A Versatile Method for Confirmatory Evaluation of the Effects of a Covariate in Multiple Models

Abstract

Summary. Modern epidemiology often requires testing of the effect of a covariate on multiple end points from the same study. However, popular state of the art methods for multiple testing require the tests to be evaluated within the framework of a single model unifying all end points. This severely limits their use in applications where there are different types of end point, e.g. binary, continuous or time to event. We use an asymptotic representation of parameter estimates to combine multiple models without additional constraints. This result enables the use of established tools for multiple testing to provide a fine‐tuned control of the overall type I error in a wide range of epidemiological experiments where in reality no other useful alternative exists. The methodology proposed is applied to a multiple‐end‐point study of the effect of neonatal bacterial colonization on development of childhood asthma.

A General Framework for the Evaluation of Genetic Association Studies Using Multiple Marginal Models

“…The proposed method is less conservative than the Bonferroni-type correction if the test statistics are substantially correlated. This results in smaller adjusted p values, as demonstrated in the Applications section (see also the Discussion section in Pipper et al [17] ).…”

“…To make a conclusion about the underlying mode of inheritance, we need to consider simultaneous inference on the parameter vectors from the three genetic models β (123) = ( β (1) , β (2) , β (3) ). We use the multiple marginal models approach of Pipper et al [17] who introduced a flexible procedure for evaluation of effects in parallel models for multiple endpoints; a related approach was proposed by So and Sham [18] . Specifically, Pipper et al [17] showed that the asymptotic results for the three single GLMs also hold when stacking the corresponding three ML estimators into a single vector:…”

“…We use the multiple marginal models approach of Pipper et al [17] who introduced a flexible procedure for evaluation of effects in parallel models for multiple endpoints; a related approach was proposed by So and Sham [18] . Specifically, Pipper et al [17] showed that the asymptotic results for the three single GLMs also hold when stacking the corresponding three ML estimators into a single vector:…”

“…The estimated variance-covariance matrix of the stacked vector of parameter estimates is obtained as the empirical variance-covariance matrix of the score functions used in the log likelihood functions for the three models; for linear models and GLMs, the score functions are explicitly derived by Pipper et al [17] (see also [18] ). We denote this matrix ∑  (123) .…”

“…Lately, a similar approach was published using the relative risk estimator [37] . These approaches consider the genotype scores as a qualitative factor with the consequence of suboptimal power for the additive mode of inheritance, because the As a comparative analysis, the genotype scores are considered as a quantitative explanatory variable according to table 1 using (i) three marginal regression models [17] , (ii) a rank transformation approach [38] , and (iii) the inverse normal transformation. Since the advantage of a particular transformation method is not clear a priori, both can be considered simultaneously while taking their correlation into account.…”