The successful identification of breast cancer (BRCA) prognostic biomarkers is essential for the strategic interference of BRCA patients. Recently, various methods have been proposed for exploring a small prognostic gene set that can distinguish the high-risk group from the low-risk group.

The frequently used Cox regression applies two critical assumptions, which might not hold for all predictors. In this study, the results from a Cox regression model (CM) and a generalized Cox regression model (GCM) are compared.

Cox's proportional hazards model (PH) is an acceptable model for survival data analysis. This work investigates PH models' performance under different efficient sampling schemes for analyzing time to event data (survival data). We will compare a modified Extreme, and Double Extreme Ranked Set Sampling (ERSS, and DERSS) schemes with a simple random sampling scheme. Observations are assumed to be selected based on an easy-to-evaluate baseline available variable associated with the survival time. Through intensive simulations, we show that these modified approaches (ERSS and DERSS) provide more powerful testing procedures and more efficient estimates of hazard ratio than those based on simple random sampling (SRS). We also showed theoretically that Fisher's information for DERSS is higher than that of ERSS, and ERSS is higher than SRS. We used the SEER Incidence Data for illustration. Our proposed methods are cost saving sampling schemes.

Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty.

Prevalence of end-stage renal disease (ESRD) in the US increased by 74% from 2000 to 2013. To investigate the role of the broader environment on ESRD survival time, we evaluated average distance to the nearest hospital by county (as a surrogate for access to healthcare) and the Environmental Quality Index (EQI), an aggregate measure of ambient environmental quality composed of five domains (air, water, land, built, and sociodemographic), at the county level across the US. Associations between average hospital distance, EQI, and survival time for 1,092,281 people diagnosed with ESRD between 2000 and 2013 (age 18+, without changes in county residence) from the US Renal Data System were evaluated using proportional-hazards models adjusting for gender, race, age at first ESRD service date, BMI, alcohol and tobacco use, and rurality. The models compared the average distance to the nearest hospital (<10, 10-20, >20 miles) and overall EQI percentiles [0-5), [5-20), [20-40), [40-60), [60-80), [80-95), and [95-100], where lower percentiles are interpreted as better EQI. In the full, non-stratified model with both distance and EQI, there was increased survival for patients over 20 miles from a hospital compared to those under 10 miles from a hospital (hazard ratio = 1.14, 95% confidence interval = 1.12-1.15) and no consistent direction of association across EQI strata. In the full model stratified by average hospital distance, under 10 miles from a hospital had increased survival in the worst EQI strata (median survival 3.0 vs. 3.5 years for best vs. worst EQI, respectively), however for people over 20 miles from a hospital, median survival was higher in the best (4.2 years) vs worst (3.4 years) EQI. This association held across different rural/urban categories and age groups. These results demonstrate the importance of considering multiple factors when studying ESRD survival and future efforts should consider additional components of the broader environment.

This study explored the prognostic factors and developed a prediction model for Chinese-American (CA) cervical cancer (CC) patients. We compared two alternative models (the restricted mean survival time (RMST) model and the proportional baselines landmark supermodel (PBLS model, producing dynamic prediction)) versus the Cox proportional hazards model in the context of time-varying effects.

From March through August 2015, nearly 60 teams from around the world participated in the Prostate Cancer Dream Challenge (PCDC). Participating teams were faced with the task of developing prediction models for patient survival and treatment discontinuation using baseline clinical variables collected on metastatic castrate-resistant prostate cancer (mCRPC) patients in the comparator arm of four phase III clinical trials. In total, over 2,000 mCRPC patients treated with first-line docetaxel comprised the training and testing data sets used in this challenge. In this paper we describe: (a) the sub-challenges comprising the PCDC, (b) the statistical metrics used to benchmark prediction performance, (c) our analytical approach, and finally (d) our team's overall performance in this challenge. Specifically, we discuss our curated, ad-hoc, feature selection (CAFS) strategy for identifying clinically important risk-predictors, the ensemble-based Cox proportional hazards regression framework used in our final submission, and the adaptation of our modeling framework based on the results from the intermittent leaderboard rounds. Strong predictors of patient survival were successfully identified utilizing our model building approach. Several of the identified predictors were new features created by our team via strategically merging collections of weak predictors. In each of the three intermittent leaderboard rounds, our prediction models scored among the top four models across all participating teams and our final submission ranked 9 th place overall with an integrated area under the curve (iAUC) of 0.7711 computed in an independent test set. While the prediction performance of teams placing between 2 nd- 10 th (iAUC: 0.7710-0.7789) was better than the current gold-standard prediction model for prostate cancer survival, the top-performing team, FIMM-UTU significantly outperformed all other contestants with an iAUC of 0.7915.  In summary, our ensemble-based Cox regression framework with CAFS resulted in strong overall performance for predicting prostate cancer survival and represents a promising approach for future prediction problems.

