Cure indicators and prevalence by stage at diagnosis for breast and colorectal cancer patients: A population-based study in Italy.

People alive many years after breast (BC) or colorectal cancer (CRC) diagnoses are increasing. This paper aimed to estimate the indicators of cancer cure and complete prevalence for Italian patients with BC and CRC by stage and age. A total of 31 Italian Cancer Registries (47% of the population) data until 2017 were included. Mixture cure models allowed estimation of net survival (NS); cure fraction (CF); time to cure (TTC, 5-year conditional NS >95%); cure prevalence (who will not die of cancer); and already cured (prevalent patients living longer than TTC). 2.6% of all Italian women (806,410) were alive in 2018 after BC and 88% will not die of BC. For those diagnosed in 2010, CF was 73%, 99% when diagnosed at stage I, 81% at stage II, and 36% at stages III-IV. For all stages combined, TTC was >10 years under 45 and over 65 years and for women with advanced stages, but ≤1 year for all BC patients at stage I. The proportion of already cured prevalent BC women was 75% (94% at stage I). Prevalent CRC cases were 422,407 (0.7% of the Italian population), 90% will not die of CRC. For CRC patients, CF was 56%, 92% at stage I, 71% at stage II, and 35% at stages III-IV. TTC was ≤10 years for all age groups and stages. Already cured were 59% of all prevalent CRC patients (93% at stage I). Cancer cure indicators by stage may contribute to appropriate follow-up in the years after diagnosis, thus avoiding patients' discrimination.

Indicators of cure for women living after uterine and ovarian cancers: a population-based study.

This study aims to estimate long-term survival, cancer prevalence, and several cure indicators for Italian women with gynecological cancers. Thirty-one cancer registries, representing 47% of the Italian female population, were included. Mixture cure models were used to estimate net survival, cure fraction, time to cure (when 5-year conditional net survival becomes > 95%), cure prevalence (women who will not die of cancer), and already cured (living longer than time to cure). In 2018, 0.4% (121 704) of Italian women were alive after diagnosis of corpus uteri cancer, 0.2% (52 551) after cervical cancer, and 0.2% (52 153) after ovarian cancer. More than 90% of patients with uterine cancers and 83% with ovarian cancer will not die from their neoplasm (cure prevalence). Women with gynecological cancers have a residual excess risk of death <5% at 5 years after diagnosis. The cure fraction was 69% for corpus uteri, 32% for ovarian, and 58% for cervical cancer patients. Time to cure was ≤10 years for women with gynecological cancers aged <55 years; 74% of patients with cervical cancer, 63% with corpus uteri cancer, and 55% with ovarian cancer were already cured. These results can contribute to improving follow-up programs for women with gynecological cancers and supporting efforts against discrimination of already cured ones. This article is part of a Special Collection on Gynecological Cancers.

On variable selection in a semiparametric AFT mixture cure model.

In clinical studies, one often encounters time-to-event data that are subject to right censoring and for which a fraction of the patients under study never experience the event of interest. Such data can be modeled using cure models in survival analysis. In the presence of cure fraction, the mixture cure model is popular, since it allows to model probability to be cured (called the incidence) and the survival function of the uncured individuals (called the latency). In this paper, we develop a variable selection procedure for the incidence and latency parts of a mixture cure model, consisting of a logistic model for the incidence and a semiparametric accelerated failure time model for the latency. We use a penalized likelihood approach, based on adaptive LASSO penalties for each part of the model, and we consider two algorithms for optimizing the criterion function. Extensive simulations are carried out to assess the accuracy of the proposed selection procedure. Finally, we employ the proposed method to a real dataset regarding heart failure patients with left ventricular systolic dysfunction.

The estimation of long and short term survival time and associated factors of HIV patients using mixture cure rate models.

BACKGROUND: HIV is one of the deadliest epidemics and one of the most critical global public health issues. Some are susceptible to die among people living with HIV and some survive longer. The aim of the present study is to use mixture cure models to estimate factors affecting short- and long-term survival of HIV patients. METHODS: The total sample size was 2170 HIV-infected people referred to the disease counseling centers in Kermanshah Province, in the west of Iran, from 1998 to 2019. A Semiparametric PH mixture cure model and a mixture cure frailty model were fitted to the data. Also, a comparison between these two models was performed. RESULTS: Based on the results of the mixture cure frailty model, antiretroviral therapy, tuberculosis infection, history of imprisonment, and mode of HIV transmission influenced short-term survival time (p-value < 0.05). On the other hand, prison history, antiretroviral therapy, mode of HIV transmission, age, marital status, gender, and education were significantly associated with long-term survival (p-value < 0.05). The concordance criteria (K-index) value for the mixture cure frailty model was 0.65 whereas for the semiparametric PH mixture cure model was 0.62. CONCLUSION: This study showed that the frailty mixture cure models is more suitable in the situation where the studied population consisted of two groups, susceptible and non-susceptible to the event of death. The people with a prison history, who received ART treatment, and contracted HIV through injection drug users survive longer. Health professionals should pay more attention to these findings in HIV prevention and treatment.

