A novel approach to estimation of the time to biomarker threshold: applications to HIV

Random effects models for estimation of the probability and time to progression of a continuous biomarker

Biomarkers play a key role in the monitoring of disease progression. The time taken for an individual to reach a biomarker exceeding or lower than a meaningful threshold is often of interest. Due to the inherent variability of biomarkers, persistence criteria are sometimes included in the definitions of progression, such that only two consecutive measurements above or below the relevant threshold signal that "true" progression has occurred. In previous work, a novel approach was developed, which allowed estimation of the time to threshold using the parameters from a linear mixed model where the residual variance was assumed to be pure measurement error. In this paper, we extend this methodology so that serial correlation can be accommodated. Assuming that the Markov property holds and applying the chain rule of probabilities, we found that the probability of progression at each timepoint can be expressed simply as the product of conditional probabilities. The methodology is applied to a cohort of HIV positive individuals, where the time to reach a CD4 count threshold is estimated. The second application we present is based on a study on abdominal aortic aneurysms, where the time taken for an individual to reach a diameter exceeding 55 mm is studied. We observed that erroneously ignoring the residual correlation when it is strong may result in substantial overestimation of the time to threshold. The estimated probability of the biomarker reaching a threshold of interest, expected time to threshold, and confidence intervals are presented for selected patients in both applications.

Model-based prediction of CD4 cells counts in HIV-infected adults on antiretroviral therapy in Northwest Ethiopia: A flexible mixed effects approach

Background

CD4 cell counts is widely used as a biomarker for treatment progression when studying the efficacy of drugs to treat HIV-infected patients. In the past, it had been also used in determining eligibility to initiate antiretroviral therapy. The main aim of this was to model the evolution of CD4 counts over time and use this model for an early prediction of subject-specific time to cross a pre-specified CD4 threshold.

Methods

Hospital based retrospective cohort study of HIV-infected patients was conducted from January 2009 to December 2014 at University of Gondar hospital, Northwest Ethiopia. Fractional polynomial random effect model is used to model the evolution of CD4 counts over time in response to treatment and to estimate the individual probability to be above a pre-selected CD4 threshold. Human subject research approval for this study was received from University of Gondar Research Ethics Committee and the medical director of the hospital.

Results

A total of 1347 patients were included in the analysis presented in this paper. The cohort contributed a total of 236.58 per 100 person-years of follow-up. Later the data were divided into two periods: the first is the estimation period in which the parameters of the model are estimated and the second is the prediction period. Based on the parameters from the estimation period, model based prediction for the time to cross a threshold was estimated. The correlations between observed and predicted values of CD4 levels in the estimation period were 0.977 and 0.982 for Neverapine and Efavirenz containing regimens, respectively; while the correlation between the observed and predicted CD4 counts in the prediction period are 0.742 and 0.805 for NVP and EFV, respectively.

Conclusions

The model enables us to estimate a subject-specific expected time to cross a CD4 threshold and to estimate a subject-specific probability to have CD4 count above a pre-specified threshold at each time point. By predicting long-term outcomes of CD4 count of the patients one can advise patient about the potential ART benefits that accrue in the long-term.

Dynamic classification using credible intervals in longitudinal discriminant analysis

Recently developed methods of longitudinal discriminant analysis allow for classification of subjects into prespecified prognostic groups using longitudinal history of both continuous and discrete biomarkers. The classification uses Bayesian estimates of the group membership probabilities for each prognostic group. These estimates are derived from a multivariate generalised linear mixed model of the biomarker's longitudinal evolution in each of the groups and can be updated each time new data is available for a patient, providing a dynamic (over time) allocation scheme. However, the precision of the estimated group probabilities differs for each patient and also over time. This precision can be assessed by looking at credible intervals for the group membership probabilities. In this paper, we propose a new allocation rule that incorporates credible intervals for use in context of a dynamic longitudinal discriminant analysis and show that this can decrease the number of false positives in a prognostic test, improving the positive predictive value. We also establish that by leaving some patients unclassified for a certain period, the classification accuracy of those patients who are classified can be improved, giving increased confidence to clinicians in their decision making. Finally, we show that determining a stopping rule dynamically can be more accurate than specifying a set time point at which to decide on a patient's status. We illustrate our methodology using data from patients with epilepsy and show how patients who fail to achieve adequate seizure control are more accurately identified using credible intervals compared to existing methods.