Conditional Survival Probabilities Research Articles

A novel conditional survival nomogram for monitoring real-time prognosis of non-metastatic colorectal cancer

AimsThe aim of this study is to enhance the accuracy of monitoring and treatment information for patients diagnosed with colorectal cancer (CRC).MethodsUtilizing the Surveillance, Epidemiology, and End Results (SEER) database, a cohort of 335,948 eligible CRC patients was included in this investigation. Conditional survival probability and actuarial overall survival were employed as methodologies to investigate the association between clinicopathological characteristics and cancer prognosis.ResultsAmong CRC patients, the 5-year survival rate was 59%, while the 10-year survival rate was 42%. Over time, conditional survival showed a consistent increase, with rates reaching 45% and 48% for individuals surviving 1 and 2 years, respectively. Notably, patients with unfavorable tumor stages exhibited substantial improvements in conditional survival, thereby narrowing the disparity with actuarial overall survival over time.ConclusionThis study underscores the significance of time-dependent conditional survival probability, particularly for patients with a poorer prognosis. The findings suggest that long-term CRC survivors may experience improved cancer prognosis over time.

Conditional survival nomogram for patients with colon mucinous adenocarcinoma to predict prognosis: a dynamic survival analysis.

The aim was to assess conditional survival for colon mucinous adenocarcinoma (MAC) patients, and to construct nomograms to predict conditional survival probability. Survival analysis was done using conditional survival, which was defined as the probability of surviving additional y years for patients who have survived for x years. The mathematical definition was express as: CS (y|x) = S (x + y)/S (x). Cox regression analyses were used to identify prognostic factors. A nomogram is constructed to predict conditional disease-free survival (DFS) and overall survival (OS) probability according to years that already survive. A total of 179 colon MAC patients were included. The 5-year DFS was 67% after surgery, and the 5-year survival probability of patients, who already survived 1, 2, 3, and 4 years were 75%, 87%, 95%, and 98%, respectively. The 5-year OS was 73% after surgery and increased to 76%, 82%, 88%, and 92% at 1, 2, 3, and 4 years, respectively. Subgroup analyses demonstrated the superiority of conditional survival was more pronounced in advanced stages than in stage I. And pT stage, pN stage, and lymphovascular invasion were significantly associated with DFS and OS. Conditional survival nomograms were constructed to predict the 5-year conditional DFS and OS probability given survival for 1, 2, 3, 4 years after surgery. Conditional survival can provide dynamic survival probability according to years that already survive, especially for patients with advanced stages. Taking into account the years already survived accounted for, novel nomograms contributed to effectively predicting conditional survival.

Examining the impact of critical attributes on hard drive failure times: Multi‐state models for left‐truncated and right‐censored semi‐competing risks data

AbstractThe ability to predict failures in hard disk drives (HDDs) is a major objective of HDD manufacturers since avoiding unexpected failures may prevent data loss, improve service reliability, and reduce data center downtime. Most HDDs are equipped with a threshold‐based monitoring system named self‐monitoring, analysis and reporting technology (SMART). The system collects several performance metrics, called SMART attributes, and detects anomalies that may indicate incipient failures. SMART works as a nascent failure detection method and does not estimate the HDDs' remaining useful life. We define critical attributes and critical states for hard drives using SMART attributes and fit multi‐state models to the resulting semi‐competing risks data. The multi‐state models provide a coherent and novel way to model the failure time of a hard drive and allow us to examine the impact of critical attributes on the failure time of a hard drive. We derive dynamic predictions of conditional survival probabilities, which are adaptive to the state of the drive. Using a dataset of HDDs equipped with SMART, we find that drives are more likely to fail after entering critical states. We evaluate the predictive accuracy of the proposed models with a case study of HDDs equipped with SMART, using the time‐dependent area under the receiver operating characteristic curve (AUC) and the expected prediction error (PE). The results suggest that accounting for changes in the critical attributes improves the accuracy of dynamic predictions.

A commentary on 'Nomogram of conditional survival probability of long-term survival for metastatic colorectal cancer: a real-world data retrospective cohort study from SEER database'.

A commentary on 'Nomogram of conditional survival probability of long-term survival for metastatic colorectal cancer: a real-world data retrospective cohort study from SEER database'.

