Time-to-Event Analysis with Unknown Time Origins via Longitudinal Biomarker Registration

In observational studies, the time origin of interest for time-to-event analysis is often unknown, such as the time of disease onset. Existing approaches to estimating the time origins are commonly built on extrapolating a parametric longitudinal model, which rely on rigid assumptions that can lead to biased inferences. In this paper, we introduce a flexible semiparametric curve registration model. It assumes the longitudinal trajectories follow a flexible common shape function with person-specific disease progression pattern characterized by a random curve registration function, which is further used to model the unknown time origin as a random start time. This random time is used as a link to jointly model the longitudinal and survival data where the unknown time origins are integrated out in the joint likelihood function, which facilitates unbiased and consistent estimation. Since the disease progression pattern naturally predicts time-to-event, we further propose a new functional survival model using the registration function as a predictor of the time-to-event. The asymptotic consistency and semiparametric efficiency of the proposed models are proved. Simulation studies and two real data applications demonstrate the effectiveness of this new approach.

Predictors of CD4 cell recovery following initiation of antiretroviral therapy among HIV-1 positive patients with well-estimated dates of seroconversion

OBJECTIVES

To investigate factors that predict speed of recovery and long-term CD4 cell count in HIV-1 seroconverters initiating combination antiretroviral therapy (cART), and to quantify the influence of very early treatment initiation. We make use of all pre-treatment CD4 counts, because analyses using only a single observation at initiation may be subject to biases.

METHODS

We used data from the CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe) multinational cohort collaboration of HIV-1 seroconverters. We analysed pre- and post-treatment data of patients with seroconversion dates estimated January 2003-March 2014 (n = 7600 for primary analysis) using a statistical model in which the characteristics of recovery in CD4 counts are determined by multiple predictive factors. Secondary analyses were performed incorporating uncertainty in the exact timing of seroconversion to allow more precise estimation of the benefit of very early treatment initiation.

RESULTS

'True' CD4 count at cART initiation was the strongest predictor of CD4 count beyond 3 years on cART. Allowing for lack of complete certainty in the date of seroconversion, CD4 recovery was more rapid for patients in whom treatment was initiated within 4 months. For a given CD4 count, higher viral load (VL) at initiation was strongly associated with higher post-treatment CD4 recovery. For other patient and drug characteristics, associations with recovery were statistically significant but small in magnitude.

CONCLUSIONS

CD4 count at cART initiation is the most important factor in predicting post-treatment recovery, but VL provides substantial additional information. If cART is initiated in the first 4 months following seroconversion, recovery of CD4 counts appears to be more rapid.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients.