2015, Vol 29 No 11
from surveys may be inaccurate, given the evidence of over-reporting of health screening from many settings [7–9]. Estimates of numbers of HIV-positive diagnoses, frequently used in high-income countries, may be subject to double-counting due to retesting of previously diagnosed individuals and challenges in linking individual records across systems . As a result of these obstacles, there have been relatively few attempts to estimate the fraction of the HIV-positive population that is undiagnosed, particularly in the developing countries most severely affected by HIV/AIDS. South Africa is a country with a high HIV prevalence, in which access to HIV testing has historically been limited. However, in recent years, access to HCT has improved dramatically, with 13.3 million South Africans being tested through public health services between April 2010 and June 2011 . By integrating HCT data from the public and private health sectors, together with household survey estimates of the proportion of the population tested for HIV, this study aims to assess South Africa’s progress towards increasing HCT uptake and to identify biases associated with different data sources. In addition, this study aims to assess how the undiagnosed fraction of the HIV-positive population is likely to change in future, and whether the UNAIDS target of a 90% diagnosis rate is achievable.
Materials and methods Uptake of HCT was modelled using Thembisa, a deterministic mathematical model of the South African HIV epidemic. Detailed descriptions of the model have been published previously [12,13]. Briefly, the South African population is stratified by age, sex, marital status, level of sexual risk behaviour, male circumcision status and (in the HIV-positive population) CD4þ cell count and receipt of ART. Changes in the numbers of adults in each stratum are calculated over time, starting in 1985, based on assumptions regarding rates of demographic change and HIV epidemic dynamics. For the purpose of this analysis, assumptions regarding sexual behaviour, HIV transmission and HIV mortality are fixed at the posterior means estimated previously when fitting the model to South African HIV prevalence data and mortality data . The population aged 10 years and older is further divided into three HIV-testing history groups (never tested, previously tested negative and previously tested positive). Three types of HIV testing are modelled: testing in antenatal clinics, testing of HIV patients with opportunistic infections and testing for other reasons. The annual rate at which sexually experienced individuals get tested is
assumed to depend on their HIV stage (s), age (x), sex (g), HIV testing history (i) and the calendar year (t): tg;i;s ðx; tÞ ¼ b ðtÞAg ðx; tÞ ri þ Vs di ðtÞ þ Fg;s ðx; tÞvi ðtÞ
where b(t) is the base rate of HIV testing in year t, in individuals who do not have any HIV symptoms and are not pregnant; Ag(x,t) is an adjustment factor to represent the effect of age and sex on the base rate of test uptake; ri is an adjustment factor to represent the effect of testing history; Vs is the annual incidence of opportunistic infections in CD4þ stage s; di(t) is the fraction of patients with opportunistic infection who are tested for HIV in year t; Fg,s(x,t) is the fertility rate in sexually experienced women aged x, in HIV stage s, during year t (set to zero for men); and vi(t) is the proportion of pregnant women who receive HIV testing in year t. The function used to represent the effect of age and sex on the uptake of HIV testing is x ag 1 Ag ðx; tÞ ¼ Bg ðtÞ exp lg ð x 25Þ ; (2) 25 where Bg(t) is a time-dependent sex adjustment factor, and ag and lg are coefficients for the effect of age on the rate of HIV test uptake. Bg(t) is set to 1 for women (g ¼ 1), while for men, the ratio is allowed to change over time. This time dependency is modelled by specifying a constant ratio up to 2002 [B0(2002)], a constant ratio after 2010 [B0(2010)] and a linear change in the ratio between 2002 and 2010. The assumed values of the model parameters are summarized in Table 1 and in Table S4 of the supplementary material for the time-varying parameters. In the case of parameters that cannot be quantified precisely, prior distributions are specified to represent ranges of uncertainty. The b(t) parameter values are estimated in each year from reported numbers of HIV tests performed in South Africa. These reported numbers include data from public health facilities (from 2002 to 2012), the life insurance industry (from 2002 to 2011), medical schemes (2011) and other private providers (2011). A more detailed explanation of the method used to estimate the total numbers of HIV tests and the method to derive b(t) from these numbers is provided in the supplementary material, http://links.lww. com/QAD/A702. Due to lack of data from the period prior to 2002, the annual numbers of HIV tests were assumed to increase linearly from zero in 1990 to the estimated 2002 total; in a sensitivity analysis, we assess the effect of alternative nonlinear growth assumptions. A likelihood function was defined to represent the degree of model consistency with two further data sources: the HIV prevalence in individuals tested for HIV in 6 years (2004–2008 and 2010) and the proportion of adults who reported having ever been tested for HIV in three
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