Parametric cure models of relative and cause-specific survival for grouped survival times

Survival trends in chronic lymphocytic leukemia across treatment eras: US SEER database analysis (1985-2017)

In this population-based study, we used the SEER database (1985-2015) to examine survival outcomes in chronic lymphocytic leukemia (CLL) patients followed up to the era of advanced treatments including targeted therapies. Data were extracted for patients 15 years or older with a primary diagnosis of CLL. A period analysis was performed to estimate 5- and 10-year relative survival rates for patients diagnosed during different calendar periods from 1985 to 2015. A mixture cure model was used to examine long-term survivors' proportions among patients diagnosed in 1985-2015 and for two cohorts diagnosed in 2000-2003, followed up to 2012 and 2004-2007, and followed up to 2015. Cox proportional hazard modeling was used for the two cohorts to estimate hazard ratios (HRs) of death adjusted for gender and age. The 5-year and 10-year age-adjusted relative survival rate ranged between 73.7 and 89.4% and from 51.6% to "not reached," respectively, for calendar periods of 1985-1989 to 2010-2014. The long-term survivor proportions varied by age and gender from 0 to 59%. The HRs (95%CI) for the 2004-2007 cohort in comparison to the 2000-2003 cohort were 0.58 (0.43-0.78), 0.58 (0.48-0.70), 0.57 (0.49-0.0.67), 0.68 (0.54-0.85), and 0.83 (0.68-1.02) for the age categories of 45-54, 55-64, 65-74, 75-84, and ≥ 85 years, respectively. Overall, relative survival improved significantly for CLL patients diagnosed between 1985 and 2015. These improvements were markedly better following the introduction of targeted therapies.

Can We Use Survival Data from Cancer Registries to Learn about Disease Recurrence? The Case of Breast Cancer

Background: Population-representative risks of metastatic recurrence are not generally available because cancer registries do not collect data on recurrence. This article presents a novel method that estimates the risk of recurrence using cancer registry disease-specific survival.Methods: The method is based on an illness-death process coupled with a mixture cure model for net cancer survival. The risk of recurrence is inferred from the estimated survival among the noncured fraction and published data on survival after recurrence. We apply the method to disease-specific survival curves from female breast cancer cases without a prior cancer diagnosis and with complete stage and hormone receptor (HR) status in Surveillance, Epidemiology and End Results registries (1992-2013).Results: The risk of recurrence is higher for women diagnosed with breast cancer at older age, earlier period, more advanced stage, and HR-negative tumors. For women diagnosed at ages 60-74 in 2000-2013, the projected percent recurring within 5 years is 2.5%, 9.6%, and 34.5% for stages I, II, and III HR-positive, and 6.5%, 20.2%, and 48.5% for stages I, II, and III HR-negative tumors. Although HR-positive cases have lower risk of recurrence soon after diagnosis, their risk persists longer than for HR-negative cases. Results show a high degree of robustness to model assumptions.Conclusions: The results show that it is possible to extract information about the risk of recurrence using disease-specific survival, and the methods can in principle be extended to other cancer sites.Impact: This study provides the first population-based summaries of the risk of breast cancer recurrence in U.S. women. Cancer Epidemiol Biomarkers Prev; 27(11); 1332-41. ©2018 AACR.

A new approach to estimate time-to-cure from cancer registries data

BACKGROUND

Cure models have been adapted to net survival context to provide important indicators from population-based cancer data, such as the cure fraction and the time-to-cure. However existing methods for computing time-to-cure suffer from some limitations.

METHODS

Cure models in net survival framework were briefly overviewed and a new definition of time-to-cure was introduced as the time TTC at which P(t), the estimated covariate-specific probability of being cured at a given time t after diagnosis, reaches 0.95. We applied flexible parametric cure models to data of four cancer sites provided by the French network of cancer registries (FRANCIM). Then estimates of the time-to-cure by TTC and by two existing methods were derived and compared. Cure fractions and probabilities P(t) were also computed.

RESULTS

Depending on the age group, TTC ranged from to 8 to 10 years for colorectal and pancreatic cancer and was nearly 12 years for breast cancer. In thyroid cancer patients under 55 years at diagnosis, TTC was strikingly 0: the probability of being cured was >0.95 just after diagnosis. This is an interesting result regarding the health insurance premiums of these patients. The estimated values of time-to-cure from the three approaches were close for colorectal cancer only.

