Mathematical biology and medical statistics: contributions to the understanding of AIDS epidemiology

Estimating the incidence and diagnosed proportion of HIV infections in Japan: a statistical modeling study

Background

Epidemiological surveillance of HIV infection in Japan involves two technical problems for directly applying a classical backcalculation method, i.e., (i) all AIDS cases are not counted over time and (ii) people diagnosed with HIV have received antiretroviral therapy, extending the incubation period. The present study aimed to address these issues and estimate the HIV incidence and the proportion of diagnosed HIV infections, using a simple statistical model.

Methods

From among Japanese nationals, yearly incidence data of HIV diagnoses and patients with AIDS who had not previously been diagnosed as HIV positive, from 1985 to 2017, were analyzed. Using the McKendrick partial differential equation, general convolution-like equations were derived, allowing estimation of the HIV incidence and the time-dependent rate of diagnosis. A likelihood-based approach was used to obtain parameter estimates.

Results

Assuming that the median incubation period was 10.0 years, the cumulative number of HIV infections was estimated to be 29,613 (95% confidence interval (CI): 29,059, 30,167) by the end of 2017, and the proportion of diagnosed HIV infections was estimated at 80.3% (95% CI [78.7%–82.0%]). Allowing the median incubation period to range from 7.5 to 12.3 years, the estimate of the proportion diagnosed can vary from 77% to 84%.

Discussion

The proportion of diagnosed HIV infections appears to have not yet reached 90% among Japanese nationals. Compared with the peak incidence from 2005–2008, new HIV infections have clearly been in a declining trend; however, there are still more than 1,000 new HIV infections per year in Japan. To increase the diagnosed proportion of HIV infections, it is critical to identify people who have difficulty accessing consultation, testing, and care, and to explore heterogeneous patterns of infection.

Development of an individual-based model for polioviruses: implications of the selection of network type and outcome metrics

We developed an individual-based (IB) model to explore the stochastic attributes of state transitions, the heterogeneity of the individual interactions, and the impact of different network structure choices on the poliovirus transmission process in the context of understanding the dynamics of outbreaks. We used a previously published differential equation-based model to develop the IB model and inputs. To explore the impact of different types of networks, we implemented a total of 26 variations of six different network structures in the IB model. We found that the choice of network structure plays a critical role in the model estimates of cases and the dynamics of outbreaks. This study provides insights about the potential use of an IB model to support policy analyses related to managing the risks of polioviruses and shows the importance of assumptions about network structure.

Significance of variation within HIV, EBV, and KSHV subtypes

Since their initial transmission to humans, viruses have diversified extensively through recombination and mutation. The presence of intra- and inter-individual viral diversity influences disease progression, drug resistance, and therapy and presumably explains the conflicting results in many studies, including the failure of peptide-based vaccination strategies. Although HIV is a small RNA virus, coinfection with large DNA viruses, notably the oncogenic gamma-herpesviridae human herpesvirus-8 and Epstein Barr virus, is common. This coinfection occurs secondary to immunosuppression and shared transmission routes with high-risk predisposing behavior. In addition, all 3 of these viruses can lead to chronic infections, long periods of latency, and reactivation characterized by pain and suffering. The efficient targeting of their genetic diversity represents one of the major challenges in their control, both in prophylactic and therapeutic strategies. An understanding of diversity will help delineate whether population-specific vaccine strategies are necessary.

Statistical methods for HIV dynamic studies in AIDS clinical trials

Studies of HIV dynamics in AIDS research are very important for understanding pathogenesis of HIV infection and for assessing the potency of antiviral therapies. Since the viral dynamic results from clinical data were first published by Ho et al. and Wei et al., the study of HIV-1 dynamics in vivo has drawn a great attention from AIDS clinicians and researchers. Although the important findings from HIV dynamic studies have been published in many prestigious scientific journals, statistical methods for estimating viral dynamic parameters have not been paid enough attention by HIV dynamic investigators. The estimation methods in many viral dynamic studies are very crude and inefficient. In this paper, we review the statistical methods and mathematical models for HIV dynamic data analysis developed in recent years. We also address some practical issues and share our experiences in the design and analysis of viral dynamic studies. Some principles and guidelines for the design and analysis of viral dynamic studies are provided. The methodologies reviewed in this paper are also applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus. We also pose some challenging statistical problems in this area in order to stimulate further study by the statistical research community.