20. Meta-regression (20 and 9 Studies)

Heterogeneity in meta-analysis makes pooling of the overall data pretty meaningless. Instead, a careful examination of the potential causes has to be accomplished. Regression analysis is generally very helpful for that purpose.

The characteristics of the studies in a meta-analysis were pretty heterogeneous. What were the causal factors of the heterogeneity.

Twenty studies assessing the incidence of ADEs (adverse drug effects) were meta-analyzed (Atiqi et al.: Int J Clin Pharmacol Ther 2009; 47: 549–56). The studies were very heterogenous. We observed that studies performed by pharmacists (0) produced lower incidences than did the studies performed by internists (1). Also the study magnitude and age was considered as possible causes of heterogeneity. The data file is underneath.

For convenience the data file is in extras.springer.com, and is entitled “chapter20metaregression1”. We will start by opening the data file in SPSS.

A multiple linear regression will be performed with percentage ADEs as outcome variable and the study magnitude, the type of investigators (pharmacist or internist), and the age of the study populations as predictors. For analysis the statistical model Linear in the module Regression is required.

The above table is in the output sheets, and shows the results. After adjustment for the age of the study populations and study magnitude, the type of research group was the single and very significant predictor of the heterogeneity. Obviously, internists more often diagnose ADEs than pharmacists do.

Nine studies of the risk of infarction of patients with coronary artery disease and collateral coronary arteries were meta-analyzed. The studies were heterogeneous. A meta-regression was performed with the odds ratios of infarction as dependent and the odds ratios of various cardiovascular risk factors as independent variables.

For convenience the data file is in extras.springer.com. It is entitled “chapter20metaregression2”. Simple linear regressions with the odds ratios of infarction as dependent variable were performed. For analysis again the statistical model Linear in the module Regression is required.

The underneath tables show, that, with p = 0,15 as cut-off value for significance, only diabetes and smoking were significant covariates of the odds ratios of infarction in patients with coronary artery disease and collaterals. After mean imputation of the missing values (Statistics on a Pocket Calculator Part 2, Springer New York 2012, from the same authors) the results were unchanged. In the multiple linear regression none of the covariates remained significant. However, with no more than nine studies multiple linear regression is powerless. The conclusion was that the beneficial effect of collaterals on coronary artery disease was little influenced by the traditional risk factors of coronary artery disease. Heterogeneity of this meta-analysis was unexplained.

A meta-analysis of studies assessing the incidence of emergency admissions due to adverse drug effects (ADEs) was very heterogeneous. A meta-analysis of the risk of infarction in patients with coronary heart disease and collateral coronary arteries was heterogeneous. Meta-regressions are increasingly used as approach to subgroup analysis to assess heterogeneity in meta-analyses. The advantage of meta-regression compared to simple subgroup analyses is that multiple factors can be assessed simultaneously and that confounders and interacting factors can be adjusted.

More background, theoretical and mathematical information of meta-regressions is given in Statistics applied to clinical studies 5th edition, Chap. 34, Springer Heidelberg Germany, 2012, from the same authors.