The HIV Prevention Trials Network (HPTN) 024 study was a multisite, placebo-controlled, double blinded randomized trial of antibiotics to prevent perinatal MTCT of HIV-1 conducted in Tanzania, Malawi and Zambia (Taha et al., 2006
). HIV-1 infected pregnant women were enrolled at 20–24 weeks gestation and followed until delivery. Their liveborn infants were followed with HIV testing initially scheduled to be for birth, 4–6 weeks and 3, 6, 9 and 12 months. The 3 month test was dropped shortly after commencement of the study. The majority of 4–6 week visits occurred between 6 and 8 weeks. According to protocol, samples collected at 3, 6 and 9 months were only tested if the 12 month sample was positive or missing. The 12 month sample was only to be tested if an antibody test at 12 months was positive. The protocol specified that HIV-1 RNA be detected with the BioMerieux NucliSens HIV-1 QL assay for the Malawi and Zambia sites and with the Roche HIV-1 Amplicor Monitor assay version 1.5 for the Tanzania site in a reference laboratory (University of North Carolina, Chapel Hill, North Carolina, USA); however, due to logistical constraints, some infant dried blood splots from Malawi and Zambia were tested using the Roche assay. For confirmation of the infant’s HIV-1 infection a second sample (from a subsequent protocol scheduled visit) was tested whenever possible. Of primary scientific interest was the comparison of the sensitivity of these two assays.
The analysis included 1977 infants who had at least one HIV test. One hundred and eighteen infants who tested positive when they were less than 24 hours old were assigned si = 0. Six hundred and eighty six infants who had a negative antibody test at 12 months were assigned si = ∞. All other infants had si unknown and therefore sampled as part of the MCMC algorithm.
Several variables were included as predictors of timing of MTCT based on those factors shown to be information of timing of detection of HIV infection in infants in the literature. These variables along with the parameters corresponding to the regressions in which they were included in were: maternal CD4 count (θ, η), viral load (all), hemoglobin (all) and weight (all) measured at enrollment; maternal cervical viral load at delivery (all); indicators of infant (θ) and mother nevirapine (θ, η) dosing; randomization arm (θ, η); sex of the infant (all); infant birth weight (η); mode of delivery (θ, η); duration of ruptured membranes (θ, η); indicator of early infant death (θ, η); an indicator of breastfeeding for longer than 6 months (θ, η) and site (θ, β). These variables were not selected to build a model to address hypotheses of scientific interest, but instead to obtain the best possible estimate of the timing of infection, si and thus parameter estimates should be interpreted with caution. Infants born to HIV-1-infected mothers are only at risk for MTCT of HIV while breastfeeding. At one site (Tanzania), mothers were counseled to stop breastfeeding by the time their infants reached 6 months of age, and, by 6 months of age, over 90% of the the infants at this site had been weaned. In contrast, over 90% of the infants at the 3 remaining sites were still breastfeeding at six months.
Sensitivity was modeled according to Equation (1)
= 2 and x1
indicating the i
th infant’s assay type at time tij
. Information is available from several studies about the sensitivity of PCR tests in infants infected in utero or during delivery and is summarized graphically in . These data were used to construct mildly informative priors for sensitivity, where ω0
(−1, 0.06), ω1
(0, 0.05), ω2
(0, 25) and log(τ0
) ~ N
(0, 0.06). Lines representing sensitivity over time for si
= 0 based on 1,000 random draws from the prior distribution are also plotted on . The priors on ω1
suggest that the change in sensitivity over time does not depend on the mode of transmision. The prior for π
=1-specificity was set as beta(1; 1000) to reflect the belief that false positives are rare.
Priors for the distribution of the timing of MTCT were also based on historical data. With mother and infant exposed to a single dose of nevirapine, the rate of in utero/devliery transmission (not adjusted for sensitivity and therefore possibly underestimated) has been estimated to be between 0.05 and 0.10 (Thistle et al., 2007
; Taha et al., 2004
; Guay et al., 1999
). Cumulative rates of transmission into the late postnatal period for three independent studies are shown in . This plot also summarizes the prior distribution for timing of MTCT of HIV (specified as γ
~ gamma(4.2, 10), β0
(−3.4, 4), βj
(0, 4), j
= 1, …, 10, η0
(−0.4, 0.25), ηj
(0, 25), j
= 1, …, 13, θ0
(−1.1, 1) θj
(0, 25), j
= 1, …, 17). The percentiles of the distribution were calculated by simulation. The results from the previous trials were all contained within the interquartile range of the prior distribution. Additionally, the interval defined by the 2.5th and 97.5th percentiles represents a plausible range of possible outcomes (although the upper end may be higher than expected). The three studies shown also reflect a range of breastfeeding behaviors with 30–80% still breastfeeding at 12 months. Because we are modeling transmission risk conditional on breastfeeding throughout the follow-up period, we might expect our estimates to be closer to the higher estimates shown in . The parameters for the distributions were obtained using nonlinear least squares treating each time point from each study as a separate observation.
