Mixture and Non-Mixture Cure Models for the survival analysis of SARS-CoV-2 patients in Khyber Pakhtunkhwa, Pakistan.

Objective: To examine the potential difference in survival and risk of death between asymptomatic and symptomatic SARS-CoV-2 patients, controlled by age and gender for all the attendance in hospitals of Khyber Pakhtunkhwa (KP), Pakistan. Methods: In this retrospective study, the medical records of 6273 SARS-CoV-2 patients admitted to almost all hospitals in Khyber Pakhtunkhwa during the first wave of the coronavirus outbreak from March to June 2020 were analysed. The effects of gender, age, and being symptomatic on the survival of SARS-CoV-2 patients were assessed using cure-survival models as opposed to the conventional Cox proportional hazards model. Results: The prevalence of initially symptomatic patients was 55.8%, and the overall mortality rate was 11.8%. The fitted cure-survival models suggest that age affects the probability of death (incidence) but not the short-term survival time of patients (latency); symptomatic patients have a higher risk of death than their asymptomatic counterparts, but the survival time of symptomatic patients is longer on average; gender has no significant effect on the probability of death and survival time. Conclusion: The available data and statistical results suggest that asymptomatic and young patients are generally less susceptible to initial infection with SARS-CoV-2 and therefore have a lower risk of death. Our regression models show that uncured asymptomatic patients generally have poorer short-term survival than their uncured symptomatic counterparts. The association between gender and survival outcome was not significant.

Sample size calculation for mixture cure model with restricted mean survival time as a primary endpoint.

It is not uncommon for a substantial proportion of patients to be cured (or survive long-term) in clinical trials with time-to-event endpoints, such as the endometrial cancer trial. When designing a clinical trial, a mixture cure model should be used to fully consider the cure fraction. Previously, mixture cure model sample size calculations were based on the proportional hazards assumption of latency distribution between groups, and the log-rank test was used for deriving sample size formulas. In real studies, the latency distributions of the two groups often do not satisfy the proportional hazards assumptions. This article has derived a sample size calculation formula for a mixture cure model with restricted mean survival time as the primary endpoint, and did simulation and example studies. The restricted mean survival time test is not subject to proportional hazards assumptions, and the difference in treatment effect obtained can be quantified as the number of years (or months) increased or decreased in survival time, making it very convenient for clinical patient-physician communication. The simulation results showed that the sample sizes estimated by the restricted mean survival time test for the mixture cure model were accurate regardless of whether the proportional hazards assumptions were satisfied and were smaller than the sample sizes estimated by the log-rank test in most cases for the scenarios in which the proportional hazards assumptions were violated.

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.

CureAuxSP: An R package for estimating mixture cure models with auxiliary survival probabilities.

BACKGROUND AND OBJECTIVE: There is a rising interest in exploiting aggregate information from external medical studies to enhance the statistical analysis of a modestly sized internal dataset. Currently available software packages for analyzing survival data with a cure fraction ignore the potentially available auxiliary information. This paper aims at filling this gap by developing a new R package CureAuxSP that can include subgroup survival probabilities extracted outside into an interested internal survival dataset. METHODS: The newly developed R package CureAuxSP provides an efficient approach for information synthesis under the mixture cure models, including Cox proportional hazards mixture cure model and the accelerated failure time mixture cure model as special cases. It focuses on synthesizing subgroup survival probabilities at multiple time points and the underlying method development lies in the control variate technique. Evaluation of homogeneity assumption based on a test statistic can be automatically carried out by our package and if heterogeneity does exist, the original outputs can be further refined adaptively. RESULTS: The R package CureAuxSP provides a main function SMC.AxuSP() that helps us adaptively incorporate external subgroup survival probabilities into the analysis of an internal survival data. We also provide another function Print.SMC.AuxSP() for printing the results with a better presentation. Detailed usages are described, and implementations are illustrated with numerical examples, including a simulated dataset with a well-designed data generating process and a real breast cancer dataset. Substantial efficiency gain can be observed by our results. CONCLUSIONS: Our R package CureAuxSP can make the wide applications of utilizing auxiliary information possible. It is anticipated that the performance of mixture cure models can be improved for the survival data with a cure fraction, especially for those with small sample sizes.

Cost-effectiveness analysis 3L of axicabtagene ciloleucel vs tisagenlecleucel and lisocabtagene maraleucel in Japan.

Aim: Cost-effectiveness analysis (CEA) was performed to compare axicabtagene ciloleucel (axi-cel) with tisagenlecleucel (tisa-cel) and lisocabtagene (liso-cel) for treatment of relapsed or refractory large B-cell lymphoma in adult patients after ≥2 lines of therapy in Japan. Materials & methods: Cost-effectiveness analysis was conducted using the partition survival mixture cure model based on the ZUMA-1 trial and adjusted to the JULIET and TRANSCEND trials using matching-adjusted indirect comparisons. Results & conclusion: Axi-cel was associated with greater incremental life years (3.13 and 2.85) and incremental quality-adjusted life-years (2.65 and 2.24), thus generated lower incremental direct medical costs (-$976.29 [-¥137,657] and -$242.00 [-¥34,122]), compared with tisa-cel and liso-cel. Axi-cel was cost-effective option compared with tisa-cel and liso-cel from a Japanese payer's perspective.

[Box: see text].

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.

Cure models with adaptive activation for modeling cancer survival.

We propose a class of cure rate models motivated by analysis of colon cancer and triple-negative breast cancer survival data. This class is indexed by an adaptive activation parameter and a function. We establish that the class is stochastically ordered in the activation parameter and also establish two identifiability results for this class. The first- and last-activation models are members of this class whereas many cure rate models proposed in the literature are also part of this class. We illustrate that while first- and last-activation models may perform poorly under model misspecifications, the proposed model with adaptive activation provides appropriate inference in these cases. We apply the proposed approach to assess treatment-sex interaction on cure rate in a colon cancer study and to assess role of tumor heterogeneity and ethnic disparity in breast cancer.

An updated cost-effectiveness analysis of axicabtagene ciloleucel in second-line large B-cell lymphoma patients in the United States.

AIMS: This economic evaluation of axicabtagene ciloleucel (axi-cel) versus previous standard of care (SOC; salvage chemotherapy followed by high-dose therapy with autologous stem cell rescue) in the second line (2L) large B-cell lymphoma population is an update of previous economic models that contained immature survival data. METHODS: This analysis is based on primary overall survival (OS) ZUMA-7 clinical trial data (median follow-up of 47.2 months), from a United States (US) payer perspective, with a model time horizon of 50 years. Mixture cure models were used to extrapolate updated survival data; subsequent treatment data and costs were updated. Patients who remained in the event-free survival state by 5 years were assumed to have achieved long-term remission and not require subsequent treatment. RESULTS: Substantial survival and quality of life benefits were observed despite 57% of patients in the SOC arm receiving subsequent cellular therapy: median model-projected (ZUMA-7 trial Kaplan-Meier estimated) OS was 78 months (median not reached) for axi-cel versus 25 months (31 months) for SOC, resulting in incremental quality-adjusted life year (QALY) difference of 1.63 in favor of axi-cel. Incrementally higher subsequent treatment costs were observed in the SOC arm due to substantial crossover to cellular therapies, thus, when considering the generally accepted willingness to pay threshold of $150,000 per QALY in the US, axi-cel was cost-effective with an incremental cost-effectiveness ratio of $98,040 per QALY. CONCLUSIONS: Results remained consistent across a wide range of sensitivity and scenario analysis, including a crossover adjusted analysis, suggesting that the mature OS data has significantly reduced the uncertainty of axi-cel's cost-effectiveness in the 2L setting in the US. Deferring treatment with CAR T therapies after attempting a path to transplant may result in excess mortality, lower quality of life and would be an inefficient use of resources relative to 2L axi-cel.

A Bayesian proportional hazards mixture cure model for interval-censored data.

The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval-censored, the estimation of this model is challenging due to its complex data structure. In this article, we propose a computationally efficient semiparametric Bayesian approach, facilitated by spline approximation and Poisson data augmentation, for model estimation and inference with interval-censored data and a cure rate. The spline approximation and Poisson data augmentation greatly simplify the MCMC algorithm and enhance the convergence of the MCMC chains. The empirical properties of the proposed method are examined through extensive simulation studies and also compared with the R package "GORCure". The use of the proposed method is illustrated through analyzing a data set from the Aerobics Center Longitudinal Study.