CONCLUSIONS

We propose a new approach, based on estimated covariate-specific probability of being cured, to estimate time-to-cure. Compared to two existing methods, the new approach seems to be more intuitive and natural and less sensitive to the survival time distribution.

Estimating Breast Cancer Survival by Molecular Subtype in the Absence of Screening and Adjuvant Treatment

BACKGROUND

As molecular subtyping of breast cancer influences clinical management, the evaluation of screening and adjuvant treatment interventions at the population level needs to account for molecular subtyping. Performing such analyses are challenging because molecular subtype-specific, long-term outcomes are not readily accessible; these markers were not historically recorded in tumor registries. We present a modeling approach to estimate historical survival outcomes by estrogen receptor (ER) and human epidermal growth factor receptor 2 (HER2) status.

METHOD

Our approach leverages a simulation model of breast cancer outcomes and integrates data from two sources: the Surveillance Epidemiology and End Results (SEER) databases and the Breast Cancer Surveillance Consortium (BCSC). We not only produce ER- and HER2-specific estimates of breast cancer survival in the absence of screening and adjuvant treatment but we also estimate mean tumor volume doubling time (TVDT) and mean mammographic detection threshold by ER/HER2-status.

RESULTS

In general, we found that tumors with ER-negative and HER2-positive status are associated with more aggressive growth, have lower TVDTs, are harder to detect by mammography, and have worse survival outcomes in the absence of screening and adjuvant treatment. Our estimates have been used as inputs into model-based analyses that evaluate the effects of screening and adjuvant treatment interventions on population outcomes by ER and HER2 status developed by the Cancer Intervention and Surveillance Modeling Network (CISNET) Breast Cancer Working Group. In addition, our estimates enable a re-assessment of historical trends in breast cancer incidence and mortality in terms of contemporary molecular tumor characteristics.

CONCLUSION

Our approach can be generalized beyond breast cancer and to more complex molecular profiles.

On the comparison of risk of death according to different stages of breast cancer via the long-term exponentiated Weibull hazard model

Long-term survivor models have been extensively used for modelling time-to-event data with a significant proportion of patients who do not experience poor outcome. In this paper, we propose a new long-term survivor hazard model, which accommodates comprehensive families of cure rate models as particular cases, including modified Weibull, exponentiated Weibull, Weibull, exponential and Rayleigh distribution, among others. The maximum likelihood estimation procedure is presented. A simulation study evaluates bias and mean square error of the considered estimation procedure as well as the coverage probabilities of the parameters asymptotic and bootstrap confidence intervals. A real Brazilian dataset on breast cancer illustrates the methodology. From the practical point of view, under our modelling, we provide a parameter that works as a metric to quantify and compare the risk between different stages of the disease. We emphasize that, we developed an online platform for oncologists to calculate the probability of survival of patients diagnosed with breast cancer according to the stage of the disease in real time.

Current estimates of the cure fraction: a feasibility study of statistical cure for breast and colorectal cancer

BACKGROUND

The probability of cure is a long-term prognostic measure of cancer survival. Estimates of the cure fraction, the proportion of patients "cured" of the disease, are based on extrapolating survival models beyond the range of data. The objective of this work is to evaluate the sensitivity of cure fraction estimates to model choice and study design.

METHODS

Data were obtained from the Surveillance, Epidemiology, and End Results (SEER)-9 registries to construct a cohort of breast and colorectal cancer patients diagnosed from 1975 to 1985. In a sensitivity analysis, cure fraction estimates are compared from different study designs with short- and long-term follow-up. Methods tested include: cause-specific and relative survival, parametric mixture, and flexible models. In a separate analysis, estimates are projected for 2008 diagnoses using study designs including the full cohort (1975-2008 diagnoses) and restricted to recent diagnoses (1998-2008) with follow-up to 2009.

RESULTS

We show that flexible models often provide higher estimates of the cure fraction compared to parametric mixture models. Log normal models generate lower estimates than Weibull parametric models. In general, 12 years is enough follow-up time to estimate the cure fraction for regional and distant stage colorectal cancer but not for breast cancer. 2008 colorectal cure projections show a 15% increase in the cure fraction since 1985.

DISCUSSION

Estimates of the cure fraction are model and study design dependent. It is best to compare results from multiple models and examine model fit to determine the reliability of the estimate. Early-stage cancers are sensitive to survival type and follow-up time because of their longer survival. More flexible models are susceptible to slight fluctuations in the shape of the survival curve which can influence the stability of the estimate; however, stability may be improved by lengthening follow-up and restricting the cohort to reduce heterogeneity in the data.

