Advances in Mixture Cure Models: Modeling Time-to-Event Data with Long-Term Survivors

Cancer remains the second most prevalent cause of death in the United States, claiming 605,213 lives in 2021, surpassing COVID-19 fatalities. The mortality rate from cancer saw a continual decline from 2019 to 2020, dropping by 1.5%, marking a significant 33% decrease since 1991. This ongoing improvement primarily mirrors advancements in treatment, enabling patients to achieve clinical remission and recovery. Now, a cancer patient is simultaneously exposed to the risk of primary cancer as well as other risks, such as other cancer(s) or other disease, leading to a competing risks scenario. Analysis of survival data under competing risks and presence of cured patients both have been extensively studied individually, but there is limited work in the current literature that models the possibility of cure from one risk in the presence of competing risks. Moreover, such a model should allow for the possibility of cure from the cause-specific risk of the primary cancer, however, the overall survival probability should eventually approach zero, thereby incorporating the prevalent belief of eventual failure with certainty. In this talk, I will present a novel unified competing risks cure model, based on the cause-specific hazard approach, that satisfies the aforementioned desired properties. To find the maximum likelihood estimates of the model parameters, I will discuss a computationally efficient expectation maximization algorithm. To demonstrate the performance of the proposed model and estimation method, I will present results of a comprehensive simulation study. Finally, I will illustrate an application using a breast cancer data from the SEER cancer database.  

The semiparametric accelerated failure time mixture cure model is an appealing alternative to the proportional hazards mixture cure model in analyzing failure time data with long-term survivors. However, this model was only proposed for independent survival data and has not been extended to clustered or correlated survival data, partly due to the complexity of the estimation method for the model. We consider a marginal semiparametric accelerated failure time mixture cure model for clustered right-censored failure time data with a potential cure fraction. We overcome the complexity of the existing semiparametric method by proposing a generalized estimating equations approach based on the EM algorithm to estimate the regression parameters in the model. The correlation structures within clusters are modeled by working correlation matrices in the proposed generalized estimating equations. The large sample properties of the regression estimators are established. Numerical studies demonstrate that the proposed estimation method is easy to use and robust to the misspecification of working matrices and that higher efficiency is achieved when the working correlation structure is closer to the true correlation structure. We apply the proposed model and estimation method to a contralateral breast cancer study and reveal new insights when the potential correlation between patients is taken into account. 

Mixture cure models are a class of time-to-event data models for populations with long-term survivors. They have been applied in diverse areas of clinical research (e.g., pediatric oncology) and non-clinical research (e.g., credit risk and recidivism). These models require important assumptions beyond those for conventional time-to-event analysis methods: Two key assumptions are the existence of a non-zero proportion of long-term survivors (or "cure fraction") in the population and sufficient follow-up in the data to identify the cure fraction. Researchers have shown that violations to these assumptions can lead to inappropriate conclusions, so the valid application of these models requires evaluating the appropriateness of cure models for each intended analysis. Historically, methods for evaluating cure model appropriateness have been criticized for poor operating characteristics, but recently, several novel methods and improvements have been proposed to address historical weaknesses. In this talk, we will motivate the necessity for evaluating cure model appropriateness, discuss recent methodological developments, and suggest future work. 

Many researchers have sought to identify prognostic models for time-to-event outcomes. When the covariate space is high-dimensional, penalized Cox proportional hazards (PH) models are commonly fit. However, various groups have shown that advances in therapy for leukemia and myelodysplastic syndrome have increased overall survival rates and some groups have identified factors related to long-term survival, defined as survival exceeding three years, such that patients on newer treatment regimens were more likely to be long-term survivors. In fact, some argue that these improved outcomes indicate that some acute myeloid leukemia (AML) patients can be considered "potentially cured." The mixture cure model (MCM) is a time-to-event model that is used when a cured fraction exists. MCMs assume the population consists of two subgroups, those cured will not experience the event of interest and those susceptible to the event of interest. Therefore, "cured" can be considered synonymous with attaining long-term relapse-free survival. MCMs are more appropriate than the Cox PH model when the dataset includes a cured fraction, because in such situations the Cox PH model does not accurately estimate the hazard or survival primarily because the assumption of a constant hazard ratio over time is violated. Moreover, the two regression components in MCMs permit identification of features associated with cure and/or latency of susceptible patients. However, few variable selection methods exist for MCMs, especially for high-dimensional covariate spaces when there are more predictors than samples. In this talk, I will describe our recent work, namely, the development of regularized MCMs for high-dimensional covariate spaces, which allow for (1) the identification of prognostic factors associated with both cure status and/or latency as well as (2) identification of latent subgroups that may be useful in the development of cancer risk stratification systems. Our methods have been made available in our R package, hdcuremodels.

 

With the advancement of HIV medicine, some people living with HIV (PWH) may not progress to AIDS. The mortality rate among PLWH with/without AIDS condition are quite different. We extended the illness death model to address this by 1) incorporating the cure rate model to account for the AIDS-free PWH and 2) employing the background mortality to allow the AIDS-free patients to have a similar mortality rate to their counterparts in the general population. Specifically, we extended the multistate cure model to the multistate cure model with background mortality and proposed the semiparametric estimation methods based on the EM algorithm. The proposed model could provide the proportion of AIDS-free PWH and the survival rate of PWH with AIDS, and also identify the significant risk factors on each pathway. We evaluate its performance under various situations, including different cure rates and sample sizes. Furthermore, we applied the proposed model to the SC HIV data to investigate the probability of AIDS and mortality rate at different stage among PWH.