Functional proportional hazards mixture cure model with applications in cancer mortality in NHANES and post ICU recovery.

We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.

Comparison of statistical methods for extrapolating survival in previously untreated diffuse large B-cell lymphoma: results based on the POLARIX study.

OBJECTIVE: The ongoing Phase III randomized POLARIX study (GO39942; NCT03274492) demonstrated significantly improved progression-free survival (PFS) with polatuzumab vedotin plus rituximab, cyclophosphamide, doxorubicin and prednisone (Pola-R-CHP) versus rituximab plus cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP) in patients with previously untreated diffuse large B-cell lymphoma (DLBCL). We compared statistical methodologies to extrapolate long-term PFS data from POLARIX. MATERIALS AND METHODS: This analysis explored four different approaches to extrapolate the POLARIX data: standard parametric survival, mixture-cure, landmark, and spline models. The resulting extrapolation curves were validated via comparison with the corresponding Kaplan-Meier (KM) curves from POLARIX and the POLARIX-like population of the Phase III GOYA study (NCT01287741; R-CHOP arm). RESULTS: The R-CHOP PFS KM curve from the GOYA validation set was well aligned with the POLARIX KM curve. As we anticipated that PFS in POLARIX would evolve similarly to that of GOYA, the data from GOYA were used to externally validate the extrapolated modelling results. While all four statistical methods were able to fit the data to the POLARIX KM curve, the mixture-cure model was the most accurate in predicting long-term PFS in the GOYA external validation set. In the mixture-cure model, generalized gamma distribution estimated 64% (95% confidence intervals [CI]: 56-71%) of patients to have long-term remission in the R-CHOP arm of POLARIX and GOYA, and 75% (95% CI: 70-79%) in the Pola-R-CHP arm of POLARIX. A limitation of this study was the comparison of the statistical models only in the PFS KM curves, since it was not possible to determine which statistical method was more appropriate to extrapolate the overall survival KM curves. CONCLUSIONS: Within this analysis, the mixture-cure model provided the best prediction of long-term outcomes from the primary PFS analysis of the POLARIX study.

Prognostic Factors Analysis of Metastatic Recurrence in Cervical Carcinoma Patients Treated with Definitive Radiotherapy: A Retrospective Study Using Mixture Cure Model.

OBJECTIVES: This study aims to identify prognostic factors associated with metastatic recurrence-free survival of cervical carcinoma (CC) patients treated with radical radiotherapy and assess the cure probability of radical radiotherapy from metastatic recurrence. METHODS: Data were from 446 cervical carcinoma patients with radical radiotherapy for an average follow up of 3.96 years. We applied a mixture cure model to investigate the association between metastatic recurrence and prognostic factors and the association between noncure probability and factors, respectively. A nonparametric test of cure probability under the framework of a mixture cure model was used to examine the significance of cure probability of the definitive radiotherapy treatment. Propensity-score-matched (PSM) pairs were generated to reduce bias in subgroup analysis. RESULTS: Patients in advanced stages (p = 0.005) and those with worse treatment responses in the 3rd month (p = 0.004) had higher metastatic recurrence rates. Nonparametric tests of the cure probability showed that 3-year cure probability from metastatic recurrence was significantly larger than 0, and 5-year cure probability was significantly larger than 0.7 but no larger than 0.8. The empirical cure probability by mixture cure model was 79.2% (95% CI: 78.6-79.9%) for the entire study population, and the overall median metastatic recurrence time for uncured patients (patients susceptible to metastatic recurrence) was 1.60 (95% CI: 1.51-1.69) years. Locally advanced/advanced stage was a risk factor but non-significant against the cure probability (OR = 1.078, p = 0.088). The interaction of age and activity of radioactive source were statistically significant in the incidence model (OR = 0.839, p = 0.025). In subgroup analysis, compared with high activity of radioactive source (HARS), low activity of radioactive source (LARS) significantly contributed to a 16.1% higher cure probability for patients greater than 53 years old, while cure probability was 12.2% lower for the younger patients. CONCLUSIONS: There was statistically significant evidence in the data showing the existence of a large amount of patients cured by the definitive radiotherapy treatment. HARS is a protective factor against metastatic recurrence for uncured patients, and young patients tend to benefit more than the elderly from the HARS treatment.