Increasing Incidence of Oral Tongue Squamous Cell Carcinoma in Young White Women, Age 18 to 44 Years

Purpose

To evaluate the incidence of oral cavity squamous cell carcinoma (OCSCC) and oral tongue squamous cell carcinoma (OTSCC) in young white women, age 18 to 44 years.

Patients and Methods

We analyzed incidence and survival data from the Surveillance, Epidemiology and End Results (SEER) Program of the National Cancer Institute from 1975 to 2007 for OCSCC and OTSCC. Three cohorts were examined: all ages, age 18 to 44 years (ie, “young”), and age > 44 years. Individuals were stratified by sex and/or race. Percentage change (PC) and annual percentage change (APC) were calculated. Joinpoint regression analyses were performed to examine trend differences.

Results

Overall, incidence of OCSCC was decreasing for all ages. However, incidence was increasing for young white women (PC, 34.8; APC, 2.2; P < .05). Incidence of OTSCC was decreasing for all ages except in the age 18 to 44 years group (PC, 28.8; APC, 1.8; P < .05). Young white individuals had increasing incidence trends of OTSCC (white women: PC, 111.3; APC, 4; P < .05; young white men: PC, 43.7; APC, 1.6; P < .05). The APC of OTSCC was significantly greater in young white women compared with that in young white men (P = .007). Furthermore, incidence of SCC in all other subsites of the oral cavity was decreasing. Nonwhites had a decreasing incidence of OCSCC and OTSCC. Cause-specific survival was similar among whites age 18 to 44 and individuals older than age 44 years.

Conclusion

OTSCC is increasing among young white individuals age 18 to 44 years, particularly among white women. Young white women may be a new, emerging head and neck cancer patient population.

A SAS macro for parametric and semiparametric mixture cure models

Cure models have been developed to analyze failure time data with a cured fraction. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. Mixture cure models assume that the studied population is a mixture of susceptible individuals, who may experience the event of interest, and non-susceptible individuals that will never experience it. The aim of this paper is to propose a SAS macro to estimate parametric and semiparametric mixture cure models with covariates. The cure fraction can be modelled by various binary regression models. Parametric and semiparametric models can be used to model the survival of uncured individuals. The maximization of the likelihood function is performed using SAS PROC NLMIXED for parametric models and through an EM algorithm for the Cox's proportional hazards mixture cure model. Indications and limitations of the proposed macro are discussed and an example in the field of cancer clinical trials is shown.

Estimating and modeling the cure fraction in population-based cancer survival analysis

In population-based cancer studies, cure is said to occur when the mortality (hazard) rate in the diseased group of individuals returns to the same level as that expected in the general population. The cure fraction (the proportion of patients cured of disease) is of interest to patients and is a useful measure to monitor trends in survival of curable disease. There are 2 main types of cure fraction model, the mixture cure fraction model and the non-mixture cure fraction model, with most previous work concentrating on the mixture cure fraction model. In this paper, we extend the parametric non-mixture cure fraction model to incorporate background mortality, thus providing estimates of the cure fraction in population-based cancer studies. We compare the estimates of relative survival and the cure fraction between the 2 types of model and also investigate the importance of modeling the ancillary parameters in the selected parametric distribution for both types of model.

CANSURV: A Windows program for population-based cancer survival analysis

Patient survival is one of the most important measures of cancer patient care (the diagnosis and treatment of cancer). The optimal method for monitoring the progress of patient care across the full spectrum of provider settings is through the population-based study of cancer patient survival, which is only possible using data collected by population-based cancer registries. The probability of cure, "statistical cure", is defined for a cohort of cancer patients as the percent of patients whose annual death rate equals the death rate of general cancer-free population. Mixture cure models have been widely used to model failure time data. The models provide simultaneous estimates of the proportion of the patients cured from cancer and the distribution of the failure times for the uncured patients (latency distribution). CANSURV (CAN-cer SURVival) is a Windows software fitting both the standard survival models and the cure models to population-based cancer survival data. CANSURV can analyze both cause-specific survival data and, especially, relative survival data, which is the standard measure of net survival in population-based cancer studies. It can also fit parametric (cure) survival models to the individual data. The program is available at . The colorectal cancer survival data from the Surveillance, Epidemiology and End Results (SEER) program [Surveillance, Epidemiology and End Results Program, The Portable Survival System/Mainframe Survival System, National Cancer Institute, Bethesda, 1999.] of the National Cancer Institute, NIH is used to demonstrate the use of CANSURV program.

