A general HIV incidence inference scheme based on likelihood of individual level data and a population renewal equation

Abstract

We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.

Figure 1. The simulated incidence and prevalence.

Simulated age-specific incidence and prevalence at times were the surveys were simulated and at midpoint of intervals of interest.

Figure 2. Incidence rates using the MLE approach.

The number of replications was 1000 for all the analyses and confidence limits (95% CL) were obtained by the percentile method. The inclusion window was chosen as follow. a) Period 1, 2 and 3: for times in the interval , for each age from 15 to 16, for each age from 17 to 22, for each age from 23 to 35, and for ages greater than 35. b) Period 4: for times in the interval , for each age from 15 to 16, for each age from 17 to 22, for each age from 23 to 35, and for ages greater than 35.

Figure 3. Incidence rates using the approach of Brunet and Struchiner .

The number of replications was 1000 for all the analyses and confidence limits (95% CL) were obtained by the percentile method.

Figure 4. Incidence rates estimated in age bins using the approach of Hallett et al. .

The number of replications was 1000 for all the analyses and confidence limits (95% CL) were obtained by the percentile method.

Figure 5. Incidence and absolute error of the -estimator.

Contour lines for the true incidence (in percentage) and contour lines for the absolute error (in percentage as well) for the MLE approach in a cohort study in the case where the initial prevalence, is 0.1 and the time between the two surveys is 5 years.

Figure 6. Relative error of the -estimator as a function of the initial prevalence.

Contour lines for the relative error (in percentage) on the incidence when using the MLE approach in a birth cohort in the case where the duration between the two surveys or the initial prevalence, varies.