Optimal accounting for age and time structure of HIV incidence estimates based on cross-sectional survey data with ascertainment of ‘recent infection’

BackgroundMany surveys have attempted to estimate HIV incidence from cross-sectional data which includes ascertainment of ‘recent infection’, but the inevitable age and time structure of this data has never been systematically explored – no doubt partly because statistical precision in such estimates is often insufficient to allow for satisfactory disaggregation. Given the non-trivial age structure of HIV incidence and prevalence, and the enormous investments that have been made in such data sets, it is important to understand effective ways to extract valid age structure from these precious data sets. MethodsUsing a comprehensive demographic/epidemiological simulation platform developed for this, and some wider, purposes (documented in more detail separately) we simulated a complex ‘South Africa inspired’ HIV epidemic, with explicitly specified 1) age/time dependent incidence, 2) age/time dependent mortality for uninfected individuals, and 3) age/time/time-since-infection dependent mortality for infected individuals. In this simulated world, we conducted cross-sectional surveys at various times, and applied variants of the recent infection based incidence estimation methodology of Kassanjee et al. We analysed in considerable detail how to smooth, and average over, the age structure in these surveys to produce the incidence estimates, paying attention to the fundamental trade-off between bias and statistical error.ResultsWe summarise our detailed observations about incidence estimates, generated by various age smoothing or age disaggregation procedures, into a straightforward fully specified ‘one size fits most’ algorithm for processing the survey data into age-specific incidence estimates: 1) generalised linear regression to turn observations into ‘prevalence’ of ‘infection’ and ‘recent infection’ (logit, and complementary log log, link functions, respectively; fitting coefficients of up to cubic terms in age/time); 2) a ‘moving window’ data inclusion recipe which handles each age/time point of interest separately; 3) post hoc age averaging of resulting pseudo continuously fitted incidence; 4) bootstrapping as a generic variance/significance estimation procedure.ConclusionsAs far as we are aware, this is the first analysis of several fine details of how age structure in cross-sectional surveys interacts with recency-based incidence estimation. Our proposed default estimation procedure generates incidence estimates with negligible bias and near-optimal precision, and can be readily applied to complex survey data sets by any group in possession of such data. Our code is available, in part freely through the R computing platform, and in part upon request.

Optimal accounting for age and time structure of HIV incidence estimates based on cross-sectional survey data with ascertainment of ‘recent infection’

BackgroundMany surveys have attempted to estimate HIV incidence from cross-sectional data which includes ascertainment of ‘recent infection’, but the inevitable age and time structure of this data has never been systematically explored – no doubt partly because statistical precision in such estimates is often insufficient to allow for satisfactory disaggregation. Given the non-trivial age structure of HIV incidence and prevalence, and the enormous investments that have been made in such data sets, it is important to understand effective ways to extract valid age structure from these precious data sets. MethodsUsing a comprehensive demographic/epidemiological simulation platform developed for this, and some wider, purposes (documented in more detail separately) we simulated a complex ‘South Africa inspired’ HIV epidemic, with explicitly specified 1) age/time dependent incidence, 2) age/time dependent mortality for uninfected individuals, and 3) age/time/time-since-infection dependent mortality for infected individuals. In this simulated world, we conducted cross-sectional surveys at various times, and applied variants of the recent infection based incidence estimation methodology of Kassanjee et al. We analysed in considerable detail how to smooth, and average over, the age structure in these surveys to produce the incidence estimates, paying attention to the fundamental trade-off between bias and statistical error.ResultsWe summarise our detailed observations about incidence estimates, generated by various age smoothing or age disaggregation procedures, into a straightforward fully specified ‘one size fits most’ algorithm for processing the survey data into age-specific incidence estimates: 1) generalised linear regression to turn observations into ‘prevalence’ of ‘infection’ and ‘recent infection’ (logit, and complementary log log, link functions, respectively; fitting coefficients of up to cubic terms in age/time); 2) a ‘moving window’ data inclusion recipe which handles each age/time point of interest separately; 3) post hoc age averaging of resulting pseudo continuously fitted incidence; 4) bootstrapping as a generic variance/significance estimation procedure.ConclusionsAs far as we are aware, this is the first analysis of several fine details of how age structure in cross-sectional surveys interacts with recency-based incidence estimation. Our proposed default estimation procedure generates incidence estimates with negligible bias and near-optimal precision, and can be readily applied to complex survey data sets by any group in possession of such data. Our code is available, in part freely through the R computing platform, and in part upon request.

An Annuitization Problem in the Tax-Deferred Annuity Model

This paper examines the optimal annuitization, investment, and consumption strategies of an individual facing a time-dependent mortality rate in the tax-deferred annuity model and considers both the case when the rate of buying annuities is unrestricted and the case when it is restricted. At the beginning, by using the dynamic programming principle, we obtain the corresponding HJB equation. Since the existence of the tax and the time-dependence of the value function make the corresponding HJB equation hard to solve, firstly, we analyze the problem in a simpler case and use some numerical methods to get the solution and some of its useful properties. Then, by using the obtained properties and Kuhn–Tucker conditions, we discuss the problem in general cases and get the value functions and the optimal annuitization strategies, respectively.