Cure fraction estimation from the mixture cure models for grouped survival data

Mixture cure models are usually used to model failure time data with long-term survivors. These models have been applied to grouped survival data. The models provide simultaneous estimates of the proportion of the patients cured from disease and the distribution of the survival times for uncured patients (latency distribution). However, a crucial issue with mixture cure models is the identifiability of the cure fraction and parameters of kernel distribution. Cure fraction estimates can be quite sensitive to the choice of latency distributions and length of follow-up time. In this paper, sensitivity of parameter estimates under semi-parametric model and several most commonly used parametric models, namely lognormal, loglogistic, Weibull and generalized Gamma distributions, is explored. The cure fraction estimates from the model with generalized Gamma distribution is found to be quite robust. A simulation study was carried out to examine the effect of follow-up time and latency distribution specification on cure fraction estimation. The cure models with generalized Gamma latency distribution are applied to the population-based survival data for several cancer sites from the Surveillance, Epidemiology and End Results (SEER) Program. Several cautions on the general use of cure model are advised.

Refined measurement of outcome for adjuvant breast carcinoma therapy

BACKGROUND

Traditional nonparametric statistical methods do not provide a quantitative measure of the lifetime benefit from adjuvant therapy. This deficiency makes it difficult to determine the long-term difference in impact between the two treatment arms of a clinical trial.

METHODS

To assess the impact of breast carcinoma recurrence, parametric survival models were derived from two randomized, controlled clinical trials of adjuvant therapy for Stage II breast carcinoma. To assess time to death from causes other than breast carcinoma, actuarial models derived from 1980 Census data were used. These two models were then combined to estimate the mean time to event (MTE) as a function of patient age, with the event being either recurrence or death from other causes. The MTE was then used to measure the differential benefit between two arms of a clinical trial.

RESULTS

In the first trial, differences in MTE between treatment groups varied from 2.7 years for 35-year-old patients to 1.4 years for 75-year-old patients. For this trial, the mechanism of survival benefit was an increase in time to recurrence. In the second trial, differences in MTE varied from 7.6 to 1.6 years over the same age ranges. For this trial, the mechanism of survival benefit was an increase in the likelihood of cure, i.e., an increase in the asymptote of the curve that represents proportion of patients without relapse.

CONCLUSIONS

When applied to data from controlled clinical trials, MTE offers a quantitative measure of long-term outcome from adjuvant therapy. The greatest benefit is achieved when therapy that increases the likelihood of cure is provided to young patients.

The long-term clinical course of patients with cutaneous melanoma

BACKGROUND

The clinical course of cutaneous melanoma is associated with pathologic and clinical factors, such as thickness, ulceration, and location of tumor and gender of the patient. The authors used a parametric survival model that incorporated a cured fraction of patients to translate these factors into specific estimates of long-term outcome.

METHODS

A cohort study was conducted of 5837 patients who were treated for localized cutaneous melanoma between 1978 and 1990 at the Duke Comprehensive Cancer Center. Of these, 495 patients were excluded because the survival status or one or more of the prognostic factors was unknown. Maximum follow-up was 22 years. The primary outcome measures examined were cured fraction (probability of cure), median tumor specific survival (i.e., median time to death from tumor), and the probability of tumor-related survival at fixed intervals after treatment.

RESULTS

For an example of a class of patients with a relatively good prognosis, consider women with nonulcerated lesions measuring 0.5 mm thick on an extremity. The probability of cure (+/- standard error) for these patients was estimated at 80.8% +/- 2.0%, and the median tumor specific survival was 10.0 years +/- 0.8 years. This suggests that, in these patients, half of the deaths from melanoma will occur more than 10 years after treatment, barring death from other causes. Conversely, men with ulcerated lesions measuring 8.00 mm thick on the trunk have a relatively poor prognosis. The probability of cure for these patients was 16.8% +/- 2.4%, and the median tumor specific survival was 2.7 years +/- 0.2 years. Despite this poor initial prognosis, the conditional probability of cure increased to 90%; after 15 years of recurrence free survival.

CONCLUSIONS

Parametric statistical analysis provides quantitative measures of long-term survival. These measures show that late recurrence-longer than a decade after treatment-is to be expected in a significant portion of patients, although the probability of cure increases with progressively longer recurrence free survival.