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

Abstract

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.

Keywords: Ascertainment; Epidemic; Forecasting; Opportunistic infection; Outbreak; Statistical estimation; Statistical model; Test and treat.

Figure 1. Data-generating process of HIV infections and AIDS cases in Japan.

New HIV infections occur at rate λ(t). While going undiagnosed as h(t, τ), there would be an increase in the time since infection τ. Diagnosis of HIV takes place at a time-dependent rate α(t), and AIDS illness onset occurs at rate ρ(τ), which depends on the time since infection. Newly diagnosed HIV infections, and AIDS cases that had not been previously diagnosed with HIV, were notified to the surveillance system.

Figure 2. Estimated HIV incidence and rate of diagnosis in Japan.

(A) The yearly incidence of HIV infection, assuming that the median incubation period is 10.0 years. The step function for every 4 years was used to model the incidence. The 95% confidence intervals were derived from profile likelihood. (B) The yearly rate of diagnosis of HIV infection, assuming that the median incubation period is 10.0 years. (C) Maximum likelihood estimates of the yearly incidence with different median incubation periods: 7.5, 10.0, and 12.3 years. (D) Maximum likelihood estimates of the yearly rate of diagnosis with different median incubation periods: 7.5, 10.0, and 12.3 years. (E) Yearly incidence estimates by sex and different median incubation periods. Maximum likelihood estimates are shown. Note that a common logarithmic scale is used on the vertical axis, to ease comparisons. (F) Yearly rate of diagnosis estimates by sex and different median incubation periods. Maximum likelihood estimates are shown.

Figure 3. HIV diagnoses and AIDS cases in Japan, 1985–2017.

(A) Comparisons between observed and predicted yearly number of HIV diagnoses and AIDS cases. Different median incubation periods (i.e., 7.5, 10.0, and 12.3 years) were assumed, but predicted values are mostly overlapped. (B) Comparisons between observed and predicted values by sex. Circles represent the observed number of HIV diagnoses whereas triangles represent that of AIDS cases. Solid marks represent males; empty marks represent females. A common logarithmic scale is used on the vertical axis. In A and B, bold grey lines represent lower and upper 95% confidence intervals with the median incubation period of 10.0 years based on the parametric bootstrap method.

Figure 4. Undiagnosed number and proportion of HIV infections in Japan, 1986–2017.

(A) Estimates of undiagnosed HIV infections, assuming that the median incubation period is 10.0 years. The 95% confidence intervals were derived from profile likelihood. (B) Maximum likelihood estimates of undiagnosed HIV infections with different median incubation periods: 7.5, 10.0, and 12.3 years. (C) Proportion of diagnosed infections out of the cumulative number of HIV infections, inclusive of AIDS cases. (D) Proportion of diagnosed infections out of the cumulative number of HIV infections, excluding AIDS cases. (E) Maximum likelihood estimates of undiagnosed HIV infections by sex, with different median incubation periods: 7.5, 10.0, and 12.3 years. Note that common logarithmic scale is used on the vertical axis. (D) Proportion of diagnosed infections out of the cumulative number of HIV infections, excluding AIDS cases, by sex.

Figure 5. Estimated undiagnosed HIV infections and proportion of diagnosed infections at the end of 2017.

(A) Estimates of undiagnosed HIV infections with different incubation periods. Whiskers extend to lower and upper 95% confidence intervals derived using a parametric bootstrapping method. (B) Proportion of diagnosed infections out of the cumulative number of HIV infections, excluding AIDS cases (solid circles) or including AIDS cases but subtracting 2,321 deaths (empty circles). Whiskers extend to lower and upper 95% confidence intervals derived using a parametric bootstrapping method.