Competing risk model in dental cost-effective research

Background: Different survival analysis techniques such as nonparametric, semi-parametric, parametric Accelerated Failure Time (AFT) models have been generally applied to analyze time to event data. In order to identify the prognostic factors for survival of Acute Liver Failure (ALF) patients, previous studies applied Cox Proportional hazards (CPH) model, Lognormal AFT and Log-Logistic AFT model satisfying respective model’s assumptions and goodness of fit of each model. However, comparison of CPH model and AFT model has not been reported so far for ALF data with short follow up time.
 Objective: To compare CPH model and Lognormal AFT model based on different parameters for assessing the model performance and prospective validation of the finally selected model.
 Materials and Methods: Altogether 1099 ALF patients’ data from liver clinic of All India Institute of Medical Sciences, New Delhi India were analyzed based on the retrospective cohort study design. For validating the final model, a separate data set of 138 ALF patients from the same clinic was used. CPH model and Lognormal model’s performance was assessed through selection of variables in the final model, R2 type statistic, goodness of fit of the model, visual assessment of Cox-Snell’s residuals plot and robustness of the model. The prospective validation of the over scored CPH model was done by comparing overall survival, regression coefficients, observed and predicted survival curves between original and validation data set.
 Results: It is found that 60% of variation in the partial log-likelihood is explained by the CPH model whereas 39% of variation in full log-likelihood is explained by Lognormal AFT model. Cox-Snell residuals plot for CPH model seems less deviated from the line of ideal fit, replications of variables measured through bootstrapping resampling technique in CPH model are on the higher side, model predicted and observed survival curves in each risk stratum were closer than that of Lognormal model. The survival experience of original data and validation data set for CPH model does not seem to be very different (p = 0.07) at 5% level of significance.
 Conclusion: Both CPH and Lognormal AFT model are found well fitted and can be applied either of them for this ALF data. While comparing the model performance, the CPH model for the identification of prognostic factors for the survival of ALF patients is found comparatively better.

Background:C-reactive protein (CRP) is gaining credibility as a prognostic factor in different cancers. Cox's proportional hazard (PH) model is usually used to assess prognostic factors. However, this model imposes a priori assumptions, which are rarely tested, that (1) the hazard ratio associated with each prognostic factor remains constant across the follow-up (PH assumption) and (2) the relationship between a continuous predictor and the logarithm of the mortality hazard is linear (linearity assumption).Methods:We tested these two assumptions of the Cox's PH model for CRP, using a flexible statistical model, while adjusting for other known prognostic factors, in a cohort of 269 patients newly diagnosed with non-small cell lung cancer (NSCLC).Results:In the Cox's PH model, high CRP increased the risk of death (HR=1.11 per each doubling of CRP value, 95% CI: 1.03–1.20, P=0.008). However, both the PH assumption (P=0.033) and the linearity assumption (P=0.015) were rejected for CRP, measured at the initiation of chemotherapy, which kept its prognostic value for approximately 18 months.Conclusion:Our analysis shows that flexible modeling provides new insights regarding the value of CRP as a prognostic factor in NSCLC and that Cox's PH model underestimates early risks associated with high CRP.

A Bayesian network interpretation of the Cox's proportional hazard model

Cox proportional hazard (CPH) model is the most widely used model for survival analysis. When there are unobserved/unmeasured individuals factor, then the results of the Cox proportional hazard model may not be reliable. The purpose of this study was to compare the results of CPH and frailty models in breast cancer (BC) patients. A historical cohort study was carried out using medical records gathered from the Fars Province Cancer Registry. The dataset consisted of 769 women having BC referred to Shiraz Namazi Hospital, south of Iran. These patients had been followed for 6 years. After selecting the most important prognostic risk factors on survival, CPH and gamma-frailty Cox models were used to estimate the effects of the risk factors. The results of CPH model showed that, tumor characteristics and number of involved lymph nodes increase the mortality hazard of BC(P<0.05). In addition, the frailty model showed that there is at least a latent factor in the model (P=0.005). Both of the frailty and CPH model emphasis that the early detection of BC improves survival in BC patients.

