Article type
Year
Abstract
Objective: The purpose of this study was to compare the general linear mixed model (GLM) with the generalized linear mixed model (GLMM) for describing heterogeneity in meta-analysis involving cluster randomized trials in binary outcome.
Methods: The two approaches of GLM and GLMM were exemplified in two published meta-analyses involving cluster randomized trials. The first meta-analysis was done to assess the effectiveness of multiple risk factor interventions to reduce cardiovascular risk factors from coronary heart disease. Analysis was performed in the 14 trials included that provided smoking prevalence outcome. The second meta-analysis comprised fewer trials of 8, which was performed to evaluate the effect of mammographic screening on reduction of breast cancer mortality. Observed log-relative risks for individual trials are fitted to the GLM as a continuous response. Randomization design was treated as a covariate of the model. The model parameters were estimated with the restricted maximum likelihood (REML) under the normality assumption of random effects. For the GLMM, observed frequencies of the outcome for each treatment group that approached to poisson distribution were used rather than the observed log-relative risks for individual trials. A canonical link function of the observed mean proportions was associated with linear predictors model of which treatment and randomization design were treated as covariates. The model parameters were estimated non-parametrically under a discrete mixture distribution of random effects for K components. Maximum posterior probability were used to classified trials to each component.
Results: The two approaches shown that the covariates effects and variability of random effects from the models easily explained heterogeneity between trials. The GLMM was superior to the GLM in some aspects. The GLMM gave further heterogeneity information from random treatment effects. In addition, it provided component (or subgroup)-specific treatment effect and trial classification according to the optimal components. This was very useful in further explaining the heterogeneity that might be beyond the effects found in the model.
Conclusions: The GLM and GLMM approaches were preferable for meta-analyses involving cluster randomized trials. However, care should be taken when using the GLM because the GLM needed a strong assumption of normality distribution of random effects components. It was also difficult to verify validity of the assumption. For the GLMM, care should be taken when interpreting treatment effect in terms of risk since the inference on treatment effect obtained from a discrete mixing distribution had not been ruled out. Nevertheless, these two approaches would be much more efficient when they were applied to large meta-analyses.
Methods: The two approaches of GLM and GLMM were exemplified in two published meta-analyses involving cluster randomized trials. The first meta-analysis was done to assess the effectiveness of multiple risk factor interventions to reduce cardiovascular risk factors from coronary heart disease. Analysis was performed in the 14 trials included that provided smoking prevalence outcome. The second meta-analysis comprised fewer trials of 8, which was performed to evaluate the effect of mammographic screening on reduction of breast cancer mortality. Observed log-relative risks for individual trials are fitted to the GLM as a continuous response. Randomization design was treated as a covariate of the model. The model parameters were estimated with the restricted maximum likelihood (REML) under the normality assumption of random effects. For the GLMM, observed frequencies of the outcome for each treatment group that approached to poisson distribution were used rather than the observed log-relative risks for individual trials. A canonical link function of the observed mean proportions was associated with linear predictors model of which treatment and randomization design were treated as covariates. The model parameters were estimated non-parametrically under a discrete mixture distribution of random effects for K components. Maximum posterior probability were used to classified trials to each component.
Results: The two approaches shown that the covariates effects and variability of random effects from the models easily explained heterogeneity between trials. The GLMM was superior to the GLM in some aspects. The GLMM gave further heterogeneity information from random treatment effects. In addition, it provided component (or subgroup)-specific treatment effect and trial classification according to the optimal components. This was very useful in further explaining the heterogeneity that might be beyond the effects found in the model.
Conclusions: The GLM and GLMM approaches were preferable for meta-analyses involving cluster randomized trials. However, care should be taken when using the GLM because the GLM needed a strong assumption of normality distribution of random effects components. It was also difficult to verify validity of the assumption. For the GLMM, care should be taken when interpreting treatment effect in terms of risk since the inference on treatment effect obtained from a discrete mixing distribution had not been ruled out. Nevertheless, these two approaches would be much more efficient when they were applied to large meta-analyses.