Conditional survival probability of distant-metastatic hepatocellular carcinoma: A population-based study

BACKGROUND The prognosis of many patients with distant metastatic hepatocellular carcinoma (HCC) improved after they survived for several months. Compared with traditional survival analysis, conditional survival (CS) which takes into account changes in survival risk could be used to describe dynamic survival probabilities. AIM To evaluate CS of distant metastatic HCC patients. METHODS Patients diagnosed with distant metastatic HCC between 2010 and 2015 were extracted from the Surveillance, Epidemiology and End Results database. Univariate and multivariate Cox regression analysis were used to identify risk factors for overall survival (OS), while competing risk model was used to identify risk factors for cancer-specific survival (CSS). Six-month CS was used to calculate the probability of survival for an additional 6 mo at a specific time after initial diagnosis, and standardized difference (d) was used to evaluate the survival differences between subgroups. Nomograms were constructed to predict CS. RESULTS Positive -fetoprotein expression, higher T stage (T3 and T4), N1 stage, non-primary site surgery, non-chemotherapy, non-radiotherapy, and lung metastasis were independent risk factors for actual OS and CSS through univariate and multivariate analysis. Actual survival rates decreased over time, while CS rates gradually increased. As for the 6-month CS, the survival difference caused by chemotherapy and radiotherapy gradually disappeared over time, and the survival difference caused by lung metastasis reversed. Moreover, the influence of age and gender on survival gradually appeared. Nomograms were fitted for patients who have lived for 2, 4 and 6 mo to predict 6-month conditional OS and CSS, respectively. The area under the curve (AUC) of nomograms for conditional OS decreased as time passed, and the AUC for conditional CSS gradually increased. CONCLUSION CS for distant metastatic HCC patients substantially increased over time. With dynamic risk factors, nomograms constructed at a specific time could predict more accurate survival rates.

Conditional Prostate Cancer-Specific Survival Probabilities in Recurrent Prostate Cancer Patients Receiving Radiation ± Antiandrogen Therapy: Secondary Analysis of a Randomized Clinical Trial

Salvage radiation therapy (SRT) and androgen-deprivation therapy (ADT) are routinely used in patients with elevated prostate-specific antigen (PSA) levels after radical prostatectomy (RP) for prostate cancer (PCa). Although prostate cancer-specific survival (PCSS) following SRT is useful when counseling patients at the time of treatment, the utility of this data from time of diagnosis diminishes over time. Conditional survival (CS) can provide more relevant estimates, especially given long-term PCa survivorship. The primary aim of this study was to analyze CS estimates for recurrent PCa patients undergoing SRT ± ADT. The secondary objective was to determine if factors prognostic of PCSS at diagnosis remain relevant in survivorship. We analyzed data from 760 post-RP patients enrolled in NRG/RTOG 9601 (1998-2003). Eligible patients included men who had undergone prior RP and had pT2/T3 disease without nodal involvement and detectable PSA levels of 0.2-4.0 ng/mL. Patients were randomly assigned to undergo SRT and receive either 24 mo of ADT or placebo. OS was calculated (Kaplan-Meier), cumulative incidence was used to estimate PCSS rates, and prognostic factors associated with PCSS were analyzed by multivariable Cox proportional hazards modeling (MVA). Patients were followed for a median of 13 y. The 5- and 10-y PCSS estimates from diagnosis were 98.52% and 92.7%, respectively. At 1- (n = 755), 3- (n = 727), 5- (n = 680), and 8-y (n = 602) survivorship, chances of PCSS at an additional 5-y were 97.41%, 95.29%, 93.76%, and 91.04%, respectively. On MVA at diagnosis, omission of ADT (HR 2.156, P = 0.0003), increasing age (HR 1.833, P = 0.03), Gleason score (GS) 7 (HR 2.356, P = 0.0057), and GS 8-10 (HR 4.841, P < 0.0001) were associated with PCa-specific mortality. For those who achieved survivorship at 1-, 3-, 5-, and 8-y, all variables remained prognostic of PCa-specific mortality on MVA. Conditional risk of death from PCa for patients treated with SRT increases over time. The initial risk of dying from PCa over a given period, however, is higher than if already having survived a portion of that period. ADT, younger age, and lower GS continue to confer a reduced risk of PCa-specific mortality for long-term survivors. This data can be used to inform survivorship care planning, giving patients more relevant prognostic information during continued surveillance after completion of treatment.

A new method of estimating prevalence of childhood cancer survivors (POCCS): example of the 20-year prevalence in The Netherlands.