Defective 3-parameter Gompertz model with frailty term for estimating cure fraction in survival data.

In several survival data, a proportion of units is not susceptible to the event of interest, even if, accompanied by a sufficiently large time, which is so-called immune or cured. In this paper, the defective Gamma 3-parameter Gompertz model with a frailty term is proposed for estimating the cure fraction. This model does not require adding extra parameters for modeling the cure rate, and it accommodates unimodal hazard shapes as well as monotone hazards. A simulation study has been carried out to assess the performance of the maximum likelihood estimators. The model was applied to two real data sets.

Estimating causal effects in observational studies for survival data with a cure fraction using propensity score adjustment.

In observational studies, covariates are often confounding factors for treatment assignment. Such covariates need to be adjusted to estimate the causal treatment effect. For observational studies with survival outcomes, it is usually more challenging to adjust for the confounding covariates for causal effect estimation because of censoring. The challenge becomes even thornier when there exists a nonignorable cure fraction in the population. In this paper, we propose a causal effect estimation approach in observational studies for survival data with a cure fraction. We extend the absolute treatment effects on survival outcomes-including the restricted average causal effect and SPCE-to survival outcomes with cure fractions, and construct the corresponding causal effect estimators based on propensity score stratification. We prove the asymptotic properties of the proposed estimators and conduct simulation studies to evaluate their performances. As an illustration, the method is applied to a stomach cancer study.

Controlled variable selection in Weibull mixture cure models for high-dimensional data.

Medical breakthroughs in recent years have led to cures for many diseases. The mixture cure model (MCM) is a type of survival model that is often used when a cured fraction exists. Many have sought to identify genomic features associated with a time-to-event outcome which requires variable selection strategies for high-dimensional spaces. Unfortunately, currently few variable selection methods exist for MCMs especially when there are more predictors than samples. This study develops high-dimensional penalized Weibull MCMs, which allow for identification of prognostic factors associated with both cure status and/or survival. We demonstrated how such models may be estimated using two different iterative algorithms. The model-X knockoffs method was combined with these algorithms to control the false discovery rate (FDR) in variable selection. Through extensive simulation studies, our penalized MCMs have been shown to outperform alternative methods on multiple metrics and achieve high statistical power with FDR being controlled. In an acute myeloid leukemia (AML) application with gene expression data, our proposed approach identified 14 genes associated with potential cure and 12 genes with time-to-relapse, which may help inform treatment decisions for AML patients.

EM algorithm for the additive risk mixture cure model with interval-censored data.

Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation-maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.

The chances of hepatic resection curing hepatocellular carcinoma.

BACKGROUND & AIMS: The popular sense of the word "cure" implies that a patient treated for a specific disease will return to have the same life expectancy as if he/she had never had the disease. In analytic terms, it translates into the concept of statistical cure which occurs when a group of patients returns to having similar mortality to a reference population. The aim of this study was to assess the probability of being cured from hepatocellular carcinoma (HCC) by hepatic resection. METHODS: Data from 2,523 patients undergoing resection for HCC were used to fit statistical cure models, to compare disease-free survival (DFS) after surgery to the survival expected for patients with chronic hepatitis and/or cirrhosis and the general population, matched by sex, age, race/ethnicity and year of diagnosis. RESULTS: The probability of resection enabling patients with HCC to achieve the same life expectancy as those with chronic hepatitis and/or cirrhosis was 26.3%. The conditional probability of achieving this result was time-dependent, requiring about 8.9 years to be accomplished with 95% certainty. Considering the general population as a reference, the cure fraction decreased to 17.1%. Uncured patients had a median DFS of 1.5 years. In multivariable analysis, patient's age and the risk of early HCC recurrence (within 2 years) were independent determinants of the chance of cure (p <0.001). The chances of being cured ranged between 36.0% for individuals at low risk of early recurrence to approximately 3.6% for those at high risk. CONCLUSION: Estimates of the chance of being cured of HCC by resection showed that cure is achievable, and its likelihood increases with the passing of recurrence-free time. The data presented herein can be used to inform decision making and to provide patients with accurate information. LAY SUMMARY: Data from 2,523 patients who underwent resection for hepatocellular carcinoma were used to estimate the probability that resection would enable treated patients to achieve the same life expectancy as patients with chronic hepatitis and/or cirrhosis, and the general population. Herein, the cure model suggests that in patients with hepatocellular carcinoma, resection can enable patients to achieve the same life expectancy as those with chronic liver disease in 26.3% of cases and as the general population in 17.1% of cases.

