maprop.twostep {altmeta}

Meta-Analysis of Proportions Using Two-Step Methods

Description

Performs a meta-analysis of proportions using conventional two-step methods with various data transformations.

Usage

maprop.twostep(e, n, data, link = "logit", method = "ML", alpha = 0.05,
               pop.avg = TRUE, int.approx = 10000, b.iter = 1000,
               seed = 1234)

Arguments

e

a numeric vector specifying the event counts in the collected studies.

n

a numeric vector specifying the sample sizes in the collected studies.

data

an optional data frame containing the meta-analysis dataset. If data is specified, the previous arguments, e and n, should be specified as their corresponding column names in data.

link

a character string specifying the data transformation for each study's proportion used in the two-step method, which can be one of "log" (log transformation), "logit" (logit transformation, the default), "arcsine" (arcsine transformation), and "double.arcsine" (Freeman–Tukey double-arcsine transformation).

method

a character string specifying the method to perform the meta-analysis, which is passed to the argument method in the function rma.uni in the package metafor. It can be one of "ML" (maximum likelihood, the default), "REML" (restricted maximum likelihood), and many other options; see more details in the manual of metafor. The default is set to "ML" for consistency with the function maprop.glmm, where generalized linear mixed models are often estimated via the maximum likelihood approach. For the two-step method, users might also use "REML" because the restricted maximum likelihood estimation may have superior performance in many cases.

alpha

a numeric value specifying the statistical significance level.

pop.avg

a logical value indicating whether the population-averaged proportion and its confidence interval are to be produced. This quantity is the marginal mean of study-specific proportions, while the commonly-reported overall proportion usually represents the median (or interpreted as a conditional measure); see more details about this quantity in Section 13.2.3 in Agresti (2013), Chu et al. (2012), Lin and Chu (2020), and Zeger et al. (1988). If pop.avg = TRUE (the default), the bootstrap resampling is used to produce the confidence interval of the population-averaged proportion; the confidence interval of the commonly-reported median proportion will be also produced, in addition to its conventional confidence interval (by back-transforming the Wald-type confidence interval derived on the scale specified by link).

int.approx

an integer specifying the number of independent standard normal samples for numerically approximating the integration involved in the calculation of the population-averaged proportion; see details in Lin and Chu (2020). It is only used when pop.avg = TRUE. For the commonly-used data transformations available for link, the population-averaged proportion does not have a closed form.

b.iter

an integer specifying the number of bootstrap iterations; it is only used when pop.avg = TRUE.

seed

an integer for specifying the seed of the random number generation for reproducibility during the bootstrap resampling (and numerical approximation for the population-averaged proportion); it is only used when pop.avg = TRUE.

Value

This function returns a list containing the point and interval estimates of the overall proportion. Specifically, prop.c.est is the commonly-reported median (or conditional) proportion, and prop.c.ci is its confidence interval. If pop.avg = TRUE, the following additional elements will be also in the produced list: prop.c.ci.b is the bootstrap confidence interval of the commonly-reported median (conditional) proportion, prop.m.est is the point estimate of the population-averaged (marginal) proportion, prop.m.ci.b is the bootstrap confidence interval of the population-averaged (marginal) proportion, and b.w.e is a vector of two numeric values, indicating the counts of warnings and errors occurred during the bootstrap iterations. Moreover, if the Freeman–Tukey double-arcsine transformation (link = "double.arcsine") is used, the back-transformation will be implemented at four values as the overall sample size: the harmonic, geometric, and arithmetic means of the study-specific sample sizes, and the inverse of the synthesized result's variance. See details in Barendregt et al. (2013) and Schwarzer et al. (2019).

Note

This function implements the two-step method for the meta-analysis of proportions via the rma.uni function in the package metafor. It is possible that the algorithm of the maximum likelihood or restricted maximum likelihood estimation may not converge for some bootstrapped meta-analyses when pop.avg = TRUE, and the rma.uni function may report warnings or errors about the convergence issue. The bootstrap iterations are continued until b.iter replicates without any warnings or errors are obtained; those replicates with any warnings or errors are discarded.

