maprop.glmm {altmeta}

Meta-Analysis of Proportions Using Generalized Linear Mixed Models

Description

Performs a meta-analysis of proportions using generalized linear mixed models (GLMMs) with various link functions.

Usage

maprop.glmm(e, n, data, link = "logit", 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 link function used in the GLMM, which can be one of "log" (log link), "logit" (logit link, the default), "probit" (probit link), "cauchit" (cauchit link), and "cloglog" (complementary log-log link).

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 and link is not "probit". The probit link leads to a closed form of the population-averaged proportion, so it does not need the numerical approximation; for other links, 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.

...

other arguments that can be passed to the function glmer in the package lme4.

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. It also returns information about AIC, BIC, log likelihood, deviance, and residual degrees-of-freedom. 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.

Note

This function implements the GLMM for the meta-analysis of proportions via the function glmer in the package lme4. It is possible that the algorithm of the GLMM estimation may not converge for some bootstrapped meta-analyses when pop.avg = TRUE, and the function glmer 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.

Bakbergenuly I, Kulinskaya E (2018). "Meta-analysis of binary outcomes via generalized linear mixed models: a simulation study." BMC Medical Research Methodology, 18, 70. <doi: 10.1186/s12874-018-0531-9>

Chu H, Nie L, Chen Y, Huang Y, Sun W (2012). "Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk." Statistical Methods in Medical Research, 21(6), 621–633. <doi: 10.1177/0962280210393712>

Hamza TH, van Houwelingen HC, Stijnen T (2008). "The binomial distribution of meta-analysis was preferred to model within-study variability." Journal of Clinical Epidemiology, 61(1), 41–51. <doi: 10.1016/j.jclinepi.2007.03.016>

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

Stijnen T, Hamza TH, Ozdemir P (2010). "Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data." Statistics in Medicine, 29(29), 3046–3067. <doi: 10.1002/sim.4040>

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.twostep

Examples

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

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

# GLMM with the log link
out.chor.glmm.log <- maprop.glmm(e, n, data = dat.chor,
  link = "log", b.iter = 10, seed = 1234)
out.chor.glmm.log
# GLMM with the probit link
out.chor.glmm.probit <- maprop.glmm(e, n, data = dat.chor,
  link = "probit", b.iter = 10, seed = 1234)
out.chor.glmm.probit
# GLMM with the cauchit link
out.chor.glmm.cauchit <- maprop.glmm(e, n, data = dat.chor,
  link = "cauchit", b.iter = 10, seed = 1234)
out.chor.glmm.cauchit
# GLMM with the cloglog link
out.chor.glmm.cloglog <- maprop.glmm(e, n, data = dat.chor,
  link = "cloglog", b.iter = 10, seed = 1234)
out.chor.glmm.cloglog


# depression data
data("dat.beck17")
out.beck17.glmm.log <- maprop.glmm(e, n, data = dat.beck17,
  link = "log", b.iter = 10, seed = 1234)
out.beck17.glmm.log
out.beck17.glmm.logit <- maprop.glmm(e, n, data = dat.beck17,
  link = "logit", b.iter = 10, seed = 1234)
out.beck17.glmm.logit
out.beck17.glmm.probit <- maprop.glmm(e, n, data = dat.beck17,
  link = "probit", b.iter = 10, seed = 1234)
out.beck17.glmm.probit
out.beck17.glmm.cauchit <- maprop.glmm(e, n, data = dat.beck17,
  link = "cauchit", b.iter = 10, seed = 1234)
out.beck17.glmm.cauchit
out.beck17.glmm.cloglog<- maprop.glmm(e, n, data = dat.beck17,
  link = "cloglog", b.iter = 10, seed = 1234)
out.beck17.glmm.cloglog