# Hybrid Test for Publication Bias/Small-Study Effects in Meta-Analysis With Generic Outcomes Performs the hybrid test for publication bias/small-study effects introduced in Lin (2020), which synthesizes results from multiple popular publication bias tests, in a meta-analysis with generic outcomes. ```r pb.hybrid.generic(y, s2, n, data, methods, iter.resam = 1000, theo.pval = TRUE) ``` ## Arguments - `y`: a numeric vector or the corresponding column name in the argument `data`, specifying the observed effect sizes in the collected studies. - `s2`: a numeric vector or the corresponding column name in the argument `data`, specifying the within-study variances. - `n`: an optional numeric vector or the corresponding column name in the argument `data`, specifying the study-specific total sample sizes. This argument is required if the sample-size-based test (`"inv.sqrt.n"`) is included in `method`. - `data`: an optional data frame containing the meta-analysis dataset. If `data` is specified, the previous arguments, `y`, `s2`, and `n`, should be specified as their corresponding column names in `data`. - `methods`: a vector of character strings specifying the publication bias tests to be included in the hybrid test. They can be a subset of `"rank"` (Begg's rank test; see Begg and Mazumdar, 1994), `"reg"` (Egger's regression test under the fixed-effect setting; see Egger et al., 1997), `"reg.het"` (Egger's regression test accounting for additive heterogeneity), `"skew"` (the skewness-based test under the fixed-effect setting; see Lin and Chu, 2018), `"skew.het"` (the skewness-based test accounting for additive heterogeneity), `"inv.sqrt.n"` (the regression test based on sample sizes; see Tang and Liu, 2000), and `"trimfill"` (the trim-and-fill method; see Duval and Tweedie, 2000). The default is to include all aforementioned tests. - `iter.resam`: a positive integer specifying the number of resampling iterations for calculating the p-value of the hybrid test. - `theo.pval`: a logical value indicating whether additionally calculating the p-values of the tests specified in `methods` based on the test statistics' theoretical null distributions. Regardless of this argument, the resampling-based p-values are always produced by this function for the tests specified in `methods`. ## Details The hybrid test statistic is defined as the minimum p-value among the publication bias tests considered in the set specified by the argument `methods`. Note that the minimum p-value is no longer a genuine p-value because it cannot control the type I error rate. Its p-value needs to be calculated via the resampling approach. See more details in Lin (2020). ## Returns This function returns a list containing p-values of the publication bias tests specified in `methods` as well as the hybrid test. Each element's name in this list has the format of `pval.x`, where `x` stands for the character string corresponding to a certain publication bias test, such as `rank`, `reg`, `skew`, etc. The hybrid test's p-value has the name `pval.hybrid`. If `theo.pval` = `TRUE`, additional elements of p-values of the tests in `methods` based on theorectical null distributions are included in the produced list; their names have the format of `pval.x.theo`. Another p-value of the hybrid test is also produced based on them; its corresponding element has the name `pval.hybrid.theo`. ## References Begg CB, Mazumdar M (1994). "Operating characteristics of a rank correlation test for publication bias." **Biometrics**, 50 (4), 1088--1101. Duval S, Tweedie R (2000). "A nonparametric `trim and fill' method of accounting for publication bias in meta-analysis." **Journal of the American Statistical Association**, 95 (449), 89--98. Egger M, Davey Smith G, Schneider M, Minder C (1997). "Bias in meta-analysis detected by a simple, graphical test." **BMJ**, 315 (7109), 629--634. Lin L (2020). "Hybrid test for publication bias in meta-analysis." **Statistical Methods in Medical Research**, 29 (10), 2881--2899. Lin L, Chu H (2018). "Quantifying publication bias in meta-analysis." **Biometrics**, 74 (3), 785--794. Tang J-L, Liu JLY (2000). "Misleading funnel plot for detection of bias in meta-analysis." **Journal of Clinical Epidemiology**, 53 (5), 477--484. Thompson SG, Sharp SJ (1999). "Explaining heterogeneity in meta-analysis: a comparison of methods." **Statistics in Medicine**, 18 (20), 2693--2708. 3.0.CO;2-V") > ## See Also `pb.bayesian.binary`, `pb.hybrid.binary` ## Examples ```r ## meta-analysis of mean differences data("dat.plourde") # based on only 10 resampling iterations set.seed(1234) out.plourde <- pb.hybrid.generic(y = y, s2 = s2, n = n, data = dat.plourde, iter.resam = 10) out.plourde # only produces resampling-based p-values set.seed(1234) pb.hybrid.generic(y = y, s2 = s2, n = n, data = dat.plourde, iter.resam = 10, theo.pval = FALSE) # increases the number of resampling iterations to 10000, # taking longer time ## meta-analysis of standardized mean differences data("dat.paige") # based on only 10 resampling iterations set.seed(1234) out.paige <- pb.hybrid.generic(y = y, s2 = s2, n = n, data = dat.paige, iter.resam = 10) out.paige # increases the number of resampling iterations to 10000, # taking longer time ```

pb.hybrid.generic function