Estimating the number of childhood cancer survivors is crucial for cancer control, including clinical guidelines. To compare estimates across countries despite data sharing restrictions, we propose a new method of computing limited-duration prevalence of childhood cancer survivors (POCCS) using aggregated data. We developed a Markov model that simulates, for each calendar year and birth cohort in a population, the proportion of individuals in the following health states: healthy, newly diagnosed with cancer, surviving with cancer, and deceased. Transitions between health states were informed using annual sex- and age-specific incidence rates, conditional 1-year net survival probabilities from the Netherlands Cancer Registry (1989-2011), and annual mortality probability by sex and age group for The Netherlands from the Human Mortality Database. Applying a Markov model, we computed 20-year prevalence of childhood cancer survivors. The resulting POCCS estimates, stratified by sex, were compared with SEER*Stat estimates derived from individual cancer records from the same registry. In 2011, POCCS predicted 654 males [95% confidence interval (95% CI): 637-672] and 539 females (95% CI: 523-555) per million persons living in The Netherlands after childhood cancer diagnosed within the previous 20 years. Using SEER*Stat, the 20-year prevalence was 665 males (95% CI: 647-683) and 544 females (95% CI: 529-560) per million persons on 1 July 2011. Using the POCCS model and aggregated cancer data, our estimates of childhood cancer survivors limited-duration prevalence were consistent with those computed by a standard method requiring individual cancer records. The POCCS method provides relevant information for planning follow-up and care for childhood cancer survivors.

Semiparametric model averaging method for survival probability predictions of patients

In biomedical and clinical research, predicting the survival probabilities for patients is a core task. Accurate survival probability predictions can help physicians make better treatments or prevention plans for patients. A novel semiparametric proportional hazards model averaging prediction technique is introduced to address this problem. Under the potential partly linear additive structures, the conditional survival probabilities of individuals can be predicted by the weighted averages of submodels which are estimated by maximizing the partial likelihood functions. The selection of weights is a crucial part of model averaging since the weights can affect the accuracy of survival probability prediction. A Brier score type criterion is employed to choose the optimal model averaging weights and the rate of convergence of the selected weights is studied. In addition, the finite sample performance of the proposed method is evaluated via abundant simulation studies. To further illustrate the effectiveness of the proposed approach, the model averaging is applied to heart failure data.

Log odds of negative lymph nodes/T stage ratio (LONT): A new prognostic tool for differentiated thyroid cancer without metastases in patients aged 55 and older.

The optimal approach to assess the postoperative status of lymph nodes in differentiated thyroid cancer (DTC) remains controversial. Our aim was to determine if the log odds of negative lymph nodes/T stage ratio (LONT) could serve as a new prognostic and predictive tool for DTC without metastases in patients aged ≥ 55 years. The Surveillance, Epidemiology, and End Results (SEER) database was used to study the role of LONT in patients aged ≥55 years diagnosed with DTC without metastases. The primary outcome was overall survival (OS). The Kaplan-Meier method and the Cox proportional hazard regression model were used to calculate the outcome. Moreover, the robustness of research findings was evaluated using sensitivity analyses. A total of 21,172 DTC patients aged ≥55 years without distant metastasis were enrolled. Multivariate Cox regression analyses and a "floating absolute risk" analysis showed that a LONT ≥0.920 (vs. -0.56 to 0.92) was a protective factor for OS in DTC patients. Sensitivity analyses revealed an E-value of 1.98 for the obtained LONT value. In subgroup analyses, LONT was correlated significantly with OS in different subgroups of negative lymph nodes, stage-I-II subgroups and the N0 subgroup. The conditional probability of survival of DTC improved with prolonged survival time in the LONT ≥0.920 group. A high LONT was associated with longer OS compared with low LONT in patients aged ≥55 years with non-metastatic DTC. LONT could provide valuable information for undertaking postoperative evaluations.