Concordance measure and discriminatory accuracy in transformation cure models.

Many populations of early-stage cancer patients have non-negligible latent cure fractions that can be modeled using transformation cure models. However, there is a lack of statistical metrics to evaluate prognostic utility of biomarkers in this context due to the challenges associated with unknown cure status and heavy censorship. In this article, we develop general concordance measures as evaluation metrics for the discriminatory accuracy of transformation cure models including the so-called promotion time cure models and mixture cure models. We introduce explicit formulas for the consistent estimates of the concordance measures, and show that their asymptotically normal distributions do not depend on the unknown censoring distribution. The estimates work for both parametric and semiparametric transformation models as well as transformation cure models. Numerical feasibility of the estimates and their robustness to the censoring distributions are illustrated via simulation studies and demonstrated using a melanoma data set.

Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset.

Different cure fraction models have been used in the analysis of lifetime data in presence of cured patients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent event data in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place of usual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, and covariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. An extensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposed model. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related to lifetimes in a retrospective cohort study conducted by Puchner et al. (2017) that consists of 147 consecutive cases with surgical treatment of a sarcoma of the pelvis between the years of 1980 and 2012.

A class of semiparametric cure models with current status data.

Current status data occur in many biomedical studies where we only know whether the event of interest occurs before or after a particular time point. In practice, some subjects may never experience the event of interest, i.e., a certain fraction of the population is cured or is not susceptible to the event of interest. We consider a class of semiparametric transformation cure models for current status data with a survival fraction. This class includes both the proportional hazards and the proportional odds cure models as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the maximum likelihood estimators for the regression coefficients are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in finite samples. For illustration, we provide an application of the models to a study on the calcification of the hydrogel intraocular lenses.

Semiparametric accelerated failure time cure rate mixture models with competing risks.

Modern medical treatments have substantially improved survival rates for many chronic diseases and have generated considerable interest in developing cure fraction models for survival data with a non-ignorable cured proportion. Statistical analysis of such data may be further complicated by competing risks that involve multiple types of endpoints. Regression analysis of competing risks is typically undertaken via a proportional hazards model adapted on cause-specific hazard or subdistribution hazard. In this article, we propose an alternative approach that treats competing events as distinct outcomes in a mixture. We consider semiparametric accelerated failure time models for the cause-conditional survival function that are combined through a multinomial logistic model within the cure-mixture modeling framework. The cure-mixture approach to competing risks provides a means to determine the overall effect of a treatment and insights into how this treatment modifies the components of the mixture in the presence of a cure fraction. The regression and nonparametric parameters are estimated by a nonparametric kernel-based maximum likelihood estimation method. Variance estimation is achieved through resampling methods for the kernel-smoothed likelihood function. Simulation studies show that the procedures work well in practical settings. Application to a sarcoma study demonstrates the use of the proposed method for competing risk data with a cure fraction.

Survival probability and prognostic factors of Iranian breast cancer patients using cure rate model.

Breast cancer, the major concern of the global health, is the fifth cause of death of women in Iran. In this longitudinal study, 3048 cases of breast cancer who visited and were treated at the Cancer Research Center in Shahid Beheshti University, were studied. During study, 518 patients died. The overall survival rate of 1, 5, 10, 15, and 20-year were 95%, 76%, 59%, 47% and 46%, respectively. A significant relation was observed between survival time and the variables such as age, size of tumor, number of lymph nodes, stage, grade, and lymphovascular invasion.

Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach.

A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4+ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002-2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states.

Two new defective distributions based on the Marshall-Olkin extension.

The presence of immune elements (generating a fraction of cure) in survival data is common. These cases are usually modeled by the standard mixture model. Here, we use an alternative approach based on defective distributions. Defective distributions are characterized by having density functions that integrate to values less than 1, when the domain of their parameters is different from the usual one. We use the Marshall-Olkin class of distributions to generalize two existing defective distributions, therefore generating two new defective distributions. We illustrate the distributions using three real data sets.