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.

Mean residual life cure models for right-censored data with and without length-biased sampling.

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equations to estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equations to estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetes mellitus.

Goodness-of-fit test for a parametric mixture cure model with partly interval-censored data.

Partly interval-censored event time data arise naturally in medical, biological, sociological and demographic studies. In practice, some patients may be immune from the event of interest, invoking a cure model for survival analysis. Choosing an appropriate parametric distribution for the failure time of susceptible patients is an important step to fully structure the mixture cure model. In the literature, goodness-of-fit tests for survival models are usually restricted to uncensored or right-censored data. We fill in this gap by proposing a new goodness-of-fit test dealing with partly interval-censored data under mixture cure models. Specifically, we investigate whether a parametric distribution can fit the susceptible part by using a Cramér-von Mises type of test, and establish the asymptotic distribution of the test . Empirically, the critical value is determined from the bootstrap resamples. The proposed test, compared to the traditional leveraged bootstrap approach, yields superior practical results under various settings in extensive simulation studies. Two clinical data sets are analyzed to illustrate our method.

Evaluations of Factors Affecting of Short-and Long-Time of Occurrence of Disease Relapse in Patients with Tuberculosis Using Parametric Mixture Cure Model: A Cohort Study.

Background: The success of treatment strategies to control the disease relapse requires determining factors affecting the incident short-time and long-time of disease relapse. Therefore, this study was aimed to identify the factors affecting of short-and long-time of occurrence of disease relapse in patients with tuberculosis (TB) using a parametric mixture cure model. Materials and Methods: In this historical cohort study; the data was collected from 4564 patients with TB who referred to the Tuberculosis and Lung Diseases Research Center of Dr. Masih Daneshvari Hospital from 2005 to 2015. In order to evaluate the factors affecting of short-and long-time of occurrence of disease relapse, a parametric mixture cure model was used. Results: In this study, the estimation of the annual incidence of TB relapse showed that the probability of recurrence in the first year is 1% and in the third and tenth years after treatment is 3% and 5%, respectively. In addition, the results of this study showed that the variables of residence, exposure to cigarette smoke, adverse effects of drug use, incarceration, and pulmonary and extra- pulmonary tuberculosis were the factors affecting the short-time recurrence of TB. The variables of drug use, pulmonary and extra- pulmonary tuberculosis, and also incarceration affected the long-term recurrence of this disease. Conclusion: Cure models by separating factors affecting the short-time occurrence from the long-time occurrence of disease relapse can provide more accurate information to researchers to control and reduce TB relapse.

Long-term outcomes of non-metastatic breast cancer patients by molecular subtypes.

BACKGROUND: Today, with the progress of medical sciences, increasing the cure probability and survival time is an important goal of cancer treatment. This study compared long-term disease-free survival (DFS) of non-metastatic breast cancer patients based on different molecular subtypes. METHODS: This retrospective cohort study consisted of 1287 patients diagnosed with breast cancer and treated at Motamed Cancer Institute from 2000 to 2016 and followed up until 2018. Kaplan-Meier curve was fitted to data based on molecular subtypes. Then the semi-parametric mixture cure model was applied to determine the survival and cure probability of molecular subtypes by adjusting clinical and demographic factors. RESULTS: Among 1287 breast cancer patients, 200 (15.5%) cases died. The mean age of patients was 47.00 ± 10.72 years. Women with the HR+/HER2-subtype had the best 5-year survival rate (84.2%), whereas other subtypes had a lower rate as follows: HR+/HER2+ (77.3%), triple-negative (76.5%), and HR-/HER2+ (62.3%). Kaplan-Meier curve calculated a cure rate of about 60% and patients who survived more than 150 months were intuitively considered cured. After adjustment for clinical and demographic variables, the cure probability of HR-/Her2+ patients was substantially lower than HR+/HER2- patients (OR = 0.22), though there were no significant variations in short-term DFS based on molecular subtypes (HR = 0.91). CONCLUSIONS: Our results confirm that the most prevalent breast cancer was HR+/HER2- tumor type which had the best prognosis. It is also concluded that HR-/HER2+ patients had the worst outcomes, with the highest rates of recurrence and metastasis and the lowest overall and disease-free survival rates.