Ten-year conditional probability of survival for patients with ovarian cancer: A new metric tailored to Long-term survivors

ObjectivesWe assessed a conditional probability of survival (CPS) model to determine the probability of living 10 years after ovarian cancer diagnosis after having already survived 5 years. MethodsWe identified patients newly diagnosed with high-grade epithelial ovarian cancer from 1/1/2001–12/31/2009 and treated at our institution. Patients with <3 years follow-up were excluded. CPS was defined as the probability of surviving additional years (y) based on the condition a patient had already survived a given time (x): S(x + y)/S(x). Confidence intervals were estimated using a variation of Greenwood's formula. ResultsOf 916 patients meeting inclusion criteria, 473 (52%) were diagnosed from 2001 to 2005 and 443 (48%) from 2006 to 2009. Median age at diagnosis was 60 years (range, 25–95). The conventional 10-year OS rate for all patients was 29% (95% CI: 26%–32%)—75% (95% CI: 68%–82%) for stage I/II disease, 22% (95% CI: 19%–26%) for stage III, and 6.9% (95% CI: 3.9%–12%) for stage IV. For patients <65 years, the 10-year CPS for 5-year survivors was 65% (95% CI: 59%–70%); for those ≥65 years, it was 48% (95% CI: 38%–57%). For patients <65 years, the 10-year CPS for 5-year survivors by stage was: stage I/II, 89% (95% CI: 81%–94%); stage III, 58% (95% CI: 50%–66%); and stage IV, 26% (95% CI: 12%–42%). For patients ≥65 years, rates by stage were 78% (95% CI: 53%–91%), 42% (95% CI: 30%–53%), and 29% (95% CI: 7%–56%), respectively. ConclusionsFor long-term survivors with high-grade epithelial ovarian cancer, CPS provides better prediction of survival than conventional methods.

Conditional Survival Probabilities in Recurrent Prostate Cancer (PCa) Patients Receiving Radiation ± Antiandrogen Therapy: Secondary Analysis of a Randomized Clinical Trial

<h3>Purpose/Objective(s)</h3> Salvage radiation therapy (SRT) and androgen-deprivation therapy (ADT) are routinely used in patients with elevated prostate-specific antigen (PSA) levels after radical prostatectomy (RP). Although overall survival (OS) and biochemical-failure (BF) following SRT are useful when counseling patients at the time of treatment, the utility of survival data from time of diagnosis diminishes over time. Conditional survival (CS) can provide more relevant estimates, especially given long-term PCa survivorship. The primary aim of this study was to analyze CS estimates for recurrent PCa patients undergoing SRT ± ADT. The secondary objective was to determine if factors prognostic of OS and BF at diagnosis remain relevant in survivorship. <h3>Materials/Methods</h3> We analyzed data from 760 post-RP patients enrolled in NRG/RTOG 9601 (1998–2003). Eligible patients included men who had undergone prior RP and had pT2/T3 disease without nodal involvement and detectable PSA levels of 0.2–4.0 ng/mL. Patients were randomly assigned to undergo SRT and receive either 24 mo of ADT or placebo. OS was calculated (Kaplan–Meier), cumulative incidence was used to estimate BF rates, and prognostic factors associated with OS and BF were analyzed by multivariable Cox proportional hazards modeling (MVA). <h3>Results</h3> Patients were followed for a median of 13 y. The 5- and 10-y OS estimates from diagnosis were 93% and 80%, respectively. At 1- (<i>n</i> = 755), 3- (<i>n</i> = 727), 5- (<i>n</i> = 680), 8- (<i>n</i> = 602), and 10-y (<i>n</i> = 543) survivorship, chances of surviving an additional 5 y were 92%, 89%, 86%, 80%, and 72%, respectively. On MVA at diagnosis, omission of ADT (HR 1.308, <i>P</i> = 0.0403), increasing age (HR 2.761, <i>P</i> < 0.0001), and Gleason score (GS) 8−10 (HR 1.054, <i>P</i> =0.01), were associated with all-cause mortality. For those who achieved survivorship at 5 y, only age (HR 2.973, <i>P</i> < 0.0001) and GS 8–10 (HR 1.801, <i>P</i> = 0.0063) were prognostic of mortality on MVA. The 5- and 10-y rates of BF from diagnosis were 36% and 52%, respectively. For patients who survived 1 (<i>n</i> = 725), 3 (<i>n</i> = 560), 5 (<i>n</i> = 435), 8 (<i>n</i> = 320), and 10 (<i>n</i> = 268) y without BF, chances of BF at an additional 5 y were 39%, 33%, 26%, 20%, and 20%, respectively. On MVA at time of SRT, omission of ADT (HR 2.139, <i>P</i> < 0.0001), GS 7 (HR 1.376, <i>P</i> = 0.0062), GS 8–10 (HR 1.717, <i>P</i> = 0.0005), and higher pretreatment PSA (HR 1.442, <i>P</i> = 0.0215), were associated with BF. For those who survived 5 y after treatment without failure, only omission of ADT (HR 1.407, <i>P</i> < 0.0384) was prognostic of BF. <h3>Conclusion</h3> Conditional risk of BF for patients treated with SRT remains elevated at levels similar to those at initial treatment for up to 3 y after SRT, after which BF rates decrease. ADT continues to confer a reduced risk for BF for long-term survivors. This data can be used to inform survivorship care planning and highlights the need for continued PSA surveillance after completion of treatment.

