Longitudinal models for chronic disease risk: an evaluation of logistic multiple regression and alternatives

The logistic multiple regression model is often used in the analysis of the relation between chronic disease risk and selected risk factors in longitudinal data. Unfortunately, the logistic function has certain properties that make it inappropriate as a mode of risk analysis for longitudinal studies. The consequences of applying the logistic function to longitudinal data is that the numerical values of logistic regression coefficients cannot be meaningfully compared between studies of different durations. Sample calculations are presented to illustrate the magnitude of the problem for a range of relative study lengths and levels of risk. Two solutions are offered for the problem. First, a series of approximations are derived which permit such comparisons if the studies are not greatly dissimilar in length. Second, if comparisons of the risk coefficients are to be made across studies of greatly dissimilar duration, it is necessary to model risk via an appropriate statistical model. Criteria for assessing the appropriateness of risk functions for the analysis of longitudinal data are proposed and alternatives evaluated.