Candidate for the Lee B. Lusted Student Prize Competition
Purpose: Standard methods of health-policy evaluation assume that future cohorts are similar to the modeled cohort. Moreover, standard value-of-information (VOI) calculations regard per-person VOI constant across cohorts and do not consider the option to collect information in the future. We show that when model parameters vary across cohorts it may be optimal to delay information collection. We provide a framework for evaluating the marginal value of sample information and thus the optimal timing and scale of information acquisition.
Methods: The value of a disease screening program is evaluated for future cohorts. Disease prevalence for future cohorts is (imperfectly) observable by collecting costly sample information and otherwise evolves randomly with drift across periods. We formulate a Markov decision problem with linear stochastic dynamics and a hidden state. The incremental net monetary benefit is assumed linear in the uncertain parameter which, itself, is decreasing in expectation. Using a dynamic-programming approach it is possible to determine decision rules for optimal continuation and information acquisition policies that govern the dynamic implementation (and eventual discontinuation) of the health program.
Results: The optimal policy is characterized by a map from the state space to actions, featuring three regions (Figure). In region III, the expected prevalence is above the upper threshold and the optimal policy is to continue the disease-screening intervention without information acquisition. In region I, the expected prevalence is below the lower threshold and it is optimal to terminate the disease-screening program. Between the two thresholds, it is optimal to continue the disease-screening program and collect information about the current cohort's disease prevalence. Further, for any initial belief about cohort prevalence, we can numerically calculate the expected value of sample information given the possibility of collecting information in the future. The results of this analysis are provided in a ready-to-use format for decision makers so as to quickly determine the currently optimal policy, the length its implementation horizon, and the subsequent action (which then leads to a state update). 
Conclusions: When cohort or intervention characteristics vary over time, the recurrent intervention and information-collection decisions can be determined by solving a stochastic dynamic program. Evaluating VOI without considering the possibility of collecting information in future periods, when the information may be more valuable, may result in sub-optimal actions.