristics of the random coefficient meta-analysis model.

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is true, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

• Hedges LV, Olkin I (1985). Statistical methods for meta-analysis. Academic Press, New York. ISBN 01-233-63802.

• Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2009). Introduction to meta-analysis. Wiley, New York.

See Also

meta.ave.gen

Examples

est <- c(.022, .751, .421, .287, .052, .146, .562, .904)
se <- c(.124, .464, .102, .592, .864, .241, .252, .318)
meta.ave.gen.rc(.05, est, se, bystudy = TRUE)

# Should return: 
#               Estimate        SE          LL        UL
# Tau-squared 0.03772628 0.0518109  0.00000000 0.1392738
# Average     0.35394806 0.1155239  0.12752528 0.5803708
# Study 1     0.02200000 0.1240000 -0.22103553 0.2650355
# Study 2     0.75100000 0.4640000 -0.15842329 1.6604233
# Study 3     0.42100000 0.1020000  0.22108367 0.6209163
# Study 4     0.28700000 0.5920000 -0.87329868 1.4472987
# Study 5     0.05200000 0.8640000 -1.64140888 1.7454089
# Study 6     0.14600000 0.2410000 -0.32635132 0.6183513
# Study 7     0.56200000 0.2520000  0.06808908 1.0559109
# Study 8     0.90400000 0.3180000  0.28073145 1.5272685

Description

Computes the estimate, standard error, and confidence interval for an average mean difference from two or more paired-samples studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval for the average effect size. Equality of variances within or across studies is not assumed.

Usage

meta.ave.mean.ps(alpha, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
meta.ave.mean.ps(.05, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)

# Should return:
#        Estimate        SE        LL         UL      df
# Average   -3.25 0.2471557 -3.739691 -2.7603091 112.347
# Study 1   -2.00 0.5871400 -3.200836 -0.7991639  29.000
# Study 2   -2.00 0.4918130 -2.988335 -1.0116648  49.000
# Study 3   -5.00 0.5471136 -6.118973 -3.8810270  29.000
# Study 4   -4.00 0.3023716 -4.603215 -3.3967852  69.000

Description

Computes the estimate, standard error, and confidence interval for an average mean difference from two or more 2-group studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence intervals. Equality of variances within or across studies is not assumed.

Usage

meta.ave.mean2(alpha, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(7.4, 6.9)
m2 <- c(6.3, 5.7)
sd1 <- c(1.72, 1.53)
sd2 <- c(2.35, 2.04)
n1 <- c(40, 60)
n2 <- c(40, 60)
meta.ave.mean2(.05, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

# Should return:
#         Estimate        SE        LL       UL        df
# Average     1.15 0.2830183 0.5904369 1.709563 139.41053
# Study 1     1.10 0.4604590 0.1819748 2.018025  71.46729
# Study 2     1.20 0.3292036 0.5475574 1.852443 109.42136

Description

Computes the estimate, standard error, and confidence interval for a geometric average mean ratio from two or more paired-samples studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval for the average effect size. Equality of variances within or across studies is not assumed.

Usage

meta.ave.meanratio.ps(alpha, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

• df - degrees of freedom

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
meta.ave.meanratio.ps(.05, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)

# Should return:
#            Estimate          SE          LL          UL
# Average -0.05695120 0.004350863 -0.06558008 -0.04832231
# Study 1 -0.03704127 0.010871086 -0.05927514 -0.01480740
# Study 2 -0.03278982 0.008021952 -0.04891054 -0.01666911
# Study 3 -0.09015110 0.009779919 -0.11015328 -0.07014892
# Study 4 -0.06782260 0.004970015 -0.07773750 -0.05790769
#         exp(Estimate)   exp(LL)   exp(UL)       df
# Average     0.9446402 0.9365240 0.9528266 103.0256
# Study 1     0.9636364 0.9424474 0.9853017  29.0000
# Study 2     0.9677419 0.9522663 0.9834691  49.0000
# Study 3     0.9137931 0.8956968 0.9322550  29.0000
# Study 4     0.9344262 0.9252073 0.9437371  69.0000

Description

Computes the estimate, standard error, and confidence interval for a geometric average mean ratio from two or more 2-group studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence intervals. Equality of variances within or across studies is not assumed.

Usage

meta.ave.meanratio2(alpha, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

• df - degrees of freedom

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. ISSN 1076-9986, doi:10.3102/1076998620934125.

Examples

m1 <- c(7.4, 6.9)
m2 <- c(6.3, 5.7)
sd1 <- c(1.7, 1.5)
sd2 <- c(2.3, 2.0)
n1 <- c(40, 20)
n2 <- c(40, 20)
meta.ave.meanratio2(.05, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)

# Should return:
#          Estimate         SE          LL        UL  exp(Estimate)
# Average 0.1759928 0.05738065 0.061437186 0.2905484       1.192429
# Study 1 0.1609304 0.06820167 0.024749712 0.2971110       1.174603
# Study 2 0.1910552 0.09229675 0.002986265 0.3791242       1.210526
#          exp(LL)  exp(UL)       df
# Average 1.063364 1.337161 66.26499
# Study 1 1.025059 1.345965 65.69929
# Study 2 1.002991 1.461004 31.71341

Description

Computes the estimate, standard error, and confidence interval for a geometric average odds ratio from two or more studies.

