Finite Mixtures of Time-Varying Effect Models with an Application to Smoking Cessation Data

Introduction. In studies on nicotine or other drug addiction, participants’ symptoms and psychological states are often assessed at many time points. There is interest in studying heterogeneity among participants in terms of the relationship among these variables, and between these variables and time. Latent class growth modeling (LCGM) and growth mixture modeling are powerful methods for studying this heterogeneity. However, they typically assume a fixed parametric form (linear, quadratic, etc.), for the mean trajectory over time, and assume time-invariant effects of covariates. In contrast, time-varying effect modeling (TVEM) represents the time-varying association between variables flexibly, but often ignores heterogeneity among the participants. A recently developed technique, which we call MixTVEM, combines these approaches. MixTVEM identifies latent classes of individuals with similar coefficient functions across time. Class membership can be predicted by baseline covariates, and also used to predict later outcomes. Here we introduce MixTVEM to prevention scientists and demonstrate its practicality.

Method. A preliminary MixTVEM analysis was done using data from ecological momentary assessments on the process of smoking cessation. The analysis sample consists of 200 adult smokers attempting to quit (Shiffman, 1997) who are assessed at random multiple times per day. We examined heterogeneity of relationships between time, negative affect, and urge to smoke.

Results. In each of three latent classes identified from the data, a nonlinear trajectory of urge to smoke over time was estimated. Higher-urge trajectory class membership appears related to stronger prior addiction and higher relapse risk. A MixTVEM regression of urge to smoke on time-varying negative affect was also performed. In one class, urge to smoke quickly declined, and had a relatively weak relationship with negative affect. In another, the urge to smoke remained high, and was strongly related to negative affect. In the third class, the urge to smoke was moderate on average, but its relationship with negative affect, a known predictor of relapse, sharply increased during the first few days after quit. The increasing coefficient might reflect craving becoming increasingly driven by external stress in these individuals.

Conclusion. Participants showed heterogeneity in urge and in its relationship to negative affect. A free SAS macro and R function are available from the authors for performing MixTVEM. Improved MixTVEM software for handling within-subject correlation, via an autoregressive moving average structure, is being developed. This may promote improved selection of the number of classes and more accurate estimation of relationships between covariates and class membership.