RESUMEN
Estimation and inference in time-to-event analysis typically focus on hazard functions and their ratios under the Cox proportional hazards model. These hazard functions, while popular in the statistical literature, are not always easily or intuitively communicated in clinical practice, such as in the settings of patient counseling or resource planning. Expressing and comparing quantiles of event times may allow for easier understanding. In this article we focus on residual time, i.e., the remaining time-to-event at an arbitrary time t given that the event has yet to occur by t. In particular, we develop estimation and inference procedures for covariate-specific quantiles of the residual time under the Cox model. Our methods and theory are assessed by simulations, and demonstrated in analysis of two real data sets.
Asunto(s)
Modelos de Riesgos Proporcionales , Fármacos Anti-VIH/uso terapéutico , Simulación por Computador , Femenino , Infecciones por VIH/complicaciones , Infecciones por VIH/tratamiento farmacológico , Infecciones por VIH/mortalidad , Humanos , Lactante , Recién Nacido , Transmisión Vertical de Enfermedad Infecciosa/prevención & control , Modelos Estadísticos , Neoplasias Orofaríngeas/mortalidad , Neoplasias Orofaríngeas/terapia , Embarazo , Complicaciones Infecciosas del Embarazo/tratamiento farmacológico , Complicaciones Infecciosas del Embarazo/mortalidad , Ensayos Clínicos Controlados Aleatorios como Asunto/estadística & datos numéricos , Análisis de Regresión , Análisis de Supervivencia , Factores de TiempoRESUMEN
For randomized clinical trials where the endpoint of interest is a time-to-event subject to censoring, estimating the treatment effect has mostly focused on the hazard ratio from the Cox proportional hazards model. Since the model's proportional hazards assumption is not always satisfied, a useful alternative, the so-called additive hazards model, may instead be used to estimate a treatment effect on the difference of hazard functions. Still, the hazards difference may be difficult to grasp intuitively, particularly in a clinical setting of, e.g., patient counseling, or resource planning. In this paper, we study the quantiles of a covariate's conditional survival function in the additive hazards model. Specifically, we estimate the residual time quantiles, i.e., the quantiles of survival times remaining at a given time t, conditional on the survival times greater than t, for a specific covariate in the additive hazards model. We use the estimates to translates the hazards difference into the difference in residual time quantiles, which allows a more direct clinical interpretation. We determine the asymptotic properties, assess the performance via Monte-Carlo simulations, and demonstrate the use of residual time quantiles in two real randomized clinical trials.