Efficiency of the Breslow estimator in semiparametric transformation models.

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we derive the relative efficiency of the Breslow estimator and consider the properties of the two estimators using simulations and real data on prostate cancer survival.

Increase in the Life Expectancy of Patients with Cancer in the United States.

BACKGROUND: Cancer is becoming more of a chronic disease due to improvements in treatment and early detection for multiple cancer sites. To gain insight on increased life expectancy due to these improvements, we quantified trends in the loss in expectation of life (LEL) due to a cancer diagnosis for six cancer sites from 1975 through 2018. METHODS: We focused on patients diagnosed with female breast cancer, chronic myeloid leukemia (CML), colon and rectum cancer, diffuse large B-cell lymphoma (DLBCL), lung cancer, or melanoma between 1975 and 2018 from nine Surveillance, Epidemiology, and End Results cancer registries. Life expectancies for patients with cancer ages 50+ were modeled using flexible parametric survival models. LEL was calculated as the difference between general population life expectancy and life expectancy for patients with cancer. RESULTS: Over 2 million patients were diagnosed with one of the six cancers between 1975 and 2018. Large increases in life expectancy were observed between 1990 and 2010 for female breast, DLBCL, and CML. Patients with colon and rectum cancer and melanoma had more gradual improvements in life expectancy. Lung cancer LEL only began decreasing after 2005. Increases in life expectancy corresponded with decreases in LEL for patients with cancer. CONCLUSIONS: The reported gains in life expectancy largely correspond to progress in the screening, management, and treatment of these six cancers since 1975. IMPACT: LEL provides an important public health perspective on how improvements in treatment and early detection and their impacts on survival translate into changes in cancer patients' life expectancy.

Long-term Cancer Survival Trends by Updated Summary Stage.

BACKGROUND: Stage is the most important prognostic factor for understanding cancer survival trends. Summary stage (SS) classifies cancer based on the extent of spread: In situ, Localized, Regional, or Distant. Continual updating of staging systems poses challenges to stage comparisons over time. We use a consistent summary stage classification and present survival trends for 25 cancer sites using the joinpoint survival (JPSurv) model. METHODS: We developed a modified summary stage variable, Long-Term Site-Specific Summary Stage, based on as consistent a definition as possible and applied it to a maximum number of diagnosis years, 1975-2019. We estimated trends by stage by applying JPSurv to relative survival data for 25 cancer sites in SEER-8, 1975-2018, followed through December 31, 2019. To help interpret survival trends, we report incidence and mortality trends using the joinpoint model. RESULTS: Five-year relative survival improved for nearly all sites and stages. Large improvements were observed for localized pancreatic cancer [4.25 percentage points annually, 2007-2012 (95% confidence interval, 3.40-5.10)], distant skin melanoma [2.15 percentage points annually, 2008-2018 (1.73-2.57)], and localized esophagus cancer [1.18 percentage points annually, 1975-2018 (1.11-1.26)]. CONCLUSIONS: This is the first analysis of survival trends by summary stage for multiple cancer sites. The largest survival increases were seen for cancers with a traditionally poor prognosis and no organized screening, which likely reflects clinical management advances. IMPACT: Our study will be particularly useful for understanding the population-level impact of new treatments and identifying emerging trends in health disparities research.

Estimating the Number of Men Living with Metastatic Prostate Cancer in the United States.

BACKGROUND: Metastatic prostate cancer (MPC) includes metastases detected at diagnosis (de novo) and those occurring after diagnosis with early-stage disease (recurrent). Cancer registries collect data only on de novo MPC, providing a partial picture of the burden of MPC. We use cancer registry data to estimate the number of men living with MPC in the United States including both de novo and recurrent cases. METHODS: We apply a back-calculation method to estimate MPC incidence and prevalence from U.S. prostate cancer mortality and de novo MPC relative survival for cases diagnosed between 2000 and 2017 in 18 Surveillance, Epidemiology, and End Results registries. We hold overall prostate cancer mortality and MPC survival constant for future prevalence projections. RESULTS: On January 1, 2018, we estimated 120,400 U.S. men living with MPC (45% de novo, 55% recurrent). The age-adjusted prevalence in 2018 for Black men was over double that of White men (137.1 vs. 62.2 per 100,000 men). By 2030, 192,500 men are expected to be living with MPC, with the increase being driven by population growth projections. CONCLUSIONS: The number of men living with MPC in the United States exceeds 100,000 and represents a small fraction of the >3 million men living with a prior diagnosis of prostate cancer. IMPACT: Relatively similar fractions of de novo and recurrent MPC among prevalent cases highlight opportunities for management of localized disease in reducing the MPC burden. Changes in diagnostic technologies could lead to greater growth in MPC cases in the United States than projected. See related commentary by Stopsack et al., p. 585.

