Meta analysis of continuous covariates in observa­tional studies

Article type
Authors
Sauerbrei W, Royston P
Abstract
Background: Assessing the effect of a continuous covariate in a single study requires the determination of a dose-response relationship in a model adjusting for other covariates. Even with individual patient data (IPD), summarizing the results of several dose-response functions in a meta-analysis is not straightforward. Objectives: To describe a new procedure which determines in single studies an adjusted dose-response function for a continuous variable of interest and which summarizes such functions across studies in an IPD meta-analysis. Methods: The fractional polynomial approach offers a sensible compromise between flexibility and stability for the determination of a dose response function in a single study, with or without adjustment for confounders. To average functions from several studies we propose three approaches: a pooled function, a fixed effect and a random effect function. Results: Using breast cancer data from the US SEER database in which each individual registry is treated as a single study, we illustrate how our approach can produce an adjusted overall estimate of the functional form for the association between time to recurrence and a continuous covariate. We demonstrate our approach by estimating adjusted continuous dose-response functions for the effect of the number of positive lymph nodes, a factor with a large effect, and age, a covariate whose prognostic effect is controversial. Whereas the individual functions for nodes are similar across studies, those for age show considerable variability. Because of their different weights, whether to use a fixed or a random effects model affects the average function. Conclusions: For an ‘ideal’ situation with IPD and only minor variations between studies with respect to measurement techniques and confounders, our approach allows one to model dose-response relationships in single studies and to summarize them in an average function. Modifications are available if the data situation is less than ideal.