Background:In malaria endemic areas such as sub-Saharan Africa, repeated exposure to malaria results in acquired immunity to clinical disease but not infection. In prospective studies, time-to-clinical malaria and longitudinal parasite count trajectory are often analysed separately which may result in inefficient estimates since these two processes can be associated. Including parasite count as a time-dependent covariate in a model of time-to-clinical malaria episode may also be inaccurate because while clinical malaria disease frequently leads to treatment which may instantly affect the level of parasite count, standard time-to-event models require that time-dependent covariates be external to the event process. We investigated whether jointly modelling time-to-clinical malaria disease and longitudinal parasite count improves precision in risk factor estimates and assessed the strength of association between the hazard of clinical malaria and parasite count.Methods:Using a cohort data of participants enrolled with uncomplicated malaria in Malawi, a conventional Cox Proportional Hazards (PH) model of time-to-first clinical malaria episode with time-dependent parasite count was compared with three competing joint models. The joint models had different association structures linking a quasi-Poisson mixed-effects of parasite count and event-time Cox PH sub-models.Results:There were 120 participants of whom 115 (95.8%) had >1 follow-up visit and 100 (87.5%) experienced the episode. Adults >15 years being reference, log hazard ratio for children <5 years was 0.74 (95% CI: 0.17, 1.26) in the joint model with best fit vs. 0.62 (95% CI: 0.04, 1.18) from the conventional Cox PH model. The log hazard ratio for the 5–15 years was 0.72 (95% CI: 0.22, 1.22) in the joint model vs.0.63 (95% CI: 0.11, 1.17) in the Cox PH model. The area under parasite count trajectory was strongly associated with the risk of clinical malaria, with a unit increase corresponding to-0.0012 (95% CI: −0.0021, −0.0004) decrease in log hazard ratio.Conclusion:Jointly modelling longitudinal parasite count and time-to-clinical malaria disease improves precision in log hazard ratio estimates compared to conventional time-dependent Cox PH model. The improved precision of joint modelling may improve study efficiency and allow for design of clinical trials with relatively lower sample sizes with increased power.

Many biological features are expressed as “time-to-event” traits, such as time to first reproduction or response to some stimulus. The analysis of these traits frequently produces right-censored data in cases where no event has occurred within a certain timeframe. The Cox proportional hazards (CPH) model, a type of survival analysis, accounts for censored data by estimating the hazard of an event occurring at each time point. While random effect variances can be estimated in CPH models, it is currently not possible to estimate within-cluster variance. Consequently, we lack a general method for calculating ecologically and evolutionary relevant variances and metrics like repeatability from time-to-event data. We here present a solution to this issue. We first describe the characteristics of CPH models and introduce repeatability as an intra-class correlation coefficient (ICC). We demonstrate how CPH models with discrete-time intervals are comparable to binomial generalized linear mixed-effects models (GLMMs) with the complementary log-log link. Through this equivalence, we show how to estimate an ICC using the estimates of the random effects variance component(s) resulting from CPH models and the distribution-specific variance (within-cluster variance) from the binomial GLMM. We provide a case study and online materials to demonstrate how our new method for ICC for time-to-event data can be implemented and used. We conclude that the proposed method will not only generate a standard way to quantify consistent individual differences (ICC) from time-to-event data, but also broaden the use of survival analysis outside of the typical implementation for survivorship studies.

Predicting hepatocellular carcinoma in people with hepatitis B: a comparison between Cox proportional hazard and machine learning models.

