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Semi‐parametric modelling of the distribution of the baseline risk in meta‐analysis
Author(s) -
Ghidey W.,
Lesaffre E.,
Stijnen T.
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3066
Subject(s) - normality , statistics , mathematics , baseline (sea) , econometrics , bivariate analysis , expectation–maximization algorithm , parametric statistics , randomness , maximum likelihood , oceanography , geology
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.