Ten-year conditional probability of survival for patients with ovarian cancer: A new metric for the new millennium (480)

Objectives: To demonstrate the utility of conditional probability of survival (CPS) as a metric in analyzing survival outcomes for women with ovarian cancer. Methods: We analyzed the records of all patients (pts) with newly diagnosed high-grade epithelial ovarian cancer who underwent treatment at our institution from January 2001 to December 2009. Pts lost to follow-up were excluded if they had less than three years of follow-up. CPS was defined as the probability of surviving additional years (y) based on the condition that a patient had already survived at a given time (x): S(x + y)/S(x). Confidence intervals (CIs) were estimated using a variation of Greenwood’s formula. Results: A total of 916 pts met the inclusion criteria. The median age at diagnosis was 60 years (range: 25-95) with 37% (337/916) <65 years old (yo). FIGO stage was as follows: stage I 14% (132/916), stage II 6% (59/916), stage III 57% (519/916), and stage IV 23% (206/916). Histology was high-grade serous in 83% pts (759/916). Among the 907 pts who underwent surgical management, 64% (584/907) had a primary debulking surgery, 16% (143/907) had an interval debulking after neoadjuvant chemotherapy and 20% (180/907) underwent staging. A total of 84% (757/907) had an optimal cytoreduction (<1 cm of residual disease), whereas 49% (440/907) had a complete gross resection. The Median follow-up time for the entire cohort was 55 months, and the median overall survival (OS) was 57 months. Twenty percent (183/916) had an OS >10-years. Ten-year OS for pts aged <65 yo with early-stage I/II, stage III, and stage IV ovarian cancer was 48%, 24%, and 11%, respectively. For patients >65 yo, 10-year OS was 22%, 11%, and 4%, respectively. For patients <65 yo, the 10-year CPS for 5-year survivors was: early-stage I/II, 90.0 % (95% CI: 85.4%-94.6%); stage III, 56.8% (95%CI 51.0%-62.7%); stage IV, 38.8% (95% CI: 24.3%- 53.4%). For patients >65y, the 10-year CPS for 5-year survivors was: early-stage I/II, 63.1% (95% CI: 52.6%-73.5%); stage III, 43.8% (95% CI: 31.7%-55.9%); stage IV, 22.5% (95% CI: 6.6%-38.3%). Conclusions: For long-term 5-year survivors with advanced OC, CPS can provide a more representative estimate of future survival than conventional OS ratesl OS. Objectives: To demonstrate the utility of conditional probability of survival (CPS) as a metric in analyzing survival outcomes for women with ovarian cancer. Methods: We analyzed the records of all patients (pts) with newly diagnosed high-grade epithelial ovarian cancer who underwent treatment at our institution from January 2001 to December 2009. Pts lost to follow-up were excluded if they had less than three years of follow-up. CPS was defined as the probability of surviving additional years (y) based on the condition that a patient had already survived at a given time (x): S(x + y)/S(x). Confidence intervals (CIs) were estimated using a variation of Greenwood’s formula. Results: A total of 916 pts met the inclusion criteria. The median age at diagnosis was 60 years (range: 25-95) with 37% (337/916) <65 years old (yo). FIGO stage was as follows: stage I 14% (132/916), stage II 6% (59/916), stage III 57% (519/916), and stage IV 23% (206/916). Histology was high-grade serous in 83% pts (759/916). Among the 907 pts who underwent surgical management, 64% (584/907) had a primary debulking surgery, 16% (143/907) had an interval debulking after neoadjuvant chemotherapy and 20% (180/907) underwent staging. A total of 84% (757/907) had an optimal cytoreduction (<1 cm of residual disease), whereas 49% (440/907) had a complete gross resection. The Median follow-up time for the entire cohort was 55 months, and the median overall survival (OS) was 57 months. Twenty percent (183/916) had an OS >10-years. Ten-year OS for pts aged <65 yo with early-stage I/II, stage III, and stage IV ovarian cancer was 48%, 24%, and 11%, respectively. For patients >65 yo, 10-year OS was 22%, 11%, and 4%, respectively. For patients <65 yo, the 10-year CPS for 5-year survivors was: early-stage I/II, 90.0 % (95% CI: 85.4%-94.6%); stage III, 56.8% (95%CI 51.0%-62.7%); stage IV, 38.8% (95% CI: 24.3%- 53.4%). For patients >65y, the 10-year CPS for 5-year survivors was: early-stage I/II, 63.1% (95% CI: 52.6%-73.5%); stage III, 43.8% (95% CI: 31.7%-55.9%); stage IV, 22.5% (95% CI: 6.6%-38.3%). Conclusions: For long-term 5-year survivors with advanced OC, CPS can provide a more representative estimate of future survival than conventional OS ratesl OS.