Estimation of the Number of Individuals Living With Metastatic Cancer in the United States.

BACKGROUND: The purpose of this study was to estimate the number of individuals living with metastatic breast, prostate, lung, colorectal, or bladder cancer or metastatic melanoma in the United States using population-based data. METHODS: A back-calculation method was used to estimate the number of individuals living with metastatic cancer for each cancer type from US cancer mortality and survival statistics from the Surveillance, Epidemiology, and End Results registries. The percentages of those living with metastatic cancer who advanced to metastatic disease from early stage cancer vs who were diagnosed with metastatic cancer de novo were calculated. One- and 5-year relative survival rates for de novo metastatic cancer were compared by year of diagnosis to assess time trends in survival. RESULTS: It is estimated that, in 2018, 623 405 individuals were living with metastatic breast, prostate, lung, colorectal, or bladder cancer, or metastatic melanoma in the United States. This number is expected to increase to 693 452 in 2025. In 2018, the percentage of metastatic cancer survivors who were initially diagnosed with early stage cancer and advanced to metastatic cancer ranged from 30% for lung cancer to 72% for bladder cancer. CONCLUSIONS: This study demonstrates increasing numbers of individuals living with metastatic cancer of the 6 most common cancer types in the United States. This information is critical for informing the allocation of research efforts and healthcare infrastructure needed to address the needs of these individuals.

Pretreatment Levels of Soluble Tumor Necrosis Factor Receptor 1 and Hepatocyte Growth Factor Predict Toxicity and Overall Survival After 90Y Radioembolization: Potential Novel Application of Biomarkers for Personalized Management of Hepatotoxicity.

Liver function may be negatively affected by radiation for treatment of hepatic malignancy. Pretreatment blood cytokine levels are biomarkers for prediction of toxicity and survival after external-beam radiation therapy. We hypothesized that cytokines may also predict outcomes after radioembolization, enabling a biomarker-driven personalized approach to treatment. Methods: Pretherapy blood samples from patients enrolled on a prospective protocol evaluating 90Y radioembolization for management of intrahepatic malignancy were analyzed for 2 cytokines selected on the basis of prior studies in stereotactic body radiotherapy, soluble tumor necrosis factor receptor 1 (sTNFR1) and hepatocyte growth factor (HGF), via enzyme-linked immunosorbent assay, and key dosimetric parameters were derived from posttreatment 90Y PET/CT imaging. Toxicity was defined as a change in albumin-bilirubin score from baseline to follow-up (3-6 mo after treatment). Associations of cytokine levels, dose metrics, and baseline liver function with toxicity and overall survival were assessed. Results: Data from 43 patients treated with 90Y radioembolization for primary (48.8% [21/43]) or secondary (51.2% [22/43]) malignancy were assessed. Examined dose metrics and baseline liver function were not associated with liver toxicity; however, levels of sTNFR1 (P = 0.045) and HGF (P = 0.005) were associated with liver toxicity in univariate models. Cytokines were the only predictors of toxicity in multivariable models including dose metrics and prior liver-directed therapy. sTNFR1 (hazard ratio, 12.3; 95% CI, 3.5-42.5, P < 0.001) and HGF (hazard ratio, 7.5; 95% CI, 2.4-23.1, P < 0.001) predicted overall survival, and findings were similar when models were controlled for absorbed dose and presence of metastatic disease. Conclusion: Pretreatment cytokine levels predict liver toxicity and overall survival. These pathways can be targeted with available drugs, an advantage over previously studied dose metrics and liver function tests. Interventions directed at the TNFα-axis should be considered in future studies for prevention of liver toxicity, and HGF should be explored further to determine whether its elevation drives toxicity or indicates ongoing liver regeneration after prior injury.

A Novel Time-Activity Information-Sharing Approach Using Nonlinear Mixed Models for Patient-Specific Dosimetry with Reduced Imaging Time Points: Application in SPECT/CT After 177Lu-DOTATATE.