Usage

meta.ave.odds(alpha, f1, f2, n1, n2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - the exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Bonett DG, Price RM (2015). “Varying coefficient meta-analysis methods for odds ratios and risk ratios.” Psychological Methods, 20(3), 394–406. ISSN 1939-1463, doi:10.1037/met0000032.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
meta.ave.odds(.05, f1, f2, n1, n2, bystudy = TRUE)

# Should return:
#           Estimate        SE          LL        UL 
# Average 0.86211102 0.2512852  0.36960107 1.3546210
# Study 1 0.02581353 0.3700520 -0.69947512 0.7511022
# Study 2 0.91410487 0.3830515  0.16333766 1.6648721
# Study 3 0.41496672 0.2226089 -0.02133877 0.8512722
# Study 4 1.52717529 0.6090858  0.33338907 2.7209615
# Study 5 1.42849472 0.9350931 -0.40425414 3.2612436
#         exp(Estimate)   exp(LL)   exp(UL)
# Average      2.368155 1.4471572  3.875292
# Study 1      1.026150 0.4968460  2.119335
# Study 2      2.494541 1.1774342  5.284997
# Study 3      1.514320 0.9788873  2.342625
# Study 4      4.605150 1.3956902 15.194925
# Study 5      4.172414 0.6674745 26.081952

Description

Computes the estimate, standard error, and confidence interval for an average slope coefficient in a general linear model (ANOVA, ANCOVA, multiple regression) or a path model from two or more studies.

Usage

meta.ave.path(alpha, n, slope, se, s, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

n <- c(75, 85, 250, 160)
slope <- c(1.57, 1.38, 1.08, 1.25)
se <- c(.658, .724, .307, .493)
meta.ave.path(.05, n, slope, se, 2, bystudy = TRUE)

#  Should return:
#         Estimate         SE          LL       UL       df
#  Average     1.32 0.2844334  0.75994528 1.880055 263.1837
#  Study 1     1.57 0.6580000  0.25830097 2.881699  72.0000
#  Study 2     1.38 0.7240000 -0.06026664 2.820267  82.0000
#  Study 3     1.08 0.3070000  0.47532827 1.684672 247.0000
#  Study 4     1.25 0.4930000  0.27623174 2.223768 157.0000

Description

Computes the estimate, standard error, and confidence interval for an average point-biserial correlation from two or more studies. Two types of point-biserial correlations can be meta-analyzed. One type uses an unweighted variance and is appropriate in 2-group experimental designs. The other type uses a weighted variance and is appropriate in 2-group nonexperimental designs with simple random sampling (but not stratified random sampling) within each study. This function requires all point-biserial correlations to be of the same type. Use the meta.ave.gen function to meta-analyze any combination of biserial correlation types.

Usage

meta.ave.pbcor(alpha, m1, m2, sd1, sd2, n1, n2, type, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2020). “Point-biserial correlation: Interval estimation, hypothesis testing, meta-analysis, and sample size determination.” British Journal of Mathematical and Statistical Psychology, 73(S1), 113–144. ISSN 0007-1102, doi:10.1111/bmsp.12189.

Examples

m1 <- c(21.9, 23.1, 19.8)
m2 <- c(16.1, 17.4, 15.0)
sd1 <- c(3.82, 3.95, 3.67)
sd2 <- c(3.21, 3.30, 3.02)
n1 <- c(40, 30, 24)
n2 <- c(40, 28, 25)
meta.ave.pbcor(.05, m1, m2, sd1, sd2, n1, n2, 2, bystudy = TRUE)

# Should return:
#          Estimate         SE        LL        UL
# Average 0.6159094 0.04363432 0.5230976 0.6942842
# Study 1 0.6349786 0.06316796 0.4842098 0.7370220
# Study 2 0.6160553 0.07776700 0.4255342 0.7380898
# Study 3 0.5966942 0.08424778 0.3903883 0.7283966

Description

Generates a forest plot to visualize effect sizes estimates and overall averages from the meta.ave functions in vcmeta. If the column exp(Estimate) is present, this function plots the exponentiated effect size and CI found in columns exp(Estimate), exp(LL), and exp(UL). Otherwise, this function plots the effect size and CI found in the columns Estimate, LL, and UL.

Usage

meta.ave.plot(
  result,
  reference_line = NULL,
  diamond_height = 0.2,
  ggtheme = ggplot2::theme_classic()
)

Arguments

Value

Returns a ggplot object. If stored, can be further customized via the ggplot API

Examples

# Plot results from meta.ave.mean2
m1 <- c(7.4, 6.9)
m2 <- c(6.3, 5.7)
sd1 <- c(1.72, 1.53)
sd2 <- c(2.35, 2.04)
n1 <- c(40, 60)
n2 <- c(40, 60)
result <- meta.ave.mean2(.05, m1, m2, sd1, sd2, n1, n2, bystudy = TRUE)
meta.ave.plot(result, reference_line = 0)


# Plot results from meta.ave.meanratio2
# Note that this plots the exponentiated effect size and CI
m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
result <- meta.ave.meanratio.ps(.05, m1, m2, sd1, sd2, cor, n, bystudy = TRUE)
myplot <- meta.ave.plot(result, reference_line = 1)
myplot

# Change x-scale to log2
library(ggplot2)
myplot <- myplot + scale_x_continuous(
  trans = 'log2', 
  limits = c(0.75, 1.25), 
  name = "Estimated Ratio of Means, Log2 Scale"
)
myplot

Description

Computes the estimate, standard error, and confidence interval for an average proportion difference from two or more studies.

Usage

meta.ave.prop.ps(alpha, f11, f12, f21, f22, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

f11 <- c(17, 28, 19)
f12 <- c(43, 56, 49)
f21 <- c(3, 5, 5)
f22 <- c(37, 54, 39)
meta.ave.prop.ps(.05, f11, f12, f21, f22, bystudy = TRUE)

# Should return:
#          Estimate         SE        LL        UL
# Average 0.3809573 0.03000016 0.3221581 0.4397565
# Study 1 0.3921569 0.05573055 0.2829270 0.5013867
# Study 2 0.3517241 0.04629537 0.2609869 0.4424614
# Study 3 0.3859649 0.05479300 0.2785726 0.4933572

Description

Computes the estimate, standard error, and confidence interval for an average proportion difference from two or more studies.