Cox proportional hazards regression models are used to evaluate associations between exposures of interest and time-to-event outcomes in observational data. When exposures are measured on only a sample of participants, as they are in a case-cohort design, the sampling weights must be incorporated into the regression model to obtain unbiased estimating equations.

There have been few investigations of cancer prognosis models based on Bayesian hierarchical models. In this study, we used a novel Bayesian method to screen mRNAs and estimate the effects of mRNAs on the prognosis of patients with lung adenocarcinoma. Based on the identified mRNAs, we can build a prognostic model combining mRNAs and clinical features, allowing us to explore new molecules with the potential to predict the prognosis of lung adenocarcinoma. The mRNA data (n = 594) and clinical data (n = 470) for lung adenocarcinoma were obtained from the TCGA database. Gene set enrichment analysis (GSEA), univariate Cox proportional hazards regression, and the Bayesian hierarchical Cox proportional hazards model were used to explore the mRNAs related to the prognosis of lung adenocarcinoma. Multivariate Cox proportional hazard regression was used to identify independent markers. The prediction performance of the prognostic model was evaluated not only by the internal cross-validation but also by the external validation based on the GEO dataset (n = 437). With the Bayesian hierarchical Cox proportional hazards model, a 14-gene signature that included CPS1, CTPS2, DARS2, IGFBP3, MCM5, MCM7, NME4, NT5E, PLK1, POLR3G, PTTG1, SERPINB5, TXNRD1, and TYMS was established to predict overall survival in lung adenocarcinoma. Multivariate analysis demonstrated that the 14-gene signature (HR 3.960, 95% CI 2.710-5.786), T classification (T1, reference; T3, HR 1.925, 95% CI 1.104-3.355) and N classification (N0, reference; N1, HR 2.212, 95% CI 1.520-3.220; N2, HR 2.260, 95% CI 1.499-3.409) were independent predictors. The C-index of the model was 0.733 and 0.735, respectively, after performing cross-validation and external validation, a nomogram was provided for better prediction in clinical application. Bayesian hierarchical Cox proportional hazards models can be used to integrate high-dimensional omics information into a prediction model for lung adenocarcinoma to improve the prognostic prediction and discover potential targets. This approach may be a powerful predictive tool for clinicians treating malignant tumours.

Synthesis of clinical effectiveness from multiple trials is a well-established component of decision-making. Time-to-event outcomes are often synthesised using the Cox proportional hazards model assuming a constant hazard ratio over time. However, with an increasing proportion of trials reporting treatment effects where hazard ratios vary over time and with differing lengths of follow-up across trials, alternative synthesis methods are needed.

Identifying factors that affect mortality requires a robust statistical approach. This study's objective is to assess an optimal set of variables that are independently associated with the mortality risk of 433 older comorbid adults that have been discharged from the geriatric ward. We used both the stepwise backward variable selection and the iterative Bayesian model averaging (BMA) approaches to the Cox proportional hazards models. Potential predictors of the mortality rate were based on a broad range of clinical data; functional and laboratory tests, including geriatric nutritional risk index (GNRI); lymphocyte count; vitamin D, and the age-weighted Charlson comorbidity index. The results of the multivariable analysis identified seven explanatory variables that are independently associated with the length of survival. The mortality rate was higher in males than in females; it increased with the comorbidity level and C-reactive proteins plasma level but was negatively affected by a person's mobility, GNRI and lymphocyte count, as well as the vitamin D plasma level.

Microarray technology results in high-dimensional and low-sample size data sets. Therefore, fitting sparse models is substantial because only a small number of influential genes can reliably be identified. A number of variable selection approaches have been proposed for high-dimensional time-to-event data based on Cox proportional hazards where censoring is present. The present study applied three sparse variable selection techniques of Lasso, smoothly clipped absolute deviation and the smooth integration of counting, and absolute deviation for gene expression survival time data using the additive risk model which is adopted when the absolute effects of multiple predictors on the hazard function are of interest. The performances of used techniques were evaluated by time dependent ROC curve and bootstrap .632+ prediction error curves. The selected genes by all methods were highly significant (P < 0.001). The Lasso showed maximum median of area under ROC curve over time (0.95) and smoothly clipped absolute deviation showed the lowest prediction error (0.105). It was observed that the selected genes by all methods improved the prediction of purely clinical model indicating the valuable information containing in the microarray features. So it was concluded that used approaches can satisfactorily predict survival based on selected gene expression measurements.

