Partly linear single-index cure models with a nonparametric incidence link function

In cancer studies, it is commonplace that a fraction of patients participating in the study are cured, such that not all of them will experience a recurrence, or death due to cancer. Also, it is plausible that some covariates, such as the treatment assigned to the patients or demographic characteristics, could affect both the patients' survival rates and cure/incidence rates. A common approach to accommodate these features in survival analysis is to consider a mixture cure survival model with the incidence rate modeled by a logistic regression model and latency part modeled by the Cox proportional hazards model. These modeling assumptions, though typical, restrict the structure of covariate effects on both the incidence and latency components. As a plausible recourse to attain flexibility, we study a class of semiparametric mixture cure models in this article, which incorporates two single-index functions for modeling the two regression components. A hybrid nonparametric maximum likelihood estimation method is proposed, where the cumulative baseline hazard function for uncured subjects is estimated nonparametrically, and the two single-index functions are estimated via Bernstein polynomials. Parameter estimation is carried out via a curated expectation-maximization algorithm. We also conducted a large-scale simulation study to assess the finite-sample performance of the estimator. The proposed methodology is illustrated via application to two cancer datasets.

Cancer cure for 32 cancer types: results from the EUROCARE-5 study

BACKGROUND

Few studies have estimated the probability of being cured for cancer patients. This study aims to estimate population-based indicators of cancer cure in Europe by type, sex, age and period.

METHODS

7.2 million cancer patients (42 population-based cancer registries in 17 European countries) diagnosed at ages 15-74 years in 1990-2007 with follow-up to 2008 were selected from the EUROCARE-5 dataset. Mixture-cure models were used to estimate: (i) life expectancy of fatal cases (LEF); (ii) cure fraction (CF) as proportion of patients with same death rates as the general population; (iii) time to cure (TTC) as time to reach 5-year conditional relative survival (CRS) >95%.

RESULTS

LEF ranged from 10 years for chronic lymphocytic leukaemia patients to <6 months for those with liver, pancreas, brain, gallbladder and lung cancers. It was 7.7 years for patients with prostate cancer at age 65-74 years and >5 years for women with breast cancer. The CF was 94% for testis, 87% for thyroid cancer in women and 70% in men, 86% for skin melanoma in women and 76% in men, 66% for breast, 63% for prostate and <10% for liver, lung and pancreatic cancers. TTC was <5 years for testis and thyroid cancer patients diagnosed below age 55 years, and <10 years for stomach, colorectal, corpus uteri and melanoma patients of all ages. For breast and prostate cancers, a small excess (CRS < 95%) remained for at least 15 years.

CONCLUSIONS

Estimates from this analysis should help to reduce unneeded medicalization and costs. They represent an opportunity to improve patients' quality of life.

Comparing cure rates for gemtuzumab ozogamicin plus standard chemotherapy vs standard chemotherapy alone in acute myeloid leukemia patients

Aim: Assess the suitability of standard parametric, piecewise and mixture cure models (MCMs) for modeling long-term survival of acute myeloid leukemia patients achieving remission following treatment with gemtuzumab ozogamicin (GO) + standard chemotherapy (SC) or SC alone. MCMs can model survival data comprising of statistically cured (patients in long-term remission) and uncured patients. Materials & methods: Models were fit to patient-level data corresponding to individual treatment arms. Results: Visual inspection showed that MCMs fit the clinical data best. Survival modeling with MCMs showed that treatment with GO + SC versus SC alone results in higher statistical cure rates for event-free survival (rates: 26-35% vs 21-23%) and overall survival (rates: 48-52% vs 38-44%). Conclusion: MCMs are well suited to modeling long-term survival in acute myeloid leukemia patients. Clinical trial registration: NCT00927498 (ClinicalTrials.gov).