Multiple-time-point SPECT/CT imaging for dosimetry is burdensome for patients and lacks statistical efficiency. A novel method for joint kidney time-activity estimation based on a statistical mixed model, a prior cohort of patients with complete time-activity data, and only 1 or 2 imaging points for new patients was compared with previously proposed single-time-point methods in virtual and clinical patient data. Methods: Data were available for 10 patients with neuroendocrine tumors treated with 177Lu-DOTATATE and imaged up to 4 times between days 0 and 7 using SPECT/CT. Mixed models using 1 or 2 time points were evaluated retrospectively in the clinical cohort, using the multiple-time-point fit as the reference. Time-activity data for 250 virtual patients were generated using parameter values from the clinical cohort. Mixed models were fit using 1 (∼96 h) and 2 (4 h, ∼96 h) time points for each virtual patient combined with complete data for the other patients in each dataset. Time-integrated activities (TIAs) calculated from mixed model fits and other reduced-time-point methods were compared with known values. Results: All mixed models and single-time-point methods performed well overall, achieving mean bias < 7% in the virtual cohort. Mixed models exhibited lower bias, greater precision, and substantially fewer outliers than did single-time-point methods. For clinical patients, 1- and 2-time-point mixed models resulted in more accurate TIA estimates for 94% (17/18) and 72% (13/18) of kidneys, respectively. In virtual patients, mixed models resulted in more than a 2-fold reduction in the proportion of kidneys with |bias| > 10% (6% vs. 15%). Conclusion: Mixed models based on a historical cohort of patients with complete time-activity data and new patients with only 1 or 2 SPECT/CT scans demonstrate less bias on average and significantly fewer outliers when estimating kidney TIA, compared with popular reduced-time-point methods. Use of mixed models allows for reduction of the imaging burden while maintaining accuracy, which is crucial for clinical implementation of dosimetry-based treatment.

TNFR1 and the TNFα axis as a targetable mediator of liver injury from stereotactic body radiation therapy.

INTRODUCTION: Radiation therapy for the management of intrahepatic malignancies can adversely affect liver function. Liver damage has been associated with increased levels of inflammatory cytokines, including tumor necrosis factor alpha (TNFα). We hypothesized that an inflammatory state, characterized by increased soluble TNFα receptor (sTNFR1), mediates sensitivity of the liver to radiation. MATERIALS/METHODS: Plasma samples collected during 3 trials of liver radiation for liver malignancies were assayed for sTNFR1 level via enzyme-linked immunosorbent assay (ELISA). Univariate and multivariate logistic regression and longitudinal models were used to characterize associations between liver toxicity (defined as a ≥2-point increase in Child-Pugh [CP] score within 6 months of radiation treatment) and sTNFR1 levels, ALBI score, biocorrected mean liver dose (MLD), age, and baseline laboratory values. RESULTS: Samples from 78 patients given liver stereotactic body radiation therapy [SBRT] (92%) or hypofractionated radiation were examined. There was a significant association between liver toxicity and sTNFR1 levels, and higher values were associated with increased toxicity over a range of mean liver doses. When ALBI score and biocorrected dose were included in the model with sTNFR1, baseline ALBI score and change in ALBI (ΔALBI) were significantly associated with toxicity, but sTNFR1 was not. Baseline aminotransferase levels also predicted toxicity but not independently of ALBI score. CONCLUSIONS: Elevated plasma sTNFR1 levels are associated with liver injury after liver radiation, suggesting that elevated inflammatory cytokine activity is a predictor of radiation-induced liver dysfunction. Future studies should determine whether administration of agents that decrease inflammation prior to treatment is warranted.

Integrated Survival Estimates for Cancer Treatment Delay Among Adults With Cancer During the COVID-19 Pandemic.