An important application of high dimensional gene expression measurements is the risk prediction and the interpretation of the variables in the resulting survival models. A major problem in this context is the typically large number of genes compared to the number of observations (individuals). Feature selection procedures can generate predictive models with high prediction accuracy and at the same time low model complexity. However, interpretability of the resulting models is still limited due to little knowledge on many of the remaining selected genes. Thus, we summarize genes as gene groups defined by the hierarchically structured Gene Ontology (GO) and include these gene groups as covariates in the hazard regression models. Since expression profiles within GO groups are often heterogeneous, we present a new method to obtain subgroups with coherent patterns. We apply preclustering to genes within GO groups according to the correlation of their gene expression measurements.

Rectal gastrointestinal stromal tumors (RGISTs) are biologically characterized tumors that are relatively rare. Thus, few studies have reported a specific prognostic system for this subset of tumors but integrated it into parallel systems, such as small intestine. Our aim is to develop a new predictive staging system nomogram (named FD-ZS system) for RGISTs.

The aim of logistic regression is to estimate genetic effects on disease risk, while survival analysis aims to determine effects on age of onset. In practice, genetic variants may affect both types of outcomes. A cure survival model analyzes logistic and survival effects simultaneously. The aim of this simulation study is to assess the performance of logistic regression and traditional survival analysis under a cure model and to investigate the benefits of cure survival analysis. We simulated data under a cure model and varied the percentage of subjects at risk for disease (cure fraction), the logistic and survival effect sizes, and the contribution of genetic background risk factors. We then computed the error rates and estimation bias of logistic, Cox proportional hazards (PH), and cure PH analysis, respectively. The power of logistic and Cox PH analysis is sensitive to the cure fraction and background heritability. Our results show that traditional Cox PH analysis may erroneously detect age of onset effects if no such effects are present in the data. In the presence of genetic background risk even the cure model results in biased estimates of both the odds ratio and the hazard ratio. Cure survival analysis takes cure fractions into account and can be used to simultaneously estimate the effect of genetic variants on disease risk and age of onset. Since genome-wide cure survival analysis is not computationally feasible, we recommend this analysis for genetic variants that are significant in a traditional survival analysis.

The goal of this study was to evaluate the efficacy of machine learning (ML) techniques in predicting survival for chordoma patients in comparison with the standard Cox proportional hazards (CoxPH) model.

Accurate prognostic prediction is crucial for treatment decision-making in lung papillary adenocarcinoma (LPADC). The aim of this study was to predict cancer-specific survival in LPADC using ensemble machine learning and classical Cox regression models. Moreover, models were evaluated to provide recommendations based on quantitative data for personalized treatment of LPADC. Data of patients diagnosed with LPADC (2004-2018) were extracted from the Surveillance, Epidemiology, and End Results database. The set of samples was randomly divided into the training and validation sets at a ratio of 7:3. Three ensemble models were selected, namely gradient boosting survival (GBS), random survival forest (RSF), and extra survival trees (EST). In addition, Cox proportional hazards (CoxPH) regression was used to construct the prognostic models. The Harrell's concordance index (C-index), integrated Brier score (IBS), and area under the time-dependent receiver operating characteristic curve (time-dependent AUC) were used to evaluate the performance of the predictive models. A user-friendly web access panel was provided to easily evaluate the model for the prediction of survival and treatment recommendations. A total of 3615 patients were randomly divided into the training and validation cohorts (n = 2530 and 1085, respectively). The extra survival trees, RSF, GBS, and CoxPH models showed good discriminative ability and calibration in both the training and validation cohorts (mean of time-dependent AUC: > 0.84 and > 0.82; C-index: > 0.79 and > 0.77; IBS: < 0.16 and < 0.17, respectively). The RSF and GBS models were more consistent than the CoxPH model in predicting long-term survival. We implemented the developed models as web applications for deployment into clinical practice (accessible through https://shinyshine-820-lpaprediction-model-z3ubbu.streamlit.app/ ). All four prognostic models showed good discriminative ability and calibration. The RSF and GBS models exhibited the highest effectiveness among all models in predicting the long-term cancer-specific survival of patients with LPADC. This approach may facilitate the development of personalized treatment plans and prediction of prognosis for LPADC.

