Estimating HIV Incidence and Diagnosis Rates

The method used to estimate HIV incidence and time to diagnosis is an extension of the model used by Sweeting and colleagues^{3 (link)} (simplified model Figure 1; full model eFigure 1; http://links.lww.com/EDE/A932).^{13 (link)} In brief, the model describes HIV progression as a unidirectional flow through different stages of the infection that are characterized by CD4 counts or the presence of AIDS events.¹⁶ Immediately after infection, all individuals first enter a phase of primary HIV infection and then, in the absence of antiretroviral treatment, progress to AIDS through up to four different CD4 strata. The proportion of patients in each CD4 cell stratum immediately after primary infection and the progression rates between CD4 strata are based on data from seroconverters in the CASCADE collaboration.^{17 (link),18 (link)} A complete description of the model and its parameters is given in the eAppendix (http://links.lww.com/EDE/A932).
During each stage of infection, patients can be diagnosed at a rate that may depend on calendar time. For simplicity, we assume that HIV-infected individuals cannot be diagnosed during primary infection when antibody responses to HIV have not fully developed yet. We considered five distinct historical periods for which CD4 stratum-specific diagnosis rates are estimated: (1) 1980–1983, during which the first AIDS cases were diagnosed; (2) 1984–1995, when serological testing for HIV became widely available; (3) 1996–1999, the start of the era of combination antiretroviral treatment; (4) 2000–2004; and (5) 2005–2012.^{5 (link),19 (link)} Diagnosis rates were approximated as a piecewise linear function of calendar time with a different slope for each of the five time intervals. Thirty different parameters were thus necessary to describe diagnosis rates, six for each stage of infection. To reduce the number of parameters, we assumed that in the first time interval 1980–1983 all diagnosis rates are zero except for d₅ because no diagnostic tests were available at that time and HIV could only be diagnosed when AIDS had developed (Figure 1). Furthermore, d₅ was fixed at a high and constant value over calendar time, reflecting the high probability of being diagnosed with HIV when AIDS symptoms appear. In addition, we assumed that diagnosis rates in the second time interval 1984–1995 were also constant over time (see also eAppendix; http://links.lww.com/EDE/A932) such that the total number of diagnosis rate parameters that needed to be estimated from the data is 16. This assumption was motivated by the low number of observed HIV diagnoses for the early years of the epidemic due to data truncation (see “Fitting to Surveillance Data”) and by the fact that in The Netherlands HIV testing rates have traditionally been among the lowest in Europe before the introduction of combination antiretroviral treatment.^{20 (link),21 (link)}The HIV incidence curve was approximated using cubic M-splines, which allows for high flexibility with relatively few parameters.²² It was assumed that the incidence rate started at zero in 1980. Further details are given in the Supplementary Material (http://links.lww.com/EDE/A932).