Progression models for repeated measures: Estimating novel treatment effects in progressive diseases

Mixed Models for Repeated Measures (MMRMs) are ubiquitous when analyzing outcomes of clinical trials. However, the linearity of the fixed-effect structure in these models largely restrict their use to estimating treatment effects that are defined as linear combinations of effects on the outcome scale. In some situations, alternative quantifications of treatment effects may be more appropriate. In progressive diseases, for example, one may want to estimate if a drug has cumulative effects resulting in increasing efficacy over time or whether it slows the time progression of disease. This paper introduces a class of nonlinear mixed-effects models called Progression Models for Repeated Measures (PMRMs) that, based on a continuous-time extension of the categorical-time parametrization of MMRMs, enables estimation of novel types of treatment effects, including measures of slowing or delay of the time progression of disease. Compared to conventional estimates of treatment effects where the unit matches that of the outcome scale (e.g. 2 points benefit on a cognitive scale), the time-based treatment effects can offer better interpretability and clinical meaningfulness (e.g. 6 months delay in progression of cognitive decline). The PMRM class includes conventionally used MMRMs and related models for longitudinal data analysis, as well as variants of previously proposed disease progression models as special cases. The potential of the PMRM framework is illustrated using both simulated and historical data from clinical trials in Alzheimer's disease with different types of artificially simulated treatment effects. Compared to conventional models it is shown that PMRMs can offer substantially increased power to detect disease-modifying treatment effects where the benefit is increasing with treatment duration.