Chemoimmunotherapy with fludarabine, cyclophosphamide and rituximab (FCR) can induce long-term remissions in patients with chronic lymphocytic leukemia. Treatment efficacy with Bruton's tyrosine kinase inhibitors was found similar to FCR in untreated chronic lymphocytic leukemia patients with a mutated immunoglobulin heavy chain variable (IGHV) gene. In order to identify patients who specifically benefit from FCR, we developed integrative models including established prognostic parameters and gene expression profiling (GEP). GEP was conducted on n=337 CLL8 trial samples, "core" probe sets were summarized on gene levels and RMA normalized. Prognostic models were built using penalized Cox proportional hazards models with the smoothly clipped absolute deviation penalty. We identified a prognostic signature of less than a dozen genes, which substituted for established prognostic factors, including TP53 and IGHV gene mutation status. Independent prognostic impact was confirmed for treatment, β2-microglobulin and del(17p) regarding overall survival and for treatment, del(11q), del(17p) and SF3B1 mutation for progression-free survival. The combination of independent prognostic and GEP variables performed equal to models including only established non-GEP variables. GEP variables showed higher prognostic accuracy for patients with long progression-free survival compared to categorical variables like the IGHV gene mutation status and reliably predicted overall survival in CLL8 and an independent cohort. GEP-based prognostic models can help to identify patients who specifically benefit from FCR treatment. The CLL8 trial is registered under EUDRACT-2004- 004938-14 and clinicaltrials gov. Identifier: NCT00281918.

Multiple gene-expression-based subtypes have been proposed for the molecular subdivision of colon cancer in the last decade. We aimed to cross-validate these classifiers to explore their concordance and their power to predict survival. A gene-chip-based database comprising 2,166 samples from 12 independent datasets was set up. A total of 22 different molecular subtypes were re-trained including the CCHS, CIN25, CMS, ColoGuideEx, ColoGuidePro, CRCassigner, MDA114, Meta163, ODXcolon, Oncodefender, TCA19, and V7RHS classifiers as well as subtypes established by Budinska, Chang, DeSousa, Marisa, Merlos, Popovici, Schetter, Yuen, and Watanabe (first authors). Correlation with survival was assessed by Cox proportional hazards regression for each classifier using relapse-free survival data. The highest efficacy at predicting survival in stage 2-3 patients was achieved by Yuen (p = 3.9e-05, HR = 2.9), Marisa (p = 2.6e-05, HR = 2.6) and Chang (p = 9e-09, HR = 2.35). Finally, 61 colon cancer cell lines from four independent studies were assigned to the closest molecular subtype.

Background: Current guideline-based implantable cardioverter-defibrillator (ICD) implants fail to meet the demands for precision medicine. Machine learning (ML) designed for survival analysis might facilitate personalized risk stratification. We aimed to develop explainable ML models predicting mortality and the first appropriate shock and compare these to standard Cox proportional hazards (CPH) regression in ICD recipients. Methods and Results: Forty-five routine clinical variables were collected. Four fine-tuned ML approaches (elastic net Cox regression, random survival forests, survival support vector machine, and XGBoost) were applied and compared with the CPH model on the test set using Harrell’s C-index. Of 887 adult patients enrolled, 199 patients died (5.0 per 100 person-years) and 265 first appropriate shocks occurred (12.4 per 100 person-years) during the follow-up. Patients were randomly split into training (75%) and test (25%) sets. Among ML models predicting death, XGBoost achieved the highest accuracy and outperformed the CPH model (C-index: 0.794 vs. 0.760, p < 0.001). For appropriate shock, survival support vector machine showed the highest accuracy, although not statistically different from the CPH model (0.621 vs. 0.611, p = 0.243). The feature contribution of ML models assessed by SHAP values at individual and overall levels was in accordance with established knowledge. Accordingly, a bi-dimensional risk matrix integrating death and shock risk was built. This risk stratification framework further classified patients with different likelihoods of benefiting from ICD implant. Conclusions: Explainable ML models offer a promising tool to identify different risk scenarios in ICD-eligible patients and aid clinical decision making. Further evaluation is needed.