Modeling lottery incentives for daily adherence

Many health issues require adherence to recommended daily activities, such as taking medication to manage a chronic condition, walking a certain distance to promote weight loss, or measuring weights to assess fluid balance in heart failure. The cost of nonadherence can be high, with respect to both individual health outcomes and the healthcare system. Incentivizing adherence to daily activities can promote better health in patients and populations and potentially provide long-term cost savings. Multiple incentive structures are possible. We focus here on a daily lottery incentive in which payment occurs when both the participant's lottery number matches the number drawn and the participant adheres to the targeted daily behavior. Our objective is to model the lottery's effect on participants' probability to complete the targeted task, particularly over the short term. We combine two procedures for analyzing such binary time series: a parameter-driven regression model with an autocorrelated latent process and a comparative interrupted time series. We use the output of the regression model as the control generator for the comparative time series in order to create a quasi-experimental design.