Constrained parametric model for simultaneous inference of two cumulative incidence functions

Abstract

We propose a parametric regression model for the cumulative incidence functions (CIFs) commonly used for competing risks data. The model adopts a modified logistic model as the baseline CIF and a generalized odds-rate model for covariate effects, and it explicitly takes into account the constraint that a subject with any given prognostic factors should eventually fail from one of the causes such that the asymptotes of the CIFs should add up to one. This constraint intrinsically holds in a nonparametric analysis without covariates, but is easily overlooked in a semiparametric or parametric regression setting. We hence model the CIF from the primary cause assuming the generalized odds-rate transformation and the modified logistic function as the baseline CIF. Under the additivity constraint, the covariate effects on the competing cause are modeled by a function of the asymptote of the baseline distribution and the covariate effects on the primary cause. The inference procedure is straightforward by using the standard maximum likelihood theory. We demonstrate desirable finite-sample performance of our model by simulation studies in comparison with existing methods. Its practical utility is illustrated in an analysis of a breast cancer dataset to assess the treatment effect of tamoxifen, adjusting for age and initial pathological tumor size, on breast cancer recurrence that is subject to dependent censoring by second primary cancers and deaths.

Assessing diagnostic accuracy improvement for survival or competing‐risk censored outcomes

“…Therefore, we rely on the Cox model to obtain the predicted risks, especially for obtaining the “true” values reported in Tables and from very large datasets. There are other regression models on CIFs such as Fine (), Klein & Andersen (), Jeong & Fine (), Scheike, Zhang, & Gerds () and Shi, Cheng, & Jeong (), among others. Estimation of and will definitely affect the evaluations of added values of the new biomarkers.…”

Semiparametric regression on cumulative incidence function with interval‐censored competing risks data

“…In this paper, we extended the work by Li [10] on semiparametric analysis of the proportional subdistribution hazards or the Fine-Gray model [11] for cumulative incidence estimation with interval-censored competing risks data to the class of the semiparametric generalized odds rate transformation models. This general class includes the proportional odds model [3,6] and the proportional subdistribution hazards model as special cases. This extension is very important for medical and epidemiological applications when the proportional subdistribution hazards model does not provide good fit to the data, as was the case with our HIV data analysis.…”

“…However, the validity of these methods relies on strong assumptions for each cause of failure, and this limits their generality. One solution is to adopt more flexible three-parameter distributions as in [5] and [6]. However, while these distributions are clearly less flexible than the B-spline approximations used in this paper, they may also be plagued by non-convergence issues such as in univariate survival analysis [7].…”

“…For example, Jeong and Fine [3] proposed a parametric maximum likelihood approach along with a generalized odds rate transformation [4] to model the cause-specific cumulative incidence under the Gompertz distribution. On the other hand, Cheng [5] proposed a threeparameter modified logistic model, while Shi et al [6] considered a parametric method for explicitly modeling the cause-specific cumulative incidence of the cause of interest based on the generalized odds rate transformation [4] and the modified three-parameter logistic function proposed by Cheng [5].…”

Efficient semiparametric mixture inferences on cure rate models for competing risks

“…An attractive feature of the mixture modelling is that it does not have to make assumptions about the independence of the competing risks, which seems unreasonable and questionable in most real‐life situations. In addition, the mixture approach naturally satisfies the additivity constraint that the asymptotes of the cumulative incidence should add up to one; otherwise, it may require extra component‐wise modelling (Shi, Cheng, & Jeong, ).…”