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Abstract:
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Assessment of the regularity of a sequence of events over time is important for clinical decision-making as well as informing public health policy. Our motivating example involves determining the effect of an intervention on the regularity of HIV self-testing behavior among high-risk individuals when exact self-testing times are not recorded. Assuming that these unobserved testing times follow a renewal process, the goals of this work are to develop suitable methods for estimating its distributional parameters. We propose two approaches to estimation and inference: a likelihood-based discrete survival model using only time to first event; and a potentially more efficient quasi-likelihood approach based on the forward recurrence time distribution using all available data. Regularity is quantified by the coefficient of variation (CV) of the interevent time distribution. Focusing on the gamma renewal process, we conduct simulation studies to evaluate the performance of the proposed methods. We then apply them to our motivating example, concluding that the the use of text message reminders significantly improves the regularity of self-testing, but not its frequency.
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