References

Agresti A (2013). Categorical Data Analysis. Third edition. John Wiley & Sons, Hoboken, NJ.

Barendregt JJ, Doi SA, Lee YY, Norman RE, Vos T (2013). "Meta-analysis of prevalence." Journal of Epidemiology and Community Health, 67(11), 974–978. <doi: 10.1136/jech-2013-203104>

Freeman MF, Tukey JW (1950). "Transformations related to the angular and the square root." The Annals of Mathematical Statistics, 21(4), 607–611. <doi: 10.1214/aoms/1177729756>

Lin L, Chu H (2020). "Meta-analysis of proportions using generalized linear mixed models." Epidemiology, 31(5), 713–717. <doi: 10.1097/ede.0000000000001232>

Miller JJ (1978). "The inverse of the Freeman–Tukey double arcsine transformation." The American Statistician, 32(4), 138. <doi: 10.1080/00031305.1978.10479283>

Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rucker G (2019). "Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions." Research Synthesis Methods, 10(3), 476–483. <doi: 10.1002/jrsm.1348>

Viechtbauer W (2010). "Conducting meta-analyses in R with the metafor package." Journal of Statistical Software, 36, 3. <doi: 10.18637/jss.v036.i03>

Zeger SL, Liang K-Y, Albert PS (1988). "Models for longitudinal data: a generalized estimating equation approach." Biometrics, 44(4), 1049–1060. <doi: 10.2307/2531734>

See Also

maprop.glmm

Examples

# chorioamnionitis data
data("dat.chor")
# two-step method with the logit transformation
out.chor.twostep.logit <- maprop.twostep(e, n, data = dat.chor,
  link = "logit", b.iter = 10, seed = 1234)
out.chor.twostep.logit
# not calculating the population-averaged (marginal) proportion,
#  without bootstrap resampling
out.chor.twostep.logit <- maprop.twostep(e, n, data = dat.chor,
  link = "logit", pop.avg = FALSE)
out.chor.twostep.logit

# increases the number of bootstrap iterations to 1000,
#  taking longer time
out.chor.twostep.logit <- maprop.twostep(e, n, data = dat.chor,
  link = "logit", b.iter = 1000, seed = 1234)
out.chor.twostep.logit

# two-step method with the log transformation
out.chor.twostep.log <- maprop.twostep(e, n, data = dat.chor,
  link = "log", b.iter = 10, seed = 1234)
out.chor.twostep.log
# two-step method with the arcsine transformation
out.chor.twostep.arcsine <- maprop.twostep(e, n, data = dat.chor,
  link = "arcsine", b.iter = 10, seed = 1234)
out.chor.twostep.arcsine
# two-step method with the Freeman--Tukey double-arcsine transformation
out.chor.twostep.double.arcsine <- maprop.twostep(e, n, data = dat.chor,
  link = "double.arcsine", b.iter = 10, seed = 1234)
out.chor.twostep.double.arcsine


# depression data
data("dat.beck17")
out.beck17.twostep.log <- maprop.twostep(e, n, data = dat.beck17,
  link = "log", b.iter = 10, seed = 1234)
out.beck17.twostep.log
out.beck17.twostep.logit <- maprop.twostep(e, n, data = dat.beck17,
  link = "logit", b.iter = 10, seed = 1234)
out.beck17.twostep.logit
out.beck17.twostep.arcsine <- maprop.twostep(e, n, data = dat.beck17,
  link = "arcsine", b.iter = 10, seed = 1234)
out.beck17.twostep.arcsine
out.beck17.twostep.double.arcsine <- maprop.twostep(e, n, data = dat.beck17,
  link = "double.arcsine", b.iter = 10, seed = 1234)
out.beck17.twostep.double.arcsine