Meta-analyzing logistic regression slopes
Meta-analysis refers to the quantitative synthesis of information across different studies. Since outcomes from different studies are likely to be reported in different units, study-level results are typically transformed to the same scale before quantitative integration. Typically, this leads to the accumulation and combination of effect sizes. To date, most social scientists have synthesized, or meta-analyzed, zero-order statistics like a correlation. Synthesizing partial effect sizes is an alternative which allows a meta-analysis to account for the influence of nuisance variables when estimating the association between two variables. This dissertation proposes that logistic regression coefficients from different studies, which are a type of partial effect size, can be meta-analyzed. Logistic regression models how a set of covariates relates to a binary dependent variable. Given a key independent variable (IV) of interest, which we can call the focal IV or Xf, the slope estimate (βf) in a logistic regression measures the impact of Xf on Y on the logit (log-odds) scale, while controlling for other variables. Four assumptions justify the possibility of comparing and possibly combing logistic slopes across studies: (1) Y must be on the same scale, (2) Xf must be on the same scale, (3) all effect sizes are logistic regression slopes adjusted for the same covariates, and (4) model specifications are identical. In practice, the third assumption is particularly challenging as different studies inevitably include different sets of control variables. Three simulation studies are implemented to understand how synthesizing a logistic regression slope on the logit scale is affected by several factors. Across these three simulation studies, the following meta-analytic variables are tested: (1) the size of the partial effect size (βf), (2) Study-level sample size (k), (3) Within-study sample size (N), (4) the degree of between-study variance, (5) a continuous vs. a binary focal predictor, (6) the level of collinearity between Xf and other covariates included in primary studies, (7) the magnitude of non-focal variable slopes, (8) different covariate sets used in primary-level studies, and (9) meta-analytical method. Simulation performance is based on how the bias and mean-squared error (MSE) are affected by each of these simulation parameters. Overall, results suggest that when the four assumptions introduced above are satisfied, meta-analyzing logistic regression slopes is remarkably accurate as the summary effect resulting from the standard random-effects meta-analytic model leads to small levels of bias and MSE under a variety of conditions. When the assumptions are broken (and particularly the third assumption of identical covariate sets), the pooled slope estimator can have large degrees of bias. The bias is a function of within-study sample size, between-study sample size, distribution of the focal IV (i.e., continuous vs. categorical variable), multicollinearity, the magnitude of non-focal variable slope parameters, diversity in covariate sets, and choice of meta-analytical methods. The MSE is a function of study-level sample size, within-study sample size, distribution of the focal IV (i.e., continuous vs. categorical variable), multicollinearity, the magnitude of non-focal variable slope parameters, diversity in covariate sets, and choice of meta-analytical methods. A complex four-way interaction is discovered between collinearity, the magnitude of non-focal variable slope parameters, diversity in covariate sets, and choice of meta-analytical methods. An applied example focusing on estimating the effects of albumin on mortality is also presented to complement the simulation results.
