A Quantile Regression Model for Failure-Time Data with Time-Dependent Covariates

Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This paper provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset

General Semiparametric Shared Frailty Model Estimation and Simulation with frailtySurv

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the normal distribution. Extensive simulations demonstrate the flexibility and correct implementation of the estimator. Two case studies performed with publicly available datasets demonstrate applicability of the package. In the Diabetic Retinopathy Study, the onset of blindness is clustered by patient, and in a large hard drive failure dataset, failure times are thought to be clustered by the hard drive manufacturer and model

Discrete-time Competing-Risks Regression with or without Penalization

Many studies employ the analysis of time-to-event data that incorporates competing risks and right censoring. Most methods and software packages are geared towards analyzing data that comes from a continuous failure time distribution. However, failure-time data may sometimes be discrete either because time is inherently discrete or due to imprecise measurement. This paper introduces a novel estimation procedure for discrete-time survival analysis with competing events. The proposed approach offers two key advantages over existing procedures: first, it expedites the estimation process for a large number of unique failure time points; second, it allows for straightforward integration and application of widely used regularized regression and screening methods. We illustrate the benefits of our proposed approach by conducting a comprehensive simulation study. Additionally, we showcase the utility of our procedure by estimating a survival model for the length of stay of patients hospitalized in the intensive care unit, considering three competing events: discharge to home, transfer to another medical facility, and in-hospital death

Unlocking Retrospective Prevalent Information in EHRs -- a Pairwise Pseudolikelihood Approach

Typically, electronic health record data are not collected towards a specific research question. Instead, they comprise numerous observations recruited at different ages, whose medical, environmental and oftentimes also genetic data are being collected. Some phenotypes, such as disease-onset ages, may be reported retrospectively if the event preceded recruitment, and such observations are termed ``prevalent". The standard method to accommodate this ``delayed entry" conditions on the entire history up to recruitment, hence the retrospective prevalent failure times are conditioned upon and cannot participate in estimating the disease-onset age distribution. An alternative approach conditions just on survival up to recruitment age, plus the recruitment age itself. This approach allows incorporating the prevalent information but brings about numerical and computational difficulties. In this work we develop consistent estimators of the coefficients in a regression model for the age-at-onset, while utilizing the prevalent data. Asymptotic results are provided, and simulations are conducted to showcase the substantial efficiency gain that may be obtained by the proposed approach. In particular, the method is highly useful in leveraging large-scale repositories for replicability analysis of genetic variants. Indeed, analysis of urinary bladder cancer data reveals that the proposed approach yields about twice as many replicated discoveries compared to the popular approach

Optimal Cox Regression Subsampling Procedure with Rare Events

Massive sized survival datasets are becoming increasingly prevalent with the development of the healthcare industry. Such datasets pose computational challenges unprecedented in traditional survival analysis use-cases. A popular way for coping with massive datasets is downsampling them to a more manageable size, such that the computational resources can be afforded by the researcher. Cox proportional hazards regression has remained one of the most popular statistical models for the analysis of survival data to-date. This work addresses the settings of right censored and possibly left truncated data with rare events, such that the observed failure times constitute only a small portion of the overall sample. We propose Cox regression subsampling-based estimators that approximate their full-data partial-likelihood-based counterparts, by assigning optimal sampling probabilities to censored observations, and including all observed failures in the analysis. Asymptotic properties of the proposed estimators are established under suitable regularity conditions, and simulation studies are carried out to evaluate the finite sample performance of the estimators. We further apply our procedure on UK-biobank colorectal cancer genetic and environmental risk factors