A joint model for mixed and truncated longitudinal data and survival data, with application to HIV vaccine studies

Robust joint modelling of left-censored longitudinal data and survival data with application to HIV vaccine studies

In jointly modelling longitudinal and survival data, the longitudinal data may be complex in the sense that they may contain outliers and may be left censored. Motivated from an HIV vaccine study, we propose a robust method for joint models of longitudinal and survival data, where the outliers in longitudinal data are addressed using a multivariate t-distribution for b-outliers and using an M-estimator for e-outliers. We also propose a computationally efficient method for approximate likelihood inference. The proposed method is evaluated by simulation studies. Based on the proposed models and method, we analyze the HIV vaccine data and find a strong association between longitudinal biomarkers and the risk of HIV infection.

Nonlinear mixed-effects models for HIV viral load trajectories before and after antiretroviral therapy interruption, incorporating left censoring

OBJECTIVES

Characterizing features of the viral rebound trajectories and identifying host, virological, and immunological factors that are predictive of the viral rebound trajectories are central to HIV cure research. We investigate if key features of HIV viral decay and CD4 trajectories during antiretroviral therapy (ART) are associated with characteristics of HIV viral rebound following ART interruption.

METHODS

Nonlinear mixed effect (NLME) models are used to model viral load trajectories before and following ART interruption, incorporating left censoring due to lower detection limits of viral load assays. A stochastic approximation EM (SAEM) algorithm is used for parameter estimation and inference. To circumvent the computational intensity associated with maximizing the joint likelihood, we propose an easy-to-implement three-step method.

RESULTS

We evaluate the performance of the proposed method through simulation studies and apply it to data from the Zurich Primary HIV Infection Study. We find that some key features of viral load during ART (e.g., viral decay rate) are significantly associated with important characteristics of viral rebound following ART interruption (e.g., viral set point).

CONCLUSIONS

The proposed three-step method works well. We have shown that key features of viral decay during ART may be associated with important features of viral rebound following ART interruption.

Estimation of time of HIV seroconversion using a modified CD4 depletion model

Introduction

Several methods have been proposed to estimate the time of HIV seroconversion, including those based on CD4 cell depletion models. However, previous models have failed to consider the heterogeneity that exists in CD4 trajectories among different sub-populations. Our objective was to estimate the time from HIV seroconversion relative to the HIV diagnosis date in a population-based cohort of people living with HIV (PLWH) in the province of British Columbia, Canada.

Methods

We used linked administrative and clinical data from the British Columbia Seek and Treat for Optimal Prevention of HIV/AIDS (STOP HIV/AIDS) cohort, which contains longitudinal individual-level data on all PLWH ever diagnosed in the province. Eligible participants were aged ≥18 years and diagnosed with HIV between 1989 and 2013. The outcome was pre-antiretroviral treatment CD4 cell count measurements assessed every six months. Models were stratified by age and stage of HIV infection at diagnosis. Several explanatory variables were considered including longitudinal viral load measurements. Longitudinal CD4, square root transformed, was modeled via a non-linear mixed effects model; time was modeled using an exponential decay function. We assumed a Gaussian distribution (identity link), an AR(1) correlation structure, and a random intercept and slope for the longitudinal viral load measurements. Due to the population variation in CD4 count among uninfected individuals, we assumed 500 to 1500 cells/mm³ as the normal range when estimating the time of HIV seroconversion.

Results

Longitudinal data on 1,253 individuals were analysed: 80% male, 33% White, and the median age at diagnosis was 38 years (25^th-75^th percentile [Q₁-Q₃], 31 to 45). CD4 decay differed by stage of infection at diagnosis and age, with those ≥50 years in Stages 1 and 2 experiencing a faster decline in CD4 over time. The median duration of infection from seroconversion until HIV diagnosis was 6.9 (Q₁-Q₃, 3.9 to 10.1) years.

Conclusions

Considering the heterogeneity that exists in individual CD4 cell trajectories in a population, we presented a methodology that only relies on routinely collected HIV-related data, which can be further extended to estimate other epidemic measures.

New approaches for censored longitudinal data in joint modelling of longitudinal and survival data, with application to HIV vaccine studies

In HIV vaccine studies, longitudinal immune response biomarker data are often left-censored due to lower limits of quantification of the employed immunological assays. The censoring information is important for predicting HIV infection, the failure event of interest. We propose two approaches to addressing left censoring in longitudinal data: one that makes no distributional assumptions for the censored data-treating left censored values as a "point mass" subgroup-and the other makes a distributional assumption for a subset of the censored data but not for the remaining subset. We develop these two approaches to handling censoring for joint modelling of longitudinal and survival data via a Cox proportional hazards model fit by h-likelihood. We evaluate the new methods via simulation and analyze an HIV vaccine trial data set, finding that longitudinal characteristics of the immune response biomarkers are highly associated with the risk of HIV infection.