Usage

meta.ave.prop2(alpha, f1, f2, n1, n2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
meta.ave.prop2(.05, f1, f2, n1, n2, bystudy = TRUE)

# Should return:
#             Estimate         SE            LL         UL
# Average 0.0567907589 0.01441216  2.854345e-02 0.08503807
# Study 1 0.0009888529 0.03870413 -7.486985e-02 0.07684756
# Study 2 0.1067323481 0.04018243  2.797623e-02 0.18548847
# Study 3 0.0310980338 0.01587717 -2.064379e-05 0.06221671
# Study 4 0.0837856174 0.03129171  2.245499e-02 0.14511624
# Study 5 0.0524199553 0.03403926 -1.429577e-02 0.11913568

Description

Computes the estimate, standard error, and confidence interval for a geometric average proportion ratio from two or more studies.

Usage

meta.ave.propratio2(alpha, f1, f2, n1, n2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Price RM, Bonett DG (2008). “Confidence intervals for a ratio of two independent binomial proportions.” Statistics in Medicine, 27(26), 5497–5508. ISSN 02776715, doi:10.1002/sim.3376.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
meta.ave.propratio2(.05, f1, f2, n1, n2, bystudy = TRUE)

#  Should return:
#           Estimate        SE          LL        UL 
# Average 0.84705608 0.2528742  0.35143178 1.3426804
# Study 1 0.03604257 0.3297404 -0.61023681 0.6823220
# Study 2 0.81008932 0.3442007  0.13546839 1.4847103
# Study 3 0.38746839 0.2065227 -0.01730864 0.7922454
# Study 4 1.49316811 0.6023296  0.31262374 2.6737125
# Study 5 1.50851199 0.9828420 -0.41782290 3.4348469
#     exp(Estimate)   exp(LL)   exp(UL)
# Average  2.332769 1.4211008  3.829294
# Study 1  1.036700 0.5432222  1.978466
# Study 2  2.248109 1.1450730  4.413686
# Study 3  1.473246 0.9828403  2.208350
# Study 4  4.451175 1.3670071 14.493677
# Study 5  4.520000 0.6584788 31.026662

Description

Computes the estimate, standard error, and confidence interval for an average semipartial correlation from two or more studies.

Usage

meta.ave.semipart(alpha, n, cor, r2, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

n <- c(128, 97, 210, 217)
cor <- c(.35, .41, .44, .39)
r2 <- c(.29, .33, .36, .39)
meta.ave.semipart(.05, n, cor, r2, bystudy = TRUE)

# Should return:
#         Estimate         SE        LL        UL
# Average   0.3975 0.03221240 0.3325507 0.4586965
# Study 1   0.3500 0.07175200 0.2023485 0.4820930
# Study 2   0.4100 0.07886080 0.2447442 0.5521076
# Study 3   0.4400 0.05146694 0.3338366 0.5351410
# Study 4   0.3900 0.05085271 0.2860431 0.4848830

Description

Computes the estimate, standard error, and confidence interval for an average slope coefficient in a simple linear regression model from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval.

Usage

meta.ave.slope(alpha, n, cor, sdy, sdx, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

Examples

n <- c(45, 85, 50, 60)
cor <- c(.24, .35, .16, .20)
sdy <- c(12.2, 14.1, 11.7, 15.9)
sdx <- c(1.34, 1.87, 2.02, 2.37)
meta.ave.slope(.05, n, cor, sdy, sdx, bystudy = TRUE)

# Should return:
#          Estimate        SE         LL       UL       df
# Average 1.7731542 0.4755417  0.8335021 2.712806 149.4777
# Study 1 2.1850746 1.3084468 -0.4536599 4.823809  43.0000
# Study 2 2.6390374 0.7262491  1.1945573 4.083518  83.0000
# Study 3 0.9267327 0.8146126 -0.7111558 2.564621  48.0000
# Study 4 1.3417722 0.8456799 -0.3510401 3.034584  58.0000

Description

Computes the estimate, standard error, and confidence interval for an average Spearman correlation from two or more studies. The Spearman correlation is preferred to the Pearson correlation if the relation between the two quantitative variables is monotonic rather than linear or if the bivariate normality assumption is not plausible.

Usage

meta.ave.spear(alpha, n, cor, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2008). “Meta-analytic interval estimation for bivariate correlations.” Psychological Methods, 13(3), 173–181. ISSN 1939-1463, doi:10.1037/a0012868.

Examples

n <- c(150, 200, 300, 200, 350)
cor <- c(.14, .29, .16, .21, .23)
meta.ave.spear(.05, n, cor, bystudy = TRUE)

# Should return:
#         Estimate         SE          LL        UL
# Average    0.206 0.02944265  0.14763960 0.2629309
# Study 1    0.140 0.08031750 -0.02151639 0.2943944
# Study 2    0.290 0.06492643  0.15476515 0.4145671
# Study 3    0.160 0.05635101  0.04689807 0.2690514
# Study 4    0.210 0.06776195  0.07187439 0.3402225
# Study 5    0.230 0.05069710  0.12690280 0.3281809

Description

Computes the estimate, standard error, and confidence interval for an average standardized mean difference from two or more paired-samples studies. Squrare root Unweighted variances and a single condition standard deviation are options for the standardizer. Equality of variances within or across studies is not assumed.

Usage

meta.ave.stdmean.ps(alpha, m1, m2, sd1, sd2, cor, n, stdzr, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(23.9, 24.1)
m2 <- c(25.1, 26.9)
sd1 <- c(1.76, 1.58)
sd2 <- c(2.01, 1.76)
cor <- c(.78, .84)
n <- c(25, 30)
meta.ave.stdmean.ps(.05, m1, m2, sd1, sd2, cor, n, 1, bystudy = TRUE)

# Should return: 
#           Estimate        SE        LL         UL
# Average -1.1931045 0.1568034 -1.500433 -0.8857755
# Study 1 -0.6818182 0.1773785 -1.029474 -0.3341628
# Study 2 -1.7721519 0.2586234 -2.279044 -1.2652594

Description

Computes the estimate, standard error, and confidence interval for an average standardized mean difference from two or more 2-group studies. Square root unweighted variances, square root weighted variances, and single group standard deviation are options for the standardizer. Equality of variances within or across studies is not assumed.

