  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.
