A sup-score test for the cure fraction in mixture models for long-term survivors

Causal inference for time-to-event data with a cured subpopulation

When studying the treatment effect on time-to-event outcomes, it is common that some individuals never experience failure events, which suggests that they have been cured. However, the cure status may not be observed due to censoring which makes it challenging to define treatment effects. Current methods mainly focus on estimating model parameters in various cure models, ultimately leading to a lack of causal interpretations. To address this issue, we propose 2 causal estimands, the timewise risk difference and mean survival time difference, in the always-uncured based on principal stratification as a complement to the treatment effect on cure rates. These estimands allow us to study the treatment effects on failure times in the always-uncured subpopulation. We show the identifiability using a substitutional variable for the potential cure status under ignorable treatment assignment mechanism, these 2 estimands are identifiable. We also provide estimation methods using mixture cure models. We applied our approach to an observational study that compared the leukemia-free survival rates of different transplantation types to cure acute lymphoblastic leukemia. Our proposed approach yielded insightful results that can be used to inform future treatment decisions.

Nonparametric scanning tests of homogeneity for hierarchical models with continuous covariates

In many applications of hierarchical models, there is often interest in evaluating the inherent heterogeneity in view of observed data. When the underlying hypothesis involves parameters resting on the boundary of their support space such as variances and mixture proportions, it is a usual practice to entertain testing procedures that rely on common heterogeneity assumptions. Such procedures, albeit omnibus for general alternatives, may entail a substantial loss of power for specific alternatives such as heterogeneity varying with covariates. We introduce a novel and flexible approach that uses covariate information to improve the power to detect heterogeneity, without imposing unnecessary restrictions. With continuous covariates, the approach does not impose a regression model relating heterogeneity parameters to covariates or rely on arbitrary discretizations. Instead, a scanning approach requiring continuous dichotomizations of the covariates is proposed. Empirical processes resulting from these dichotomizations are then used to construct the test statistics, with limiting null distributions shown to be functionals of tight random processes. We illustrate our proposals and results on a popular class of two-component mixture models, followed by simulation studies and applications to two real datasets in cancer and caries research.

On a reparameterization of a flexible family of cure models

The existence of items not susceptible to the event of interest is of both theoretical and practical importance. Although researchers may provide, for example, biological, medical, or sociological evidence for the presence of such items (cured), statistical models performing well under the existence or not of a cured proportion, frequently offer a necessary flexibility. This work introduces a new reparameterization of a flexible family of cure models, which not only includes among its special cases, the most studied cure models (such as the mixture, bounded cumulative hazard, and negative binomial cure model) but also classical survival models (ie, without cured items). One of the main properties of the proposed family, apart from its computationally tractable closed form, is that the case of zero cured proportion is not found at the boundary of the parameter space, as it typically happens to other families. A simulation study examines the (finite) performance of the suggested methodology, focusing to the estimation through EM algorithm and model discrimination, by the aid of the likelihood ratio test and Akaike information criterion; for illustrative purposes, analysis of two real life datasets (on recidivism and cutaneous melanoma) is also carried out.

On testing for homogeneity with zero-inflated models through the lens of model misspecification

In many applications of two-component mixture models such as the popular zero-inflated model for discrete-valued data, it is customary for the data analyst to evaluate the inherent heterogeneity in view of observed data. To this end, the score test, acclaimed for its simplicity, is routinely performed. It has long been recognized that this test may behave erratically under model misspecification, but the implications of this behavior remain poorly understood for popular two-component mixture models. For the special case of zero-inflated count models, we use data simulations and theoretical arguments to evaluate this behavior and discuss its implications in settings where the working model is restrictive with regard to the true data generating mechanism. We enrich this discussion with an analysis of count data in HIV research, where a one-component model is shown to fit the data reasonably well despite apparent extra zeros. These results suggest that a rejection of homogeneity does not imply that the underlying mixture model is appropriate. Rather, such a rejection simply implies that the mixture model should be carefully interpreted in the light of potential model misspecifications, and further evaluated against other competing models.

Exposure assessment for Cox proportional hazards cure models with interval-censored survival data

Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

A hypothesis testing procedure for random changepoint mixed models

In biomedical research, random changepoint mixed models are used to take into account an individual breakpoint in a biomarker trajectory. This may be observed in the cognitive decline measured by psychometric tests in the prediagnosis phase of Alzheimer's disease. The existence, intensity and duration of this accelerated decline can depend on individual characteristics. The main objective of our work is to propose inferential methods to assess the existence of this phase of accelerated decline, ie, the existence of a random changepoint. To do so, we use a mixed model with two linear phases and test the nullity of the parameter measuring the difference of slopes between the two phases. Because we face the issue of nuisance parameters being unidentifiable under the null hypothesis, the supremum of the classic score test statistic on these parameters is used. The asymptotic distribution of the supremum under the null is approached with a perturbation method based on the multiplier bootstrap. The performance of our testing procedure is assessed via simulations and the test is applied to the French cohort PAQUID of elderly subjects to study the shape of the prediagnosis decline according to educational level. The test is significant for both educational levels and the estimated trajectories confirmed that educational level is a good marker for cognitive reserve.