Usage

meta.ave.stdmean2(alpha, m1, m2, sd1, sd2, n1, n2, stdzr, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated effect size

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(21.9, 23.1, 19.8)
m2 <- c(16.1, 17.4, 15.0)
sd1 <- c(3.82, 3.95, 3.67)
sd2 <- c(3.21, 3.30, 3.02)
n1 <- c(40, 30, 24)
n2 <- c(40, 28, 25)
meta.ave.stdmean2(.05, m1, m2, sd1, sd2, n1, n2, 0, bystudy = TRUE)

# Should return: 
#         Estimate        SE        LL       UL
# Average 1.526146 0.1734341 1.1862217 1.866071
# Study 1 1.643894 0.2629049 1.1286100 2.159178
# Study 2 1.566132 0.3056278 0.9671126 2.165152
# Study 3 1.428252 0.3289179 0.7835848 2.072919

Description

Computes the estimate and confidence interval for an average variance from two or more studies. The estimated average variance or the upper confidence limit could be used as a variance planning value in sample size planning.

Usage

meta.ave.var(alpha, var, n, bystudy = TRUE)

Arguments

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated variance

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

var <- c(26.63, 22.45, 34.12)
n <- c(40, 30, 50)
meta.ave.var(.05, var, n, bystudy = TRUE)

# Should return:
#         Estimate       LL       UL
# Average 27.73333 21.45679 35.84589
# Study 1 26.63000 17.86939 43.90614
# Study 2 22.45000 14.23923 40.57127
# Study 3 34.12000 23.80835 52.98319

Description

Computes a chi-square test of effect size homogeneity and p-value using effect-size estimates and their standard errors from two or more studies. This test should not be used to justify the use of a constant coeffient (fixed-effect) meta-analysis.

Usage

meta.chitest(est, se)

Arguments

Value

Returns a one-row matrix:

• Q - chi-square test statitic

• df - degrees of freedom

• p - p-value

References

Borenstein M, Hedges LV, Higgins JP, Rothstein HR (2009). Introduction to meta-analysis. Wiley, New York.

Examples

est <- c(.297, .324, .281, .149) 
se <- c(.082, .051, .047, .094)
meta.chitest(est, se)

# Should return:
#         Q df         p
#  2.706526  3 0.4391195

Description

Computes the estimate, standard error, and adjusted Wald confidence interval for a linear contrast of G-index of agreement coefficients from two or more studies. This function assumes that two raters each provide a dichotomous rating for a sample of objects.

Usage

meta.lc.agree(alpha, f11, f12, f21, f22, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

Examples

f11 <- c(43, 56, 49)
f12 <- c(7, 2, 9)
f21 <- c(3, 5, 5)
f22 <- c(37, 54, 39)
v <- c(.5, .5, -1)
meta.lc.agree(.05, f11, f12, f21, f22, v)

# Should return:
#            Estimate        SE         LL        UL
# Contrast 0.1022939 0.07972357 -0.05396142 0.2585492

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of any type of effect size from two or more studies.

Usage

meta.lc.gen(alpha, est, se, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

est <- c(.55, .59, .44, .48, .26, .19)
se <- c(.054, .098, .029, .084, .104, .065)
v <- c(.5, .5, -.25, -.25, -.25, -.25)
meta.lc.gen(.05, est, se, v)

# Should return: 
#          Estimate         SE        LL        UL
# Contrast   0.2275 0.06755461 0.0950954 0.3599046

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of paired-samples mean differences from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval. Equality of variances within or across studies is not assumed.

Usage

meta.lc.mean.ps(alpha, m1, m2, sd1, sd2, cor, n, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
v <- c(.5, .5, -.5, -.5)
meta.lc.mean.ps(.05, m1, m2, sd1, sd2, cor, n, v)

# Should return:
#          Estimate        SE       LL       UL      df
# Contrast      2.5 0.4943114 1.520618 3.479382 112.347

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of means from two or more studies. This function will use either an unequal variance (recommended) or an equal variance method. A Satterthwaite adjustment to the degrees of freedom is used with the unequal variance method.

Usage

meta.lc.mean1(alpha, m, sd, n, v, eqvar = FALSE)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Snedecor GW, Cochran WG (1980). Statistical methods, 7th edition. ISU University Pres, Ames, Iowa.

Examples

m <- c(33.5, 37.9, 38.0, 44.1)
sd <- c(3.84, 3.84, 3.65, 4.98)
n <- c(10, 10, 10, 10)
v <- c(.5, .5, -.5, -.5)
meta.lc.mean1(.05, m, sd, n, v, eqvar = FALSE)

# Should return:
#          Estimate       SE        LL        UL       df
# Contrast    -5.35 1.300136 -7.993583 -2.706417 33.52169

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of 2-group mean differences from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval. Equality of variances within or across studies is not assumed.

Usage

meta.lc.mean2(alpha, m1, m2, sd1, sd2, n1, n2, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(45.1, 39.2, 36.3, 34.5)
m2 <- c(30.0, 35.1, 35.3, 36.2)
sd1 <- c(10.7, 10.5, 9.4, 11.5)
sd2 <- c(12.3, 12.0, 10.4, 9.6)
n1 <- c(40, 20, 50, 25)
n2 <- c(40, 20, 48, 26)
v <- c(.5, .5, -.5, -.5)
meta.lc.mean2(.05, m1, m2, sd1, sd2, n1, n2, v)

# Should return:
#          Estimate       SE       LL       UL       df
# Contrast     9.95 2.837787 4.343938 15.55606 153.8362

Description

Computes the estimate, standard error, and confidence interval for a log-linear contrast of paired-sample mean ratios from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval. Equality of variances within or across studies is not assumed.

Usage

meta.lc.meanratio.ps(alpha, m1, m2, sd1, sd2, cor, n, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimatedf log-linear contrast

• SE - standard error of log-linear contrast

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - exponentiated log-linear contrast

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

• df - degrees of freedom

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. ISSN 1076-9986, doi:10.3102/1076998620934125.