Importance: Cancer treatment delay has been reported to variably impact cancer-specific survival and coronavirus disease 2019 (COVID-19)-specific mortality during the severe acute respiratory syndrome coronavirus 2 pandemic. During the pandemic, treatment delay is being recommended in a nonquantitative, nonobjective, and nonpersonalized manner, and this approach may be associated with suboptimal outcomes. Quantitative integration of cancer mortality estimates and data on the consequences of treatment delay is needed to aid treatment decisions and improve patient outcomes. Objective: To obtain quantitative integration of cancer-specific and COVID-19-specific mortality estimates that can be used to make optimal decisions for individual patients and optimize resource allocation. Design, Setting, and Participants: In this decision analytical model, age-specific and stage-specific estimates of overall survival pre-COVID-19 were adjusted by the probability of COVID-19 (individualized by county, treatment-specific variables, hospital exposure frequency, and COVID-19 infectivity estimates), COVID-19 mortality (individualized by age-specific, comorbidity-specific, and treatment-specific variables), and delay of cancer treatment (impact and duration). These model estimates were integrated into a web application (OncCOVID) to calculate estimates of the cumulative overall survival and restricted mean survival time of patients who received immediate vs delayed cancer treatment. Using currently available information about COVID-19, a susceptible-infected-recovered model that accounted for the increased risk among patients at health care treatment centers was developed. This model integrated the data on cancer mortality and the consequences of treatment delay to aid treatment decisions. Age-specific and cancer stage-specific estimates of overall survival pre-COVID-19 were extracted from the Surveillance, Epidemiology, and End Results database for 691 854 individuals with 25 cancer types who received cancer diagnoses in 2005 to 2006. Data from 5 436 896 individuals in the National Cancer Database were used to estimate the independent impact of treatment delay by cancer type and stage. In addition, data from 275 patients in a nested case-control study were used to estimate the COVID-19 mortality rate by age group and number of comorbidities. Data were analyzed from March 17 to May 21, 2020. Exposures: COVID-19 and cancer. Main Outcomes and Measures: Estimates of restricted mean survival time after the receipt of immediate vs delayed cancer treatment. Results: At the time of the study, the OncCOVID web application allowed for the selection of up to 47 individualized variables to assess net survival for an individual patient with cancer. Substantial heterogeneity was found regarding the association between delayed cancer treatment and net survival among patients with a given cancer type and stage, and these 2 variables were insufficient to discriminate the net impact of immediate vs delayed treatment. Individualized overall survival estimates were associated with patient age, number of comorbidities, treatment received, and specific local community estimates of COVID-19 risk. Conclusions and Relevance: This decision analytical modeling study found that the OncCOVID web-based application can quantitatively aid in the resource allocation of individualized treatment for patients with cancer during the COVID-19 global pandemic.

Patient-Reported Sexual Aid Utilization and Efficacy After Radiation Therapy for Localized Prostate Cancer.

PURPOSE: To report sexual health-related quality of life outcomes and utilization and efficacy of sexual aids in a contemporary cohort of patients treated for localized prostate cancer. PATIENTS AND METHODS: Between 2008 and 2013, 471 consecutive men with localized prostate cancer were treated on 2 institutional protocols (NCT01766492, NCT01618851) or on a prospective institutional registry with patient-reported health-related quality of life. All patients were treated with ultra-hypofractionated radiation therapy. Erectile function (EF) was defined as "firm enough for intercourse" with or without aids per Expanded Prostate Cancer Index Composite-26 (n = 222 at baseline); results apply to this cohort unless specifically noted. Sexual aid utilization and efficacy were patient reported. Multivariable analysis of EF was performed. RESULTS: Median follow-up was 60 months, median age was 67 years, and 70% had intermediate- or high-risk disease per National Comprehensive Cancer Network guidelines. At 24 and 60 months, questionnaire response rates were 86% and 67%, and EF was retained in 53% and 41%, respectively. Baseline sexual aid utilization was 37% (n = 82) and was associated with lower 24-month EF preservation on multivariable analysis (adjusted odds ratio 0.49, 95% confidence interval 0.26-0.92). By 60 months, 70% of men had tried aids. Of those who found aids helpful at baseline, 84% to 89% reported continued benefit at 24 to 60 months. Among aid-naïve patients, efficacy was 80% with first-time use within 12 months and 70% more than 12 months after radiation therapy (P = .02). Among men who developed erectile dysfunction but found sexual aids helpful, 25% were not current users at 60 months. CONCLUSIONS: One-third of men used sexual aids at baseline, which doubled by 5 years after radiation therapy. Self-reported efficacy was high and sustained. Despite significant declines in EF, a number of men reported helpfulness of aids but were not active users. Future study is required to understand drivers of aid utilization to optimize posttreatment sexual function.