Cause-specific Hazard Functions Research Articles

Multiple imputation with competing risk outcomes

AbstractIn time-to-event analyses, a competing risk is an event whose occurrence precludes the occurrence of the event of interest. Settings with competing risks occur frequently in clinical research. Missing data, which is a common problem in research, occurs when the value of a variable is recorded for some, but not all, records in the dataset. Multiple Imputation (MI) is a popular method to address the presence of missing data. MI uses an imputation model to generate M (M > 1) values for each variable that is missing, resulting in the creation of M complete datasets. A popular algorithm for imputing missing data is multivariate imputation using chained equations (MICE). We used a complex simulation design with covariates and missing data patterns reflective of patients hospitalized with acute myocardial infarction (AMI) to compare three