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
v <- c(.5, .5, -.5, -.5)
meta.lc.meanratio.ps(.05, m1, m2, sd1, sd2, cor, n, v)

# Should return:
#           Estimate          SE         LL         UL exp(Estimate)
# Contrast 0.0440713 0.008701725 0.02681353 0.06132907      1.045057
#           exp(LL)  exp(UL)       df
# Contrast 1.027176 1.063249 103.0256

Description

Computes the estimate, standard error, and confidence interval for a log-linear contrast of 2-group mean ratios from two or more studies. A Satterthwaite adjustment to the degrees of freedom is used to improve the accuracy of the confidence interval. Equality of variances within or across studies is not assumed.

Usage

meta.lc.meanratio2(alpha, m1, m2, sd1, sd2, n1, n2, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated log-linear contrast

• SE - standard error of log-linear contrast

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - exponentiated log-linear contrast

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

• df - degrees of freedom

References

Bonett DG, Price RM (2020). “Confidence intervals for ratios of means and medians.” Journal of Educational and Behavioral Statistics, 45(6), 750–770. ISSN 1076-9986, doi:10.3102/1076998620934125.

Examples

m1 <- c(45.1, 39.2, 36.3, 34.5)
m2 <- c(30.0, 35.1, 35.3, 36.2)
sd1 <- c(10.7, 10.5, 9.4, 11.5)
sd2 <- c(12.3, 12.0, 10.4, 9.6)
n1 <- c(40, 20, 50, 25)
n2 <- c(40, 20, 48, 26)
v <- c(.5, .5, -.5, -.5)
meta.lc.meanratio2(.05, m1, m2, sd1, sd2, n1, n2, v)

# Should return:
#           Estimate         SE        LL        UL  exp(Estimate)
# Contrast 0.2691627 0.07959269 0.1119191 0.4264064      1.308868
#           exp(LL)  exp(UL)       df
# Contrast 1.118422 1.531743 152.8665

Description

Computes the estimate, standard error, and confidence interval for an exponentiated log-linear contrast of odds ratios from two or more studies.

Usage

meta.lc.odds(alpha, f1, f2, n1, n2, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated log-linear contrast

• SE - standard error of log-linear contrast

• exp(Estimate) - exponentiated log-linear contrast

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Bonett DG, Price RM (2015). “Varying coefficient meta-analysis methods for odds ratios and risk ratios.” Psychological Methods, 20(3), 394–406. ISSN 1939-1463, doi:10.1037/met0000032.

Examples

n1 <- c(50, 150, 150)
f1 <- c(16, 50, 25)
n2 <- c(50, 150, 150)
f2 <- c(7, 15, 20)
v <- c(1, -1, 0)
meta.lc.odds(.05, f1, f2, n1, n2, v)

# Should return:
#            Estimate        SE  exp(Estimate)   exp(LL)  exp(UL)
# Contrast -0.4596883 0.5895438      0.6314805 0.1988563 2.005305

Description

Computes the estimate, standard error, and adjusted Wald confidence interval for a linear contrast of paired-samples proportion differences from two or more studies.

Usage

meta.lc.prop.ps(alpha, f11, f12, f21, f22, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

f11 <- c(17, 28, 19)
f12 <- c(43, 56, 49)
f21 <- c(3, 5, 5)
f22 <- c(37, 54, 39)
v <- c(.5, .5, -1)
meta.lc.prop.ps(.05, f11, f12, f21, f22, v)

# Should return:
#              Estimate         SE         LL       UL
#  Contrast -0.01436285 0.06511285 -0.1419817 0.113256

Description

Computes the estimate, standard error, and an adjusted Wald confidence interval for a linear contrast of proportions from two or more studies.

Usage

meta.lc.prop1(alpha, f, n, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate -estimated linear contrast

• SE - standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Price RM, Bonett DG (2004). “An improved confidence interval for a linear function of binomial proportions.” Computational Statistics and Data Analysis, 45(3), 449–456. ISSN 01679473, doi:10.1016/S0167-9473(03)00007-0.

Examples

f <- c(26, 24, 38)
n <- c(60, 60, 60)
v <- c(-.5, -.5, 1)
meta.lc.prop1(.05, f, n, v)

# Should return: 
#           Estimate         SE         LL        UL
# Contrast 0.2119565 0.07602892 0.06294259 0.3609705

Description

Computes the estimate, standard error, and adjusted Wald confidence interval for a linear contrast of 2-group proportion differences from two or more studies.

Usage

meta.lc.prop2(alpha, f1, f2, n1, n2, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the adjusted Wald confidence interval

• UL - upper limit of the adjusted Wald confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

n1 <- c(50, 150, 150)
n2 <- c(50, 150, 150)
f1 <- c(16, 50, 25)
f2 <- c(7, 15, 20)
v <- c(1, -1, 0)
meta.lc.prop2(.05, f1, f2, n1, n2, v)

# Should return:
#             Estimate         SE         LL        UL
# Contrast -0.05466931 0.09401019 -0.2389259 0.1295873

Description

Computes the estimate, standard error, and confidence interval for an exponentiated log-linear contrast of 2-group proportion ratios from two or more studies.

Usage

meta.lc.propratio2(alpha, f1, f2, n1, n2, v)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated log-linear contrast

• SE - standard error of log-linear contrast

• exp(Estimate) - exponentiated log-linear contrast

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Price RM, Bonett DG (2008). “Confidence intervals for a ratio of two independent binomial proportions.” Statistics in Medicine, 27(26), 5497–5508. ISSN 02776715, doi:10.1002/sim.3376.