Figure 2 Graphical depiction of prior on time to HIV transmission. The solid black curve represents the mean over time. The vertical bars represent pointwise 50% (black) and 95% (gray) intervals. Information from historical data is also included: circles=Taha (more ...)
We ran the Gibbs sampler twice for 100,000 iterations each based on different starting values for the parameters and seeds for the random number generator. shows density estimates from the posterior draws of the parameters that determine the time-varying sensitivity, ω
. The densities of the prior distributions are shown with the density estimates of the marginal posteriors distributions. These do not indicate that the results were driven by the prior distributions on these parameters. lists the posterior means, standard deviations, medians and highest posterior density intervals for for ω
. Estimates for the coefficient in the transmission time models are shown in Web Appendix 3
. The MCMC chains appeared to mix well.
Figure 3 Summaries of samples from the posterior distribution of the parameters describing sensitivity over time. The thick horizontal line with vertical bars at the end on the density plots represents the HPD interval. The dotted gray line indicates the prior (more ...)
Posterior summaries of sensitivity parameters
The main parameter of interest was the difference in sensitivity between the two assays, ω2, which had a posterior mean and median equal to −0.19 with a 95% HPD interval equal to (−0.45, 0.09). Although the point estimate was less than 0 suggesting that the Roche assay may be less sensitive, there was no statistically significant association. Likewise there was no statistical difference between the mean ages at detection of in utero/delivery infections or the mean times from transmission to detection for the two assays. The estimate of ω1 suggests that the sensitivity curve for breastfeeding transmission increases more slowly than the curve for in utero/delivery transmission. plots the posterior estimates and 95% credible intervals of sensitivity over time for infants infected in utero/during delivery and infants infected via breastmilk. At six weeks of age, we would expect to detect between 97 and 98% of in utero/delivery transmission. Based on the estimate of τ0, this corresponds to approximately an average of 8 weeks after transmission. The sensitivity for detecting an infection 8 weeks after breastfeeding transmission was 72–78%.
Figure 4 Posterior estimates of sensitivity over time for in utero/delivery transmission and breastfeeding transmission. 95% credible intervals are shown in grey. Solid line = BioMerieux NucliSens HIV-1 QL assay. Dashed line=Roche HIV-1 Amplicor Monitor assay. (more ...)
plots the cumulative proportion of infected and positive infants over time. The solid black line represents the posterior mean of cumulative distribution of si from the model and represents the cumulative proportion of infants who are infected. The dashed and dotted lines represent the cumulative distribution of detection times, the times we would expect to first be able to detect infection, for the two assays. The grey line represents the estimate of the cumulative distribution based on Kaplan-Meier. The event time here was taken to be the midpoint between the last negative test and the first positive test. As expected, accounting for the imperfect sensitivity suggests that the estimated proportion of infected infants at any time is smaller than the truth, but the distance between the estimates decreases with time. This decrease is expected because the rate of new infections decreases over time. The Kaplan-Meier estimates may also be lower than the model-based estimates due to the lag in testing time (i.e., the infants are not tested as soon as infection is detectable).
Posterior estimates of the cumulative proportion of HIV infected infants, detected infections by assay (1= BioMerieux NucliSens HIV-1 QL; 2= Roche HIV-1 Amplicor Monitor), and infected infants based on unadjusted Kaplan-Meier estimates.
Additional analyses were performed considering alternative prior distributions and are summarized in Web Appendix 3
. While investigating alternative prior distributions, it became apparent that for this data set mildly informative priors were necessary to prevent the MCMC sampler from getting stuck in a degenerate state. However, this may be unique to the data set under consideration as similar problems did not occur under extensive simulations (Web Appendix 2
). Given the priors were based on mulitple historic studies and are quite liberal in values they allow for sensitivity and the survival distribution ( and ), we do not see the need for well-informed priors as a drawback in the current study. It is important however, to interpret the results in the context of the prior distributions.