Defective regression models for cure rate modeling with interval‐censored data

Abstract

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.

Survival models induced by zero-modified power series discrete frailty: Application with a melanoma data set

“…Many authors have performed simulations to assess the theoretical properties of MLEs, especially when the analytical investigation is not trivial. 4,6,[28][29][30][31] In the next section, we describe some simulation studies in order to verify some of the main properties of MLEs.…”

Long-term frailty modeling using a non-proportional hazards model: Application with a melanoma dataset

“…Many authors have performed simulations to assess the asymptotic behavior of MLEs, especially when the analytical investigation is not trivial. 35,38,39 We also conducted a simulation study in order to assess the impact of unobservable heterogeneity on the cured fraction, as well as we evaluate the performance of the models in estimating correctly the parameter α (negative) when in fact there is a long-term survivors group. In addition, we investigate the performance of the GTDL frailty model in terms of the same discrimination criteria when compared to the standard GTDL model, that is, without the frailty term.…”

“…37 and Calsavara et al. 38,39 recently popularized the term “defective,” although the same idea had appeared in previous papers. Instead of estimating the cure fraction p directly, as in a standard mixture model, the defective model provides an alternative for the modeling of lifetime data with long-term survivors, once it has been made a cure rate model by changing the usual domains of its parameters.…”

On a new piecewise regression model with cure rate: Diagnostics and application to medical data

“…Along the same line, Calsavara et al 21 proposed a nonproportional hazards model with a frailty term that allows the existence or nonexistence of long-term survivors in a population. Defective models, recently popularized by Rocha et al, [22][23][24] Scudilio et al, 25 and Calsavara et al, 26,27 can also be used to model presence or absence of long-term survivors. Cucchetti et al 28 applied a cure rate model to the analysis of data from patients with colorectal liver metastases.…”