Statistical models for meta-analysis: A brief tutorial

Aggregate data meta-analysis is currently the most commonly used method for combining the results from different studies on the same outcome of interest. In this paper, we provide a brief introduction to meta-analysis, including a description of aggregate and individual participant data meta-analysis. We then focus the rest of the tutorial on aggregate data metaanalysis. We start by first describing the difference between fixed and random-effects meta-analysis, with particular attention devoted to the latter. This is followed by an example using the random-effects, method of moments approach and includes an intercept-only model as well as a model with one predictor. We then describe alternative random-effects approaches such as maximum likelihood, restricted maximum likelihood and profile likelihood as well as a non-parametric approach. A brief description of selected statistical programs available to conduct random-effects aggregate data meta-analysis, limited to those that allow both an interceptonly as well as at least one predictor in the model, is given. These descriptions include those found in an existing general statistics software package as well as one developed specifically for an aggregate data metaanalysis. Following this, some of the disadvantages of random-effects meta-analysis are described. We then describe recently proposed alternative models for conducting aggregate data meta-analysis, including the varying coefficient model. We conclude the paper with some recommendations and directions for future research. These recommendations include the continued use of the more commonly used random-effects models until newer models are more thoroughly tested as well as the timely integration of new and well-tested models into traditional as well as meta-analytic-specific software packages.

Use of the varying coefficient model in an exercise and depression meta-analysis

AIM: Use a recently developed varying coefficient model to determine the effects of exercise in adults with depression.METHODS: Data from a recent meta-analysis addressing the effects of exercise on depression in adults were used. Studies were limited to randomized controlled intervention trials of any type of chronic exercise(for example, walking and jogging) in adults greater than or equal to 18 years of age with a diagnosis of depression. For each study, the standardized mean difference(exercise minus control) effect size for depression, adjusted for small-sample bias, was calculated. Variance statistics for each effect size and pooling of results were calculated using the recently proposed varying coefficient(VC) model for standardized mean differences. Standardized effect-sizes of 0.20, 0.50 and 0.80 were considered to represent small, medium and large effects. Results were considered statistically significant if the 95% confidence intervals did not cross 0, with negative results indicative of reductions in depression.These findings were then compared with results using traditional random-effects(RE) models.RESULTS: A total of 23 studies representing 907 men and women(476 exercise, 431 control) were pooled for analysis. Both RE and VC models resulted in large, statistically significant improvements in depression as a result of exercise in adults. However, the VC model resulted in a larger overall effect size as well as confidence intervals that were narrower than previously reported using the RE model. The overall mean effect size for the RE model was-0.82 with a 95% confidence interval of-1.12 to-0.51. For the VC model, overall mean effect size was-0.88 with a 95% confidence interval of-1.08 to-0.68. The relative difference between the RE and VC approaches was 7.3%.CONCLUSION: The VC model, a potentially preferable model, confirms the positive effects of exercise on depression in adults.

Incorporating travel time reliability in predicting the likelihood of severe crashes on arterial highways using non-parametric random-effect regression

Travel time reliability(TTR) modeling has gain attention among researchers’ due to its ability to represent road user satisfaction as well as providing a predictability of a trip travel time.Despite this significant effort,its impact on the severity of a crash is not well explored.This study analyzes the effect of TTR and other variables on the probability of the crash severity occurring on arterial roads.To address the unobserved heterogeneity problem,two random-effect regressions were applied;the Dirichlet random-effect(DRE)and the traditional random-effect(TRE) logistic regression.The difference between the two models is that the random-effect in the DRE is non-parametrically specified while in the TRE model is parametrically specified.The Markov Chain Monte Carlo simulations were adopted to infer the parameters’ posterior distributions of the two developed models.Using four-year police-reported crash data and travel speeds from Northeast Florida,the analysis of goodness-of-fit found the DRE model to best fit the data.Hence,it was used in studying the influence of TTR and other variables on crash severity.The DRE model findings suggest that TTR is statistically significant,at 95 percent credible intervals,influencing the severity level of a crash.A unit increases in TTR reduces the likelihood of a severe crash occurrence by 25 percent.Moreover,among the significant variables,alcohol/drug impairment was found to have the highest impact in influencing the occurrence of severe crashes.Other significant factors included traffic volume,weekends,speed,work-zone,land use,visibility,seatbelt usage,segment length,undivided/divided highway,and age.

Comparison of two reliability models for performance degradation analysis

In order to investigate the general reliability assessment methods based on performance degradation data,two commonly used stochastic process approaches,bilinear process method and random-effect model were studied.Analyzing procedure and effectiveness of these two methodologies were studied and compared.Meanwhile,the two approaches were illustrated through practical applications.The residual plots and the 10th percentile curves of the two methods were presented to demonstrate the comparative results.The randomeffect model yielded more volatile residuals and a lower and unsafe 10th percentile curve.Consequently the bilinear process model can be concluded to derive more reasonable results due to its one-stage estimation property.