A power series beta Weibull regression model for predicting breast carcinoma.

The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had a disease, but they do not accurately predict what will happen in any particular patient's case. Pathologic explanatory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion, and enhanced lymph node staining are prognostically significant to predict these survival rates. We propose a new cure rate survival regression model for predicting breast carcinoma survival in women who underwent mastectomy. We assume that the unknown number of competing causes that can influence the survival time is given by a power series distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows the beta Weibull distribution. The new compounding regression model includes as special cases several well-known cure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Further, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess local influences. The potentiality of the new regression model to predict accurately breast carcinoma mortality is illustrated by means of real data.

Evidence of being cured for nasopharyngeal carcinoma: results of a multicenter patient-based study in China.

Background: The survival rates of patients with nasopharyngeal carcinoma (NPC) have improved significantly, but there is no consensus on whether they can be considered cured. We aimed to determine whether a statistical cure could be achieved for patients with NPC in the contemporary therapeutic landscape. Methods: This retrospective multicenter study enrolled 6315 patients with nonmetastatic NPC from nonendemic and endemic regions of China from 2007 to 2020. We applied mixture and nonmixture cure models to estimate the cure probabilities and cure times by incorporating background mortality for the general population, matching by gender, age, and diagnosed year. Findings: With death as the uncured event, the probability of patients with NPC achieving a life expectancy at par with the general population was 78.1%. Considering progression as the uncured event, the likelihood of patients attaining a life expectancy without progression equivalent to that of the general population was 72.4%. For individuals, the probabilities of achieving cure were conditional and time-dependent, requiring approximately 7.1 and 4.7 years with 95% certainty, respectively. The corresponding cure times for uncured patients were 8.9 and 6.8 years, respectively. The cure probability was correlated with age, Eastern Cooperative Oncology Group score, TNM staging, Epstein-Barr virus DNA copies, and lactate dehydrogenase. The correlation was excellent between 5-year overall survival/progression-free survival and cure fractions. Interpretation: Statistical cure is potentially achievable among patients with NPC undergoing contemporary treatment modalities. The results hold significant potential implications for both clinical practice and patient perspectives. Funding: National High Level Hospital Clinical Research Funding; Beijing Xisike Clinical Oncology Research Foundation; Beijing hope run fund.

Estimating cure and risk of death from other causes of cancer patients: EUROCARE-6 data on head & neck, colorectal, and breast cancers.

BACKGROUND: To estimate net survival and cancer cure fraction (CF), i.e. the proportion of patients no longer at risk of dying from cancer progression/relapse, a clear distinction needs to be made between mortality from cancer and from other causes. Conventionally, CF is estimated assuming no excess mortality compared to the general population. METHODS: A new modelling approach, that corrects for patients' extra risk of dying (RR) from causes other than the diagnosed cancer, was considered to estimate both indicators. We analysed EUROCARE-6 data on head and neck (H&N), colorectal, and breast cancer patients aged 40-79, diagnosed from 1998 to 2002 and followed-up to 31/12/2014, provided by 65 European cancer registries. FINDINGS: Young male H&N cancer patients have 4 times the risk of dying from other causes than their peers, this risk decreases with age to 1.6. Similar results were observed for female. We observed an absolute increase in CF of 30 % using the new model instead of the conventional one. For colorectal cancer, CF with the new model increased by a maximum of 3 % for older patients and the RR ranged from 1 to 1.2 for both sexes. CF of female breast cancer ranged from 73 % to 79 % using the new cure model, with RR between 1.2 and 1.4. INTERPRETATION: Not considering a RR> 1 leads to underestimate the proportion of patients not bound to die of their diagnosed cancer. Estimates of cancer mortality risk have an important impact on patients' quality of life.

A generalized Gompertz promotion time cure model and its fitness to cancer data.

The cure models based on standard distributions like exponential, Weibull, lognormal, Gompertz, gamma, are often used to analyze survival data from cancer clinical trials with long-term survivors. Sometimes, the data is simple, and the standard cure models fit them very well, however, most often the data are complex and the standard cure models don't fit them reasonably well. In this article, we offer a novel generalized Gompertz promotion time cure model and illustrate its fitness to gastric cancer data by three different methods. The generalized Gompertz distribution is as simple as the generalized Weibull distribution and is not computationally as intensive as the generalized F distribution. One detailed real data application is provided for illustration and comparison purposes.