A comparison of mixture cure fraction models to traditional parametric survival models in estimation of the cost-effectiveness of nivolumab for relapsed small cell lung cancer

BACKGROUND

In August 2018, the US FDA granted accelerated approval for nivolumab in small cell lung cancer (SCLC) that has progressed after platinum-based chemotherapy and at least one other line of therapy. The objective of this study was to evaluate the cost-effectiveness of nivolumab vs. usual care as third-line (3 L) therapy for patients with recurrent SCLC (rSCLC) from the health payer perspective. Given the potential for a meaningful fraction of treated patients to achieve long-term response to nivolumab, we also assessed the impact of using mixture cure modeling (MCM) vs. parametric survival modeling on survival estimates and cost-effectiveness from the US Medicare payer perspective.

METHODS

We created a partitioned survival decision model to assess the cost-effectiveness of 3 L nivolumab vs. usual care in rSCLC, based on observed US treatment patterns. Using this approach, we assessed the impact of extrapolating long-term survival from the CheckMate 032 trial, using both MCM and standard parametric curve fits. Nivolumab survival, resource use, and Grade 3/4 adverse event rates were derived from CheckMate 032. Usual care survival, resource use, and costs were derived from an analysis of patients receiving 3 L treatment for rSCLC in the SEER-Medicare registry. We applied 2020 Wholesale Acquisition Cost for drugs and 2020 CMS reimbursement for procedures. Utilities were derived from the literature. We estimated life years (LY), quality-adjusted life years (QALYs), and costs over a lifetime horizon.

RESULTS

MCM and parametric survival model extrapolations resulted in 0.43 versus 0.38 more LYs, 0.34 versus 0.30 more QALYs, and $69,308 versus $61,336 more expenditure for nivolumab vs. usual care, respectively. The costs per QALY gained using mixture cure versus parametric survival modeling were $204,386 and $207,431, respectively.

CONCLUSIONS

Mixture cure modeling was equivalent compared to parametric modeling in estimating the cost-effectiveness of nivolumab-based therapy due to the small fraction of patients achieving a long-term response with nivolumab (12.9%).

On the validity of time-dependent AUC estimation in the presence of cure fraction

During the last decades, several approaches have been proposed to estimate the time-dependent area under the receiver operating characteristic curve (AUC) of risk tools derived from survival data. The validity of these estimators relies on some regularity assumptions among which a survival function being proper. In practice, this assumption is not always satisfied because a fraction of the population may not be susceptible to experience the event of interest even for long follow-up. Studying the sensitivity of the proposed estimators to the violation of this assumption is of substantial interest. In this paper, we investigate the performance of a nonparametric simple estimator, developed for classical survival data, in the case when the population exhibits a cure fraction. Motivated from the current practice of deriving risk tools in oncology and cardiovascular disease prevention, we also assess the loss, in terms of predictive performance, when deriving risk tools from survival models that do not acknowledge the presence of cure. The simulation results show that the investigated method is valid even under the presence of cure. They also show that risk tools derived from survival models that ignore the presence of cure have smaller AUC compared to those derived from survival models that acknowledge the presence of cure. This was also attested with a real data analysis from a breast cancer study.

Temporal trends in the proportion of "cure" in children, adolescents, and young adults diagnosed with chronic myeloid leukemia in England: A population-based study

BACKGROUND

Survival probability in children, adolescents, and young adults with chronic myeloid leukemia (CML) has dramatically improved during recent years. Tyrosine kinase inhibitors (TKI), targeted drugs developed for patients with CML, were introduced in 2001 in England. We here quantify the trends in the "cure" proportion according to the year of diagnosis.

METHODS

We included all children, adolescents, and young patients with CML (0 to 24 years) diagnosed in England during 1980 to 2005. We fitted mixture cure models to estimate the "cure" proportion and the median survival time among the "uncured" patients according to the year of diagnosis, adjusted for age at diagnosis.

RESULTS

The "cure" proportion increased dramatically between 1980 and 2005, from under 10% to over 80%, while conversely, the median survival time of "uncured" patients decreased slightly between 1980 and 1999, with the trend from 2000 being uncertain.

CONCLUSIONS

The striking improvement of the "cure" fraction in young patients with CML since the early 1980s is concomitant with improvement of treatment, especially the allogeneic hematopoietic stem-cell transplant and, later, the introduction of TKI. The trends over the last years (2000-2005) remain, however, uncertain and would benefit from further studies with more recent data and updated follow-up.