Analysis of survival data with cure fraction and variable selection: A pseudo-observations approach.

In biomedical studies, survival data with a cure fraction (the proportion of subjects cured of disease) are commonly encountered. The mixture cure and bounded cumulative hazard models are two main types of cure fraction models when analyzing survival data with long-term survivors. In this article, in the framework of the Cox proportional hazards mixture cure model and bounded cumulative hazard model, we propose several estimators utilizing pseudo-observations to assess the effects of covariates on the cure rate and the risk of having the event of interest for survival data with a cure fraction. A variable selection procedure is also presented based on the pseudo-observations using penalized generalized estimating equations for proportional hazards mixture cure and bounded cumulative hazard models. Extensive simulation studies are conducted to examine the proposed methods. The proposed technique is demonstrated through applications to a melanoma study and a dental data set with high-dimensional covariates.

The analysis of COVID-19 in-hospital mortality: A competing risk approach or a cure model?

Competing risk analyses have been widely used for the analysis of in-hospital mortality in which hospital discharge is considered as a competing event. The competing risk model assumes that more than one cause of failure is possible, but there is only one outcome of interest and all others serve as competing events. However, hospital discharge and in-hospital death are two outcomes resulting from the same disease process and patients whose disease conditions were stabilized so that inpatient care was no longer needed were discharged. We therefore propose to use cure models, in which hospital discharge is treated as an observed "cure" of the disease. We consider both the mixture cure model and the promotion time cure model and extend the models to allow cure status to be known for those who were discharged from the hospital. An EM algorithm is developed for the mixture cure model. We also show that the competing risk model, which treats hospital discharge as a competing event, is equivalent to a promotion time cure model. Both cure models were examined in simulation studies and were applied to a recent cohort of COVID-19 in-hospital patients with diabetes. The promotion time model shows that statin use improved the overall survival; the mixture cure model shows that while statin use reduced the in-hospital mortality rate among the susceptible, it improved the cure probability only for older but not younger patients. Both cure models show that treatment was more beneficial among older patients.

Predicting Survival for Chimeric Antigen Receptor T-Cell Therapy: A Validation of Survival Models Using Follow-Up Data From ZUMA-1.

OBJECTIVES: Survival extrapolation for chimeric antigen receptor T-cell therapies is challenging, owing to their unique mechanistic properties that translate to complex hazard functions. Axicabtagene ciloleucel is indicated for the treatment of relapse or refractory diffuse large B-cell lymphoma after 2 or more lines of therapy based on the ZUMA-1 trial. Four data snapshots are available, with minimum follow-up of 12, 24, 36, and 48 months. This analysis explores how survival extrapolations for axicabtagene ciloleucel using ZUMA-1 data can be validated and compared. METHODS: Three different parametric modeling approaches were applied: standard parametric, spline-based, and cure-based models. Models were compared using a range of metrics, across the 4 data snapshot, including visual fit, plausibility of long-term estimates, statistical goodness of fit, inspection of hazard plots, point-estimate accuracy, and conditional survival estimates. RESULTS: Standard and spline-based parametric extrapolations were generally incapable of fitting the ZUMA-1 data well. Cure-based models provided the best fit based on the earliest data snapshot, with extrapolations remaining consistent as data matured. At 48 months, the maximum survival overestimate was 8.3% (Gompertz mixture-cure model) versus the maximum underestimate of 33.5% (Weibull standard parametric model). CONCLUSIONS: Where a plateau in the survival curve is clinically plausible, cure-based models may be helpful in making accurate predictions based on immature data. The ability to reliably extrapolate from maturing data may reduce delays in patient access to potentially lifesaving treatments. Additional research is required to understand how models compare in broader contexts, including different treatments and therapeutic areas.