Transient detectable viremia and the risk of viral rebound in patients from the Swiss HIV Cohort Study

Background Temporary increases in plasma HIV RNA ('blips') are common in HIV patients on combination antiretroviral therapy (cART). Blips above 500 copies/mL have been associated with subsequent viral rebound. It is not clear if this relationship still holds when measurements are made using newer more sensitive assays. Methods We selected antiretroviral-naive patients that then recorded one or more episodes of viral suppression on cART with HIV RNA measurements made using more sensitive assays (lower limit of detection below 50 copies/ml). We estimated the association in these episodes between blip magnitude and the time to viral rebound. Results Four thousand ninety-four patients recorded a first episode of viral suppression on cART using more sensitive assays; 1672 patients recorded at least one subsequent suppression episode. Most suppression episodes (87 %) were recorded with TaqMan version 1 or 2 assays. Of the 2035 blips recorded, 84 %, 12 % and 4 % were of low (50–199 copies/mL), medium (200–499 copies/mL) and high (500–999 copies/mL) magnitude respectively. The risk of viral rebound increased as blip magnitude increased with hazard ratios of 1.20 (95 % CI 0.89-1.61), 1.42 (95 % CI 0.96-2.19) and 1.93 (95 % CI 1.24-3.01) for low, medium and high magnitude blips respectively; an increase of hazard ratio 1.09 (95 % CI 1.03 to 1.15) per 100 copies/mL of HIV RNA. Conclusions With the more sensitive assays now commonly used for monitoring patients, blips above 200 copies/mL are increasingly likely to lead to viral rebound and should prompt a discussion about adherence. Electronic supplementary material The online version of this article (doi:10.1186/s12879-015-1120-8) contains supplementary material, which is available to authorized users.

1. The continuous time Cox model used in an earlier study, with the yearly rate of viral load measurements as a covariate [1].

2.
A discrete time Cox model, where the baseline hazard is represented by a set of intercept parameters, one for each visit where a viral load measurement was made [2]. 3. A continuous time Cox model, where the baseline hazard is represented by a second degree polynomial fit to the mid-point of the interval between successive measurements [3].

A Weibull proportional hazards model for interval censored events and time dependent
covariates [4].
Model 1 assumes the time of viral rebound is known exactly; however viral rebound is interval censored and is only known to have occurred at some point between one measurement and the next. Adding the yearly rate of viral load measurements as a covariate does not necessarily solve this problem. The value of this covariate tends to decrease the longer patients remain suppressed, as monitoring becomes less intensive in successfully treated patients. So this covariate is, at least in part, a proxy measure for the length of time the patient remains in the analysis, and then by definition viral rebound will be less likely for lower values of this covariate (as seen in Table 2 and in an earlier study [1]). Proportional hazards models are easier to interpret when the two components of the model are separate so that the baseline hazard depends on time but not on covariate values, and the effect of covariates depends on their values but not on time.
Model 2 is exact for interval censored events if the interval between subsequent measurements is the same for all patients. Where it is not, Model 2 approximates the baseline hazard by adding an offset to the model equal to the log of the time between each measurement (so 2 that rebound at a subsequent visit is more likely as the interval between visits increases) and robust standard errors are needed [2]. However Model 2 may be more appropriate if all measurements were made at regular scheduled cohort visits but less appropriate here given there were also intermediate measurements made between cohort visits for most but not all patients. However this model only allows for a single baseline hazard function and so we cannot fit this model to data from both first and subsequent suppression episodes.
A suitable model for these data should have separate baseline hazard functions for both first and subsequent episodes because although the effect of covariates may be the same in both first and subsequent episodes, the rate of viral rebound is likely to be higher in subsequent episodes. We therefore compare results from these models when fit to data from first episodes only and used these results to select a suitable model for the analysis of data from both first and subsequent episodes.

Results
The median length of first suppression episodes was 2.  (Table A1). This was due to less frequent intermediate RNA measurements because the interval between RNA measurements made at scheduled cohort visits did not vary with either the setting or the length of time suppressed.
Model 3 seemed an adequate model for these data. Using data from just first episodes, Models 3 and 4 gave similar estimates of associations between blip magnitude and subsequent viral rebound (Table A2). With Model 3, estimates were also similar when the baseline hazard function was represented by a more flexible cubic spline with five knots (Model 3B) rather than by a second order polynomial (Model 3A). Model 3 has a non-parametric baseline hazard function but approximates how this function behaves in the intervals between visits. Model 4 has a parametric baseline hazard function; this could be less flexible than non-parametric alternatives but it provides an exact likelihood for interval censored events.
The similar estimates from Models 3A and 3B suggest that the baseline hazard function is not a complicated function of time. In this case, estimates from Model 4 should be reliable. Recent simulations support this conclusion and recommend the use of parametric proportional hazard models for interval censored data [5]. Relative to Model 4, Models 1 and 2 appear to under and over estimate, respectively, although all estimates lead to the same clinical conclusions and each model shows an increase in the relative risk of viral rebound with increasing blip magnitude. Model 1 is known to underestimate hazard ratios when measurement error is added to event times [6].
We therefore used Model 3A to estimate the association between blip magnitude and the time to viral rebound in data from both first and subsequent suppression episodes. All models used the same covariates as in Table 2: gender, transmission by injection drug use, age at the start of the suppression episode, the year the suppression episode began, the assay used to measure the blip, and time updated cART categories. Model 1 also included covariates for the yearly rate of viral load measurements (as in [1]); in all other models, these three covariates were dropped and two covariates were added to represent time updated CD4 cell count.