BackgroundSemiparametric survival analysis such as the Cox proportional hazards (CPH) regression model is commonly employed in endometrial cancer (EC) study. Although this method does not need to know the baseline hazard function, it cannot estimate event time ratio (ETR) which measures relative increase or decrease in survival time. To estimate ETR, the Weibull parametric model needs to be applied. The objective of this study is to develop and evaluate the Weibull parametric model for EC patients’ survival analysis.MethodsTraining (n = 411) and testing (n = 80) datasets from EC patients were retrospectively collected to investigate this problem. To determine the optimal CPH model from the training dataset, a bi-level model selection with minimax concave penalty was applied to select clinical and radiomic features which were obtained from T2-weighted MRI images. After the CPH model was built, model diagnostic was carried out to evaluate the proportional hazard assumption with Schoenfeld test. Survival data were fitted into a Weibull model and hazard ratio (HR) and ETR were calculated from the model. Brier score and time-dependent area under the receiver operating characteristic curve (AUC) were compared between CPH and Weibull models. Goodness of the fit was measured with Kolmogorov-Smirnov (KS) statistic.ResultsAlthough the proportional hazard assumption holds for fitting EC survival data, the linearity of the model assumption is suspicious as there are trends in the age and cancer grade predictors. The result also showed that there was a significant relation between the EC survival data and the Weibull distribution. Finally, it showed that Weibull model has a larger AUC value than CPH model in general, and it also has smaller Brier score value for EC survival prediction using both training and testing datasets, suggesting that it is more accurate to use the Weibull model for EC survival analysis.ConclusionsThe Weibull parametric model for EC survival analysis allows simultaneous characterization of the treatment effect in terms of the hazard ratio and the event time ratio (ETR), which is likely to be better understood. This method can be extended to study progression free survival and disease specific survival.Trial registrationClinicalTrials.gov NCT03543215, https://clinicaltrials.gov/, date of registration: 30th June 2017.

BackgroundThe prognosis of lung cancer with malignant pericardial effusion is very terrible owing to the impact of cardiac tamponade. The aim of our study seeks to identify prognostic factors and establish a prognostic nomogram of non small cell lung cancer (NSCLC) with malignant pericardial effusion.MethodsNSCLC patients with malignant pericardial effusion between 2010 and 2014 are searched from SEER database.Cancer-specific death of these patients are analyzed through the Kaplan–Meier method, Cox proportional hazard model and competing risk model. Prognostic nomogram of cancer-specific death is performed and validated with concordance index (C-index), calibration plots and internal validation population. Propensity score matching is used to evaluate whether chemotherapy affected the survival of study population.Results696 eligible NSCLC patients are involved in the study population, with 22.7% of 1-year survival rate and 8.9% of 2-year survival rate. Laterality, AJCC N, AJCC T, and chemotherapy are regarded as independent prognostic factors of cancer-specific death in the Cox proportional hazards model and competing risk model. The C-index of established nomogram is 0.703(95%CI:0.68–0.73) for cancer-specific death in the study population with acceptable calibration, which is significantly higher than classical TNM stage(C-index = 0.56, 95%CI:0.52–0.60). After 1:1 propensity score matching, chemotherapy potentially reduces the risk of cancer-specific death (HR = 0.42 95%CI: 0.31–0.58) of NSCLC with pericardial effusion.ConclusionsNSCLC with malignant pericardial effusion harbors low overall survival. One prognostic nomogram based on laterality, AJCC N, AJCC T and chemotherapy is developed for cancer-specific death to predict 1-year and 2-year survival rate with good performance.

BackgroundSubjects with breast cancer enrolled in trials may experience multiple events such as local recurrence, distant recurrence or death. These events are not independent; the occurrence of one may increase the risk of another, or prevent another from occurring. The most commonly used Cox proportional hazards (Cox-PH) model ignores the relationships between events, resulting in a potential impact on the treatment effect and conclusions. The use of statistical methods to analyze multiple time-to-event events has mainly been focused on superiority trials. However, their application to non-inferiority trials is limited. We evaluate four statistical methods for multiple time-to-event endpoints in the context of a non-inferiority trial.MethodsThree methods for analyzing multiple events data, namely, i) the competing risks (CR) model, ii) the marginal model, and iii) the frailty model were compared with the Cox-PH model using data from a previously-reported non-inferiority trial comparing hypofractionated radiotherapy with conventional radiotherapy for the prevention of local recurrence in patients with early stage breast cancer who had undergone breast conserving surgery. These methods were also compared using two simulated examples, scenario A where the hazards for distant recurrence and death were higher in the control group, and scenario B. where the hazards of distant recurrence and death were higher in the experimental group. Both scenarios were designed to have a non-inferiority margin of 1.50.ResultsIn the breast cancer trial, the methods produced primary outcome results similar to those using the Cox-PH model: namely, a local recurrence hazard ratio (HR) of 0.95 and a 95% confidence interval (CI) of 0.62 to 1.46. In Scenario A, non-inferiority was observed with the Cox-PH model (HR = 1.04; CI of 0.80 to 1.35), but not with the CR model (HR = 1.37; CI of 1.06 to 1.79), and the average marginal and frailty model showed a positive effect of the experimental treatment. The results in Scenario A contrasted with Scenario B with non-inferiority being observed with the CR model (HR = 1.10; CI of 0.87 to 1.39), but not with the Cox-PH model (HR = 1.46; CI of 1.15 to 1.85), and the marginal and frailty model showed a negative effect of the experimental treatment.ConclusionWhen subjects are at risk for multiple events in non-inferiority trials, researchers need to consider using the CR, marginal and frailty models in addition to the Cox-PH model in order to provide additional information in describing the disease process and to assess the robustness of the results. In the presence of competing risks, the Cox-PH model is appropriate for investigating the biologic effect of treatment, whereas the CR models yields the actual effect of treatment in the study.