Examples

n1 <- c(50, 150, 150)
f1 <- c(16, 50, 25)
n2 <- c(50, 150, 150)
f2 <- c(7, 15, 20)
v <- c(1, -1, 0)
meta.lc.propratio2(.05, f1, f2, n1, n2, v)

# Should return:
#            Estimate        SE  exp(Estimate)   exp(LL)  exp(UL)
# Contrast -0.3853396 0.4828218      0.6802196 0.2640405 1.752378

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of paired-samples standardized mean differences from two or more studies. Equality of variances within or across studies is not assumed.

Usage

meta.lc.stdmean.ps(alpha, m1, m2, sd1, sd2, cor, n, v, stdzr)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(53, 60, 53, 57)
m2 <- c(55, 62, 58, 61)
sd1 <- c(4.1, 4.2, 4.5, 4.0)
sd2 <- c(4.2, 4.7, 4.9, 4.8)
cor <- c(.7, .7, .8, .85)
n <- c(30, 50, 30, 70)
v <- c(.5, .5, -.5, -.5)
meta.lc.stdmean.ps(.05, m1, m2, sd1, sd2, cor, n, v, 0)

# Should return:
#            Estimate        SE        LL        UL
# Contrast  0.5127577 0.1392232 0.2398851 0.7856302

Description

Computes the estimate, standard error, and confidence interval for a linear contrast of 2-group standardized mean differences from two or more studies. Equality of variances within or across studies is not assumed. Use the square root average variance standardizer (stdzr = 0) for 2-group experimental designs. Use the square root weighted variance standardizer (stdzr = 3) for 2-group nonexperimental designs with simple random sampling. The stdzr = 1 and stdzr = 2 options can be used with either experimental or nonexperimental designs.

Usage

meta.lc.stdmean2(alpha, m1, m2, sd1, sd2, n1, n2, v, stdzr)

Arguments

Value

Returns 1-row matrix with the following columns:

• Estimate - estimated linear contrast

• SE - standard error

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

m1 <- c(45.1, 39.2, 36.3, 34.5)
m2 <- c(30.0, 35.1, 35.3, 36.2)
sd1 <- c(10.7, 10.5, 9.4, 11.5)
sd2 <- c(12.3, 12.0, 10.4, 9.6)
n1 <- c(40, 20, 50, 25)
n2 <- c(40, 20, 48, 26)
v <- c(.5, .5, -.5, -.5)
meta.lc.stdmean2(.05, m1, m2, sd1, sd2, n1, n2, v, 0)

# Should return: 
#           Estimate        SE        LL       UL
# Contrast 0.8557914 0.2709192 0.3247995 1.386783

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a G-index of agreement. The estimates are OLS estimates with robust standard errors that accomodate residual heteroscedasticity.

Usage

meta.lm.agree(alpha, f11, f12, f21, f22, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

f11 <- c(40, 20, 25, 30)
f12 <- c(3, 2, 2, 1)
f21 <- c(7, 6, 8, 6)
f22 <- c(26, 25, 13, 25)
x1 <- c(1, 1, 4, 6)
x2 <- c(1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 4, 2)
meta.lm.agree(.05, f11, f12, f21, f22, X)

# Should return:
#     Estimate         SE         z     p          LL        UL
# b0 0.1904762 0.38772858 0.4912617 0.623 -0.56945786 0.9504102
# b1 0.0952381 0.07141957 1.3335013 0.182 -0.04474169 0.2352179
# b2 0.4205147 0.32383556 1.2985438 0.194 -0.21419136 1.0552207

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a Fisher-transformed Pearson or partial correlation. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The correlations are Fisher-transformed and hence the parameter estimates do not have a simple interpretation. However, the hypothesis test results can be used to decide if a population slope is either positive or negative.

Usage

meta.lm.cor(alpha, n, cor, s, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - Standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

n <- c(55, 190, 65, 35)
cor <- c(.40, .65, .60, .45)
q <- 0
x1 <- c(18, 25, 23, 19)
X <- matrix(x1, 4, 1)
meta.lm.cor(.05, n, cor, q, X)

# Should return: 
#       Estimate         SE         z     p           LL         UL
# b0 -0.47832153 0.48631509 -0.983563 0.325 -1.431481595 0.47483852
# b1  0.05047154 0.02128496  2.371231 0.018  0.008753794 0.09218929

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a Fisher-transformed correlation. The correlations can be of different types (e.g., Pearson, partial, Spearman). The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. This function uses estimated correlations and their standard errors as input. The correlations are Fisher-transformed and hence the parameter estimates do not have a simple interpretation. However, the hypothesis test results can be used to decide if a population slope is either positive or negative.

Usage

meta.lm.cor.gen(alpha, cor, se, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

cor <- c(.40, .65, .60, .45)
se <- c(.182, .114, .098, .132)
x1 <- c(18, 25, 23, 19)
X <- matrix(x1, 4, 1)
meta.lm.cor.gen(.05, cor, se, X)

# Should return: 
#       Estimate         SE          z     p
# b0 -0.47832153 0.63427931 -0.7541181 0.451
# b1  0.05047154 0.02879859  1.7525699 0.080

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a log-complement Cronbach reliablity. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in non-reliability associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

Usage

meta.lm.cronbach(alpha, n, rel, r, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - exponentiated OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the exponentiated confidence interval

• UL - upper limit of the exponentiated confidence interval

References

Bonett DG (2010). “Varying coefficient meta-analytic methods for alpha reliability.” Psychological Methods, 15(4), 368–385. ISSN 1939-1463, doi:10.1037/a0020142.

Examples

n <- c(583, 470, 546, 680)
rel <- c(.91, .89, .90, .89)
x1 <- c(1, 0, 0, 0)
X <- matrix(x1, 4, 1)
meta.lm.cronbach(.05, n, rel, 10, X)

# Should return:
#      Estimate         SE          z     p         LL          UL
# b0 -2.2408328 0.03675883 -60.960391 0.000 -2.3128788 -2.16878684
# b1 -0.1689006 0.07204625  -2.344336 0.019 -0.3101087 -0.02769259

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is any type of effect size. The estimates are OLS estimates with robust standard errors that accomodate residual heteroscedasticity.

