Time-varying effect models for ordinal responses with applications in substance abuse research

Abstract

Ordinal responses are very common in longitudinal data collected from substance abuse research or other behavioral research. This study develops a new statistical model with free SAS macros that can be applied to characterize time-varying effects on ordinal responses. Our simulation study shows that the ordinal-scale time-varying effects model has very low estimation bias and sometimes offers considerably better performance when fitting data with ordinal responses than a model that treats the response as continuous. Contrary to a common assumption that an ordinal scale with several levels can be treated as continuous, our results indicate that it is not so much the number of levels on the ordinal scale but rather the skewness of the distribution that makes a difference on relative performance of linear versus ordinal models. We use longitudinal data from a well-known study on youth at high risk for substance abuse as a motivating example to demonstrate that the proposed model can characterize the time-varying effect of negative peer influences on alcohol use in a way that is more consistent with the developmental theory and existing literature, in comparison with the linear time-varying effect model.

Keywords: B-spline; longitudinal data; ordinal response; substance abuse; time-varying effect.