Lipid-Based Factors: A Promising New Biomarker for Predicting Prognosis and Conditional Survival Probability in Hepatocellular Carcinoma.

PurposeAbnormalities in lipid metabolism play a vital role in the development of cancer. This retrospective study aimed to evaluate the survival prognosis of patients with hepatocellular carcinoma (HCC) in terms of (free fatty acid: high-density lipoproteins) ratio (FF-HL) and to compare it with conditional probability and annual death hazard.Patients and MethodsPatients (n=300) were enrolled. Time-dependent receiver operating characteristic (ROC) analysis was used to determine the predictive ability of survival. Survival probabilities were estimated using the Kaplan–Meier method and Log rank tests were performed for statistical significance.ResultsThe area under the ROC curve for FF-HL, which predicts overall survival (OS), was superior to other markers. Patients in the high FF-HL (>840.3) showed poorer OS and progress-free survival (PFS). In multivariable analysis, FF-HL was an independent marker in predicting OS. Younger people and those with intrahepatic metastasis in higher FF-HL groups, as well as older men without vascular invasion in higher AHLR groups showed shorter OS and PFS. 3-year conditional disease-free survival (CDFS3) was slightly higher than those with actuarial survival. The death risk for 3-year conditional OS (COS3) was stable in the group with low FF-HL and (albumin: high-density lipoproteins) ratio (AHLR) and more pronounced in high subgroups. However, risk stratification using the Barcelona Clinic Liver Cancer approach and Child-Pugh score might not accurately predict COS3.ConclusionFF-HL and AHLR are not only promising biomarkers in terms of predictive ability of OS and PFS but also provide time-dependent prognostic information for HCC patients.

Survival prediction models: an introduction to discrete-time modeling

BackgroundPrediction models for time-to-event outcomes are commonly used in biomedical research to obtain subject-specific probabilities that aid in making important clinical care decisions. There are several regression and machine learning methods for building these models that have been designed or modified to account for the censoring that occurs in time-to-event data. Discrete-time survival models, which have often been overlooked in the literature, provide an alternative approach for predictive modeling in the presence of censoring with limited loss in predictive accuracy. These models can take advantage of the range of nonparametric machine learning classification algorithms and their available software to predict survival outcomes.MethodsDiscrete-time survival models are applied to a person-period data set to predict the hazard of experiencing the failure event in pre-specified time intervals. This framework allows for any binary classification method to be applied to predict these conditional survival probabilities. Using time-dependent performance metrics that account for censoring, we compare the predictions from parametric and machine learning classification approaches applied within the discrete time-to-event framework to those from continuous-time survival prediction models. We outline the process for training and validating discrete-time prediction models, and demonstrate its application using the open-source R statistical programming environment.ResultsUsing publicly available data sets, we show that some discrete-time prediction models achieve better prediction performance than the continuous-time Cox proportional hazards model. Random survival forests, a machine learning algorithm adapted to survival data, also had improved performance compared to the Cox model, but was sometimes outperformed by the discrete-time approaches. In comparing the binary classification methods in the discrete time-to-event framework, the relative performance of the different methods varied depending on the data set.ConclusionsWe present a guide for developing survival prediction models using discrete-time methods and assessing their predictive performance with the aim of encouraging their use in medical research settings. These methods can be applied to data sets that have continuous time-to-event outcomes and multiple clinical predictors. They can also be extended to accommodate new binary classification algorithms as they become available. We provide R code for fitting discrete-time survival prediction models in a github repository.

