Inference in HIV dynamics models via hierarchical likelihood

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.

Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach

Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a "Big System" with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that the proposed matrix-based SLS method could be used to estimate the coefficient matrix more accurately and perform variable selection for a linear ODE system with thousands of dimensions and millions of parameters much better than the direct least squares (LS) method and the vector-based two-stage method that are currently available. We applied this new method to two real data sets: a yeast cell cycle gene expression data set with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters, to illustrate the utility and numerical performance of the proposed parameter estimation and variable selection method for big systems in practice.

Age and CD4 count at initiation of antiretroviral therapy in HIV-infected children: effects on long-term T-cell reconstitution

BACKGROUND

Effective therapies and reduced AIDS-related morbidity and mortality have shifted the focus in pediatric human immunodeficiency virus (HIV) from minimizing short-term disease progression to maintaining optimal long-term health. We describe the effects of children's age and pre-antiretroviral therapy (ART) CD4 count on long-term CD4 T-cell reconstitution.

METHODS

CD4 counts in perinatally HIV-infected, therapy-naive children in the Paediatric European Network for the Treatment of AIDS 5 trial were monitored following initiation of ART for a median 5.7 years. In a substudy, naive and memory CD4 counts were recorded. Age-standardized measurements were analyzed using monophasic, asymptotic nonlinear mixed-effects models.

RESULTS

One hundred twenty-seven children were studied. Older children had lower age-adjusted CD4 counts in the long term and at treatment initiation (P < .001). At all ages, lower counts before treatment were associated with impaired recovery (P < .001). Age-adjusted naive CD4 counts increased on a timescale comparable to overall CD4 T-cell reconstitution, whereas age-adjusted memory CD4 counts increased less, albeit on a faster timescale.

CONCLUSIONS

It appears the immature immune system can recover well from HIV infection via the naive pool. However, this potential is progressively damaged with age and/or duration of infection. Current guidelines may therefore not optimize long-term immunological health.