Background and purposeSurvival is frequently assessed using Cox proportional hazards (CPH) regression; however, CPH may be too simplistic as it assumes a linear relationship between covariables and the outcome. Alternative, non-linear machine learning (ML)-based approaches, such as random survival forests (RSFs) and, more recently, deep learning (DL) have been proposed; however, these techniques are largely black-box in nature, limiting explainability. We compared CPH, RSF and DL to predict overall survival (OS) of non-small cell lung cancer (NSCLC) patients receiving radiotherapy using pre-treatment covariables. We employed explainable techniques to provide insights into the contribution of each covariable on OS prediction. Materials and methodsThe dataset contained 471 stage I-IV NSCLC patients treated with radiotherapy. We built CPH, RSF and DL OS prediction models using several baseline covariable combinations. 10-fold Monte-Carlo cross-validation was employed with a split of 70%:10%:20% for training, validation and testing, respectively. We primarily evaluated performance using the concordance index (C-index) and integrated Brier score (IBS). Local interpretable model-agnostic explanation (LIME) values, adapted for use in survival analysis, were computed for each model. ResultsThe DL method exhibited a significantly improved C-index of 0.670 compared to the CPH and a significantly improved IBS of 0.121 compared to the CPH and RSF approaches. LIME values suggested that, for the DL method, the three most important covariables in OS prediction were stage, administration of chemotherapy and oesophageal mean radiation dose. ConclusionWe show that, using pre-treatment covariables, a DL approach demonstrates superior performance over CPH and RSF for OS prediction and use explainable techniques to provide transparency and interpretability.

The study aimed to construct a risk prediction model for coronary artery disease (CAD) based on competing risk model among the elderly in Beijing and develop a user-friendly CAD risk score tool.We used competing risk model to evaluate the risk of developing a first CAD event. On the basis of the risk factors that were included in the competing risk model, we constructed the CAD risk prediction model with Cox proportional hazard model. Time-dependent receiver operating characteristic (ROC) curve and time-dependent area under the ROC curve (AUC) were used to evaluate the discrimination ability of the both methods. Calibration plots were applied to assess the calibration ability and adjusted for the competing risk of non-CAD death. Net reclassification index (NRI) and integrated discrimination improvement (IDI) were applied to quantify the improvement contributed by the new risk factors. Internal validation of predictive accuracy was performed using 1000 times of bootstrap re-sampling.Of the 1775 participants without CAD at baseline, 473 incident cases of CAD were documented for a 20-year follow-up. Time-dependent AUCs for men and women at t = 10 years were 0.841 [95% confidence interval (95% CI): 0.806–0.877], 0.804 (95% CI: 0.768–0.839) in Fine and Gray model, 0.784 (95% CI: 0.738–0.830), 0.733 (95% CI: 0.692–0.775) in Cox proportional hazard model. The competing risk model was significantly superior to Cox proportional hazard model on discrimination and calibration. The cut-off values of the risk score that marked the difference between low-risk and high-risk patients were 34 points for men and 30 points for women, which have good sensitivity and specificity.A sex-specific multivariable risk factor algorithm-based competing risk model has been developed on the basis of an elderly Chinese cohort, which could be applied to predict an individual's risk and provide a useful guide to identify the groups at a high risk for CAD among the Chinese adults over 55 years old.

