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Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

 

We propose a broad class of so-called Cox–Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox–Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox–Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an expectation-solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled human immunodeficiency virus (HIV) prevention efficacy trials. The data example shows the utility of the proposed Cox–Aalen transformation models in enhancing statistical power for discovering covariate effects.

 

In this paper, we study several profile estimation methods for the generalized semiparametric varying-coefficient additive model for longitudinal data by utilizing the within-subject correlations. The model is flexible in allowing timevarying effects for some covariates and constant effects for others, and in having the option to choose different link functions which can used to analyze both discrete and continuous longitudinal responses.We investigated the profile generalized estimating equation (GEE) approaches and the profile quadratic inference function (QIF) approach. The profile estimations are assisted with the local linear smoothing technique to estimate the time-varying effects. Several approaches that incorporate the within-subject correlations are investigated including the quasi-likelihood (QL), the minimum generalized variance (MGV), the quadratic inference function and the weighted least squares (WLS). The proposed estimation procedures can accommodate flexible sampling schemes. These methods provide a unified approach that work well for discrete longitudinal responses as well as for continuous longitudinal responses. Finite sample performances of these methods are examined through Monto Carlo simulations under various correlation structures for both discrete and continuous longitudinal responses. The simulation results show efficiency improvement over the working independence approach by utilizing the within-subject correlations as well as comparative performances of different approaches. 

In the CYD14 trial of the CYD-TDV dengue vaccine in 2–14 year-olds, neutralizing antibody (nAb) titers to the vaccine-insert dengue strains correlated inversely with symptomatic, virologically-confirmed dengue (VCD). Also, vaccine efficacy against VCD was higher against dengue prM/E amino acid sequences closer to the vaccine inserts. We integrated the nAb and sequence data types by assessing nAb titers as a correlate of sequence-specific VCD separately in the vaccine arm and in the placebo arm. In both vaccine and placebo recipients the correlation of nAb titer with sequence-specific VCD was stronger for dengue nAb contact site sequences closer to the vaccine (p = 0.005 and p = 0.012, respectively). The risk of VCD in vaccine (placebo) recipients was 6.7- (1.80)-fold lower at the 90th vs 10th percentile of nAb for viruses perfectly matched to CYD-TDV, compared to 2.1- (0.78)-fold lower at the 90th vs 10th percentile for viruses with five amino acid mismatches. The evidence for a stronger sequence-distance dependent correlate of risk for the vaccine arm indicates departure from the Prentice criteria for a valid sequence-distance specific surrogate endpoint and suggests that the nAb marker may affect dengue risk differently depending on whether nAbs arise from infection or also by vaccination. However, when restricting to baselineseropositive 9–14 year-olds, the correlation pattern became more similar between the vaccine and placebo arms, supporting nAb titers as an approximate surrogate endpoint in this population. No sequencespecific nAb titer correlates of VCD were seen in baseline-seronegative participants. Integrated immune response/pathogen sequence data correlates analyses could help increase knowledge of correlates of risk and surrogate endpoints for other vaccines against genetically diverse pathogens. 

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan–Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccine study.

 

In HIV vaccine efficacy trials, mark-specific hazards models have important applications and can be used to evaluate the strain-specific vaccine efficacy. Additive hazards models have been widely used in practice, especially when continuous covariates are present. In this article, we conduct variable selection for a mark-specific additive hazards model. The proposed method is based on an estimating equation with the first derivative of the adaptive LASSO penalty function. The asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a dataset from the first HIV vaccine efficacy trial is provided. 

Deployment of the recently licensed tetravalent dengue vaccine based on a chimeric yellow fever virus, CYD-TDV, requires understanding of how the risk of dengue disease in vaccine recipients depends jointly on a host biomarker measured after vaccination (neutralization titre—neutralizing antibodies) and on a ‘mark’ feature of the dengue disease failure event (the amino acid sequence distance of the dengue virus to the dengue sequence represented in the vaccine). The CYD14 phase 3 trial of CYD-TDV measured neutralizing antibodies via case–cohort sampling and the mark in dengue disease failure events, with about a third missing marks. We addressed the question of interest by developing inferential procedures for the stratified mark-specific proportional hazards model with missing covariates and missing marks. Two hybrid approaches are investigated that leverage both augmented inverse probability weighting and nearest neighbourhood hot deck multiple imputation. The two approaches differ in how the imputed marks are pooled in estimation. Our investigation shows that nearest neighbourhood hot deck imputation can lead to biased estimation without properly selected neighbourhoods. Simulations show that the hybrid methods developed perform well with unbiased nearest neighbourhood hot deck imputations from proper neighbourhood selection. The new methods applied to CYD14 show that neutralizing antibody level is strongly inversely associated with the risk of dengue disease in vaccine recipients, more strongly against dengue viruses with shorter distances.

 

This paper studies theCox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.