Usage

meta.lm.gen(alpha, est, se, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

est <- c(4.1, 4.7, 4.9, 5.7, 6.6, 7.3)
se <- c(1.2, 1.5, 1.3, 1.8, 2.0, 2.6)
x1 <- c(10, 20, 30, 40, 50, 60)
x2 <- c(1, 1, 1, 0, 0, 0)
X <- matrix(cbind(x1, x2), 6, 2)
meta.lm.gen(.05, est, se, X)

# Should return:
#      Estimate         SE           z     p         LL         UL
# b0  3.5333333 4.37468253  0.80767766 0.419 -5.0408869 12.1075535
# b1  0.0600000 0.09058835  0.66233679 0.508 -0.1175499  0.2375499
# b2 -0.1666667 2.81139793 -0.05928249 0.953 -5.6769054  5.3435720

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a paired-samples mean difference. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity.

Usage

meta.lm.mean.ps(alpha, m1, m2, sd1, sd2, cor, n, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• t - t-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

n <- c(65, 30, 29, 45, 50)
cor <- c(.87, .92, .85, .90, .88)
m1 <- c(20.1, 20.5, 19.3, 21.5, 19.4)
m2 <- c(10.4, 10.2, 8.5, 10.3, 7.8)
sd1 <- c(9.3, 9.9, 10.1, 10.5, 9.8)
sd2 <- c(7.8, 8.0, 8.4, 8.1, 8.7)
x1 <- c(2, 3, 3, 4, 4)
X <- matrix(x1, 5, 1)
meta.lm.mean.ps(.05, m1, m2, sd1, sd2, cor, n, X)

# Should return:
#    Estimate        SE        t     p        LL        UL  df
# b0     8.00 1.2491990 6.404104 0.000 5.5378833 10.462117 217
# b1     0.85 0.3796019 2.239188 0.026 0.1018213  1.598179 217

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a mean from one group. The estimates are OLS estimates with robust standard errors that accomodate residual heteroscedasticity.

Usage

meta.lm.mean1(alpha, m, sd, n, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• t - t-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

Examples

n <- c(25, 15, 30, 25, 40)
m <- c(20.1, 20.5, 19.3, 21.5, 19.4)
sd <- c(10.4, 10.2, 8.5, 10.3, 7.8)
x1 <- c(1, 1, 0, 0, 0)
x2 <- c( 12, 13, 11, 13, 15)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.mean1(.05, m, sd, n, X)

# Should return: 
#       Estimate        SE          t     p         LL        UL  df
# b0 19.45490196 6.7873381 2.86635227 0.005  6.0288763 32.880928 132
# b1  0.25686275 1.9834765 0.12950128 0.897 -3.6666499  4.180375 132
# b2  0.04705882 0.5064693 0.09291544 0.926 -0.9547876  1.048905 132

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a 2-group mean difference. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity.

Usage

meta.lm.mean2(alpha, m1, m2, sd1, sd2, n1, n2, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• t - t-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• df - degrees of freedom

References

Bonett DG (2009). “Meta-analytic interval estimation for standardized and unstandardized mean differences.” Psychological Methods, 14(3), 225–238. ISSN 1939-1463, doi:10.1037/a0016619.

Examples

n1 <- c(65, 30, 29, 45, 50)
n2 <- c(67, 32, 31, 20, 52)
m1 <- c(31.1, 32.3, 31.9, 29.7, 33.0)
m2 <- c(34.1, 33.2, 30.6, 28.7, 26.5)
sd1 <- c(7.1, 8.1, 7.8, 6.8, 7.6)
sd2 <- c(7.8, 7.3, 7.5, 7.2, 6.8)
x1 <- c(4, 6, 7, 7, 8)
x2 <- c(1, 0, 0, 0, 1)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.mean2(.05, m1, m2, sd1, sd2, n1, n2, X)

# Should return:
#    Estimate        SE         t     p         LL        UL  df
# b0   -15.20 3.4097610 -4.457791 0.000 -21.902415 -8.497585 418
# b1     2.35 0.4821523  4.873979 0.000   1.402255  3.297745 418
# b2     2.85 1.5358109  1.855697 0.064  -0.168875  5.868875 418

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a paired-samples log mean ratio. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in the mean ratio associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

Usage

meta.lm.meanratio.ps(alpha, m1, m2, sd1, sd2, cor, n, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - the exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

Examples

n <- c(65, 30, 29, 45, 50)
cor <- c(.87, .92, .85, .90, .88)
m1 <- c(20.1, 20.5, 19.3, 21.5, 19.4)
m2 <- c(10.4, 10.2, 8.5, 10.3, 7.8)
sd1 <- c(9.3, 9.9, 10.1, 10.5, 9.8)
sd2 <- c(7.8, 8.0, 8.4, 8.1, 8.7)
x1 <- c(2, 3, 3, 4, 4)
X <- matrix(x1, 5, 1)
meta.lm.meanratio.ps(.05, m1, m2, sd1, sd2, cor, n, X)

# Should return: 
#      Estimate         SE           LL        UL        z     p
# b0 0.50957008 0.13000068  0.254773424 0.7643667 3.919749 0.000
# b1 0.07976238 0.04133414 -0.001251047 0.1607758 1.929697 0.054
#     exp(Estimate)   exp(LL)  exp(UL)
# b0       1.664575 1.2901693 2.147634
# b1       1.083030 0.9987497 1.174422

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a 2-group log mean ratio. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in the mean ratio associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

Usage

meta.lm.meanratio2(alpha, m1, m2, sd1, sd2, n1, n2, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - the exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

Examples

n1 <- c(65, 30, 29, 45, 50)
n2 <- c(67, 32, 31, 20, 52)
m1 <- c(31.1, 32.3, 31.9, 29.7, 33.0)
m2 <- c(34.1, 33.2, 30.6, 28.7, 26.5)
sd1 <- c(7.1, 8.1, 7.8, 6.8, 7.6)
sd2 <- c(7.8, 7.3, 7.5, 7.2, 6.8)
x1 <- c(4, 6, 7, 7, 8)
X <- matrix(x1, 5, 1)
meta.lm.meanratio2(.05, m1, m2, sd1, sd2, n1, n2, X)

