Functional Regression for Predicting Point Outcomes from Covariates Measured on Intensive Longitudinal Scale: Application to a Smoking-Cessation Study

An important goal of prevention research is to predict a range of outcomes (e.g., smoking, drinking, injury etc.). Statistically, prediction can be expressed as a regression model, with an outcome of interest regressed on predictors. The model set-up is such that both an outcome and predictors are measured on a similar frequency scale. If frequencies differ, data reduction techniques are applied to condense data. For example, if an outcome of a smoking-cessation program (smoking/not smoking) is predicted from affect measured on a momentary scale (e.g. collected with ecological momentary assessments), then only certain features of affect data can be used directly (e.g., person-level mean, variability, trend). In this process of data reduction, much information is lost, which affects prediction accuracy and interpretation.  

To overcome the problem of mismatched time scales, we developed a new method of function regression (FunReg). The method is suitable for data arising in studies that collect data intensively over time (for example, ecological momentary assessments). Typical features of such data include irregularly spaced time intervals, missing observations, and non-linear temporal trajectories. FunReg is a semi-parametric regression model that utilizes all information from predictors without any data reduction. Regression parameters are expressed in forms of continuous nonlinear weight functions that highlight regions of covariate importance and contribute to the overall model prediction.

We analyzed empirical data from a randomized clinical trial assessing effectiveness of nicotine-replacement therapy in a sample of 302 smokers. Participants used electronic diaries to provide assessments approximately 5 times per day for 2 weeks prior to and 6 weeks following a designated quit attempt. We examined the effect of momentary affect (measured on the 1-10 scale) on cessation success at 3 months following a quit attempt (biochemically verified with saliva samples).

We progressively modeled the smoking status as a function of personal average affect, personal average and variability, personal average and a trend, and an entire affect curve. The FunReg approach resulted in the most accurate prediction of the outcome as indicated by sensitivity and specificity indicators. Affect during the post-quit period was identified as the most informative for predicting a later smoking-cessation success. An R package was developed and will be shared with researchers. Additional on-line information will be provided for an easy model application.