Semi‐parametric modelling of the distribution of the baseline risk in meta‐analysis

Abstract

In meta‐analysis of clinical trials, often meta‐regression analyses are performed to explain the heterogeneity in treatment effects that usually exist between trials. A popular explanatory variable is the risk observed in the control group, the baseline risk. The relationship between the treatment effect and the baseline risk is investigated by fitting a linear model that allows randomness on the true baseline risk by assuming a normal distribution with unknown mean and variance. However, the normality assumption could be too strong to adequately describe the underlying distribution. Therefore, we developed a new semi‐parametric method that relaxes the normality assumption to a more flexible and general distribution. We applied a penalized Gaussian mixture distribution to represent the baseline risk distribution. Furthermore, a bivariate hierarchical model is formulated in order to take into account the correlation between the baseline and treatment effect. To fit the proposed model, a penalized likelihood function is maximized by an Expectation Maximization (EM) algorithm. We illustrate our method on a number of simulated data sets and on a published meta‐analysis data set. Copyright © 2007 John Wiley & Sons, Ltd.