Gamma frailty model for survival risk estimation: an application to cancer data

Medullary thyroid carcinoma (MTC) is an infrequent form malignant tumor with a poor prognosis. Because of the influence of competitive risk, there may suffer from bias in the analysis of prognostic factors of MTC. By extracting the data of patients diagnosed with MTC registered in the Surveillance, Epidemiology, and End Results (SEER) database from 1998 to 2016, we established the Cox proportional-hazards and competing-risks model to retrospectively analyze the impact of related factors on lymph nodes statistically. A total of 2,435 patients were included in the analysis, of which 198 died of MTC. The results of the multifactor competing-risk model showed that the number of total lymph nodes (19-89), positive lymph nodes (1-10,11-75) and positive lymph node ratio (25%-53%,>54%), age (46-60,>61), chemotherapy, mode of radiotherapy (others), tumor size(2-4cm,>4cm), number of lesions greater than 1 were poor prognostic factors for MTC. For the number of total lymph nodes, unlike the multivariate Cox proportional-hazards model results, we found that it became an independent risk factor after excluding competitive risk factors. Competitive risk factors have little effect on the number of positive lymph nodes. For the proportion of positive lymph nodes, we found that after excluding competitive risk factors, the Cox proportional-hazards model overestimates its impact on prognosis. The competitive risk model is often more accurate in analyzing the effects of prognostic factors. After excluding the competitive risk, the number of lymph nodes, the number of positive and the positive proportion are the poor prognostic factors of medullary thyroid cancer, which can help clinicians more accurately evaluate the prognosis of patients with medullary thyroid cancer and provide a reference for treatment decision-making.

Background Statin prevents occurrence and recurrence of atherosclerotic events. With regard to venous thromboembolism (VTE), a randomized controlled trial suggested that statin reduced occurrence of VTE, whereas its usefulness as secondary prevention of VTE remains to be elucidated. Purpose This study aimed to assess the association between statin prescription, recurrent VTE and bleeding events in patients with VTE. Methods The COMMAND VTE Registry is a multicentre registry enrolling consecutive 3027 patients with acute symptomatic VTE among 29 centres in Japan. We divided the cohort into the patients who were prescribed statin (N=437) and those not (N=2590), and compared the two groups. We assessed hazard ratios (HRs) of those with statin relative to those without for long-term clinical outcomes (recurrent symptomatic VTE and International Society of Thrombosis and Hemostasis [ISTH] major bleeding). Because the durations of anticoagulation therapy were widely different between the two groups, we constructed Cox's proportional hazard model incorporating status of anticoagulation during the follow-up period as a time-varying covariate. Also, because the incidences of death were strikingly different between the two groups due to the difference in the prevalence of active cancer, we used Fine-Gray's subdistribution hazard model in the presence of competing risks. We incorporated clinically relevant factors into these two models as covariates (10 factors for recurrent VTE and 11 for major bleeding). Results The statin group was significantly older than the non-statin group (statin 71.2±11.8 vs. non-statin 66.5±15.8, P&lt;0.001). The prevalence of active cancer in the statin group was less than one-half of that in the non-statin group (12% vs. 25%, P&lt;0.001), and the cumulative 3-year incidence of death was significantly lower in the statin group than in the non-statin group (12.8% vs. 26.1%, log-rank P&lt;0.001). The table shows the adjusted HRs of the statin group relative to the non-statin group. The HRs of the statin group relative to non-statin group for recurrent VTE were significantly low, but those for major bleeding were insignificant. Adjusted hazard ratios Outcome measures Model 1 P value Model 2 P value Adjusted HR [95% CI] Adjusted HR [95% CI] Recurrent VTE 0.59 [0.36–0.98] 0.042 0.53 [0.32–0.89] 0.02 Major bleeding 0.87 [0.60–1.24] 0.43 0.997 [0.69–1.43] 0.99 Model 1 derived from Cox's model with time-varying covariate of anticoagulation status. Model 2 derived from Fine-Gray's model. Study flowchart Conclusions Prescription of satin was associated with significantly low risks for recurrent VTE, whereas that was not for major bleeding events. Statin could be a potential treatment option for secondary prevention of VTE.