Description of survival data extended to the case of competing risks: a teaching approach based on frequency tables

Survival analysis is a powerful statistical tool to study failure-time data. In introductory courses students learn how to describe right-censored survival time data using the product-limit estimator of the survival function on a given end-point relying on a product of conditional survival probabilities. In the case of a composite end-point, the next step is to account for the presence of competing risks. The complement to one of the survival function is decomposed into the sum of cause-specific incidences, which are obtained as sum of unconditional probabilities due to the single competing risk. However, this algebraic decomposition is not straightforward, given the difference between the structure of the involved estimators. In addition, one is tempted to use the Kaplan-Meier estimator, leading to an erroneous decomposition of the overall incidence. Here we discuss a simple reinterpretation of the Kaplan-Meier formula in terms of sum of non-conditional probabilities of developing the end-point in time, adjusted for the presence of censoring. This approach could be used for describing survival data through simple frequency tables which are directly generalized to the case of competing risks. In addition, it makes clear how the estimation of the single cause-specific incidence through the Kaplan-Meier estimator, simply considering the occurrence of competing events as censored data, leads to an overestimation of the cause-specific incidence. Two examples are provided to support the explanation: the first one, could help to clarify the procedure described by the formulas; the second one, simulates real data in order to present graphically the results.

Cost-effectiveness of CD19 chimeric antigen receptor T-cell (CAR-T) therapy versus autologous stem cell transplantation (ASCT) for high-risk diffuse large B-cell lymphoma (DLBCL) in first relapse.

7537 Background: The recently reported ZUMA-7 and TRANSFORM trials demonstrate superior event-free survival among patients with primary refractory or early relapsed DLBCL compared to salvage chemotherapy with ASCT. However, given a cost of &gt;$370,000, it is not known whether second-line CAR-T is cost-effective compared to ASCT. Thus, we developed a state-transition microsimulation model to simulate clinical outcomes and costs associated with therapy for DLBCL patients in first relapse, using ZUMA-7 and TRANSFORM data. Methods: The model begins at initiation of second-line therapy comparing salvage chemotherapy with ASCT or CAR-T therapy. We examined a three-year time horizon, including crossover to the alternative strategy therapy in the third line, as well as subsequent lines of therapy, using open-source Amua 0.3.0 software. Base case analysis was performed using 1000 first-order Monte Carlo simulations and probabilistic sensitivity analysis (PSA) was performed with 1000 simulations to test model uncertainty. Conditional probabilities of survival and disease progression were extracted from Kaplan-Meier curves from pivotal clinical trials using the WebPlotDigitizer tool. Costs were estimated from public sources in US Dollars ($) and effects were estimated in quality-adjusted life years (QALY) using published utility values. Results: Median overall survival was 15 months (95% confidence interval [CI] 13-19 months) with ASCT and 21 months (95% CI 17-29 months) with CAR-T. The PSA demonstrated costs and effectiveness per patient of $243,581 and 1.06 QALYs with ASCT and $470,150 and 1.22 QALYs with CAR-T with an incremental cost-effectiveness ratio (ICER) of $1,383,320/QALY. Incremental net monetary benefit of CAR-T versus ASCT, based on a willingness-to-pay (WTP) threshold of $200,000/QALY, was -$193,812. The break-even price for CAR-T and all subsequent therapies, based on a one-way sensitivity analysis, was $170,489. Conclusions: The model demonstrated improved survival and QALYs for the second-line CAR-T therapy, but was not cost-effective, as the ICER exceeded $1,000,000/QALY, which is higher than most accepted WTP thresholds. A limitation of these early data is that they only assess outcomes over three years. To estimate the full effect of these therapies, we will extrapolate the Kaplan-Meier curves for additional analyses. Clinical outcomes of second-line CAR-T are promising, but prices would need to be considerably lower to enable equitable access and affordability.[Table: see text]

Improvements in life expectancy among childhood cancer survivors: Uneven gains and remaining challenges.