# Should return:
#       Estimate         SE          LL          UL         z p
# b0 -0.40208954 0.09321976 -0.58479692 -0.21938216 -4.313351 0
# b1  0.06831545 0.01484125  0.03922712  0.09740377  4.603078 0
#    exp(Estimate)  exp(LL)   exp(UL)
# b0     0.6689208 0.557219 0.8030148
# b1     1.0707030 1.040007 1.1023054

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a log odds ratio. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in the odds ratio associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

Usage

meta.lm.odds(alpha, f1, f2, n1, n2, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - the exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Bonett DG, Price RM (2015). “Varying coefficient meta-analysis methods for odds ratios and risk ratios.” Psychological Methods, 20(3), 394–406. ISSN 1939-1463, doi:10.1037/met0000032.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
x1 <- c(4, 4, 5, 3, 26)
x2 <- c(1, 1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.odds(.05, f1, f2, n1, n2, X)

# Should return:
#        Estimate         SE           z     p         LL         UL
# b0  1.541895013 0.69815801  2.20851868 0.027  0.1735305 2.91025958
# b1 -0.004417932 0.04840623 -0.09126784 0.927 -0.0992924 0.09045653
# b2 -1.071122269 0.60582695 -1.76803337 0.077 -2.2585213 0.11627674
#    exp(Estimate)   exp(LL)   exp(UL)
# b0     4.6734381 1.1894969 18.361564
# b1     0.9955918 0.9054779  1.094674
# b2     0.3426238 0.1045049  1.123307

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a paired-samples proportion difference. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity.

Usage

meta.lm.prop.ps(alpha, f11, f12, f21, f22, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

f11 <- c(40, 20, 25, 30)
f12 <- c(3, 2, 2, 1)
f21 <- c(7, 6, 8, 6)
f22 <- c(26, 25, 13, 25)
x1 <- c(1, 1, 4, 6)
x2 <- c(1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 4, 2)
meta.lm.prop.ps(.05, f11, f12, f21, f22, X)

# Should return: 
#       Estimate         SE          z     p          LL         UL
# b0 -0.21113402 0.21119823 -0.9996960 0.317 -0.62507494 0.20280690
# b1  0.02185567 0.03861947  0.5659236 0.571 -0.05383711 0.09754845
# b2  0.12575138 0.17655623  0.7122455 0.476 -0.22029248 0.47179524

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a proportion from one group. The estimates are OLS estimates with robust standard errors that accomodate residual heteroscedasticity.

Usage

meta.lm.prop1(alpha, f, n, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

Examples

f <- c(38, 26, 24, 15, 45, 38)
n <- c(80, 60, 70, 50, 180, 200)
x1 <- c(10, 15, 18, 22, 24, 30)
X <- matrix(x1, 6, 1)
meta.lm.prop1(.05, f, n, X)

# Should return: 
#       Estimate         SE         z p          LL           UL
# b0  0.63262816 0.06845707  9.241239 0  0.49845477  0.766801546
# b1 -0.01510565 0.00290210 -5.205076 0 -0.02079367 -0.009417641

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a 2-group proportion difference. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity.

Usage

meta.lm.prop2(alpha, f1, f2, n1, n2, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG, Price RM (2014). “Meta-analysis methods for risk differences.” British Journal of Mathematical and Statistical Psychology, 67(3), 371–387. ISSN 00071102, doi:10.1111/bmsp.12024.

Examples

f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
x1 <- c(4, 4, 5, 3, 26)
x2 <- c(1, 1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.prop2(.05, f1, f2, n1, n2, X)

# Should return:
#        Estimate          SE          z     p          LL          UL
# b0  0.089756283 0.034538077  2.5987632 0.009  0.02206290 0.157449671
# b1 -0.001447968 0.001893097 -0.7648672 0.444 -0.00515837 0.002262434
# b2 -0.034670988 0.034125708 -1.0159786 0.310 -0.10155615 0.032214170

Description

This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a log proportion ratio. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in the proportion ratio associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.

Usage

meta.lm.propratio2(alpha, f1, f2, n1, n2, X)

Arguments

Value

Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:

• Estimate - OLS estimate

• SE - standard error

• z - z-value

• p - p-value

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

• exp(Estimate) - the exponentiated estimate

• exp(LL) - lower limit of the exponentiated confidence interval

• exp(UL) - upper limit of the exponentiated confidence interval

References

Price RM, Bonett DG (2008). “Confidence intervals for a ratio of two independent binomial proportions.” Statistics in Medicine, 27(26), 5497–5508. ISSN 02776715, doi:10.1002/sim.3376.

Examples

n1 <- c(204, 201, 932, 130, 77)
n2 <- c(106, 103, 415, 132, 83)
f1 <- c(24, 40, 93, 14, 5)
f2 <- c(12, 9, 28, 3, 1)
x1 <- c(4, 4, 5, 3, 26)
x2 <- c(1, 1, 1, 0, 0)
X <- matrix(cbind(x1, x2), 5, 2)
meta.lm.propratio2(.05, f1, f2, n1, n2, X)

# Should return:
#         Estimate         SE           z     p          LL         UL
# b0  1.4924887636 0.69172794  2.15762393 0.031  0.13672691 2.84825062
# b1  0.0005759509 0.04999884  0.01151928 0.991 -0.09741998 0.09857188
# b2 -1.0837844594 0.59448206 -1.82307345 0.068 -2.24894789 0.08137897
#     exp(Estimate)   exp(LL)   exp(UL)
# b0      4.4481522 1.1465150 17.257565
# b1      1.0005761 0.9071749  1.103594
# b2      0.3383128 0.1055102  1.084782