10050 Background: Childhood cancer survivors are at risk for shortened lifespan. Projections of life expectancy (LE) by diagnosis can provide benchmarks for assessing improvements over time. Methods: We developed a simulation model to project risk for common, life-threatening chronic health conditions (CHCs; heart failure, myocardial infarction, valvular disease, stroke, secondary breast cancer, colorectal cancer, glial tumors, sarcomas) and excess mortality among 5-year survivors, based on patient characteristics (sex, age at diagnosis, diagnosis) and treatment exposures (chemotherapy, radiation dose). Risk was estimated using statistical models and Childhood Cancer Survivor Study data. Age-related CHC risks (SEER, NHLBI) and competing mortality (CDC Wonder) were based on national databases. We used model calibration to identify parameter sets that generated outcomes consistent with observed data. Model outcomes included conditional LE and 10-year survival probability at age 40. For comparisons to the general population, we simulated age-, sex-, and diagnosis year-matched individuals who faced only competing mortality rates. Results: Among a cohort representative of the CCSS (mean diagnosis age, 7.4 yrs), compared to the general population, the gap in LE among survivors diagnosed in the 1970s vs. 1990s decreased from 17 yrs (25%) to 11 yrs (17%). Changes in LE among survivors diagnosed in the 1990s vs. 1970s varied by diagnosis, with leukemia, lymphoma, and CNS tumor survivors estimated to live an additional 8 to 11 yrs (Table). In contrast, considerably smaller gains were estimated for sarcoma and renal tumor survivors (1–3 yrs) and a loss for neuroblastoma (-3 yrs). Among survivors who reached age 40, the probability of surviving an additional 10 years increased from 89% to 92% between 1970s vs. 1990s, with the greatest gains for lymphoma and CNS tumors. Conclusions: Although temporal changes in pediatric oncology are projected to result in LE gains among survivors, considerable variation is projected across diagnoses. These findings highlight the uneven success of improving treatments for all cancers. [Table: see text]

Cure fraction and five-year recurrence-free conditional survival probabilities after surgical resection for hepatocellular carcinoma presenting with minor gross vascular invasion

Cure fraction and five-year recurrence-free conditional survival probabilities after surgical resection for hepatocellular carcinoma presenting with minor gross vascular invasion

Reliability aspects in a dynamic time-to-failure degradation-based model

Although the ordinary time-to-failure degradation-based model has been extensively used in practice, it also has its limitations. In this paper, we consider a time-to-failure degradation-based model recently proposed by Albabtain et al., where a limiting conditional survival probability entertains further stochastic relationships between the failure time and the degree of degradation. In the particular case where the limited survival probability is available for the proportional failure rate model, the model is developed using two well-known degradation paths, namely the additive degradation path and the multiplicative degradation path, each of which has a component of random variation. Preservation of various stochastic orders and aging properties of the random variation component in the model in the described setting is developed. To illustrate the model in the modified design, some examples of interest in reliability are presented.

Secondarily estimated cure fraction and five-year recurrence-free conditional survival probabilities among patients undergoing surgical resection for hepatocellular carcinoma presenting with minor gross vascular invasion

BackgroundSurgical resection (SR) has been selectively applied in hepatocellular carcinoma (HCC) presenting with minor gross vascular invasion (mGVI) which is defined when tumor invasion is confined to second-order portal branches or segmental branches of hepatic vein. However, little data of long-term outcomes are available for supporting the role of SR as a potentially curable therapeutic option for HCC presenting with mGVI. This study is aimed to estimate a statistical cure fraction and the improvement of recurrence-free conditional survival (RFCS) over time among patients undergoing SR for HCC presenting with mGVI.MethodsThe literature search was conducted focusing on previous studies that investigated the long-term survival rates of patients after SR for HCC presenting with mGVI. The reference cohort was extracted from a study including patients undergoing SR for HCC without vascular invasion. A non-mixture cure model was adopted to estimate the statistical cure fraction. The 5-year RFCS probabilities were also calculated.ResultsThree retrospective studies were secondarily analyzed. The probability of being statistically cured after SR for HCC presenting with mGVI was 7.3% (95% confidence interval, 4.4%–11.2%) in the mGVI group, lower than that of the reference cohort (hazard ratio, 1.81; 95% confidence interval, 1.59–2.05). The estimated 5-year RFCS probabilities improved with each additional year of survival. Moreover, 1 year after SR, the 5-year RFCS probabilities of patients with HCC presenting with mGVI was essentially the same as that of the reference cohort.ConclusionsThis study shows that a cure can be expected in around seven percent of patients undergoing SR for HCC presenting with mGVI. Furthermore, recurrence-free survival expectancy improves dramatically over time among those patients who do not have recurrence. Overall, these findings suggest that SR should be considered as a potentially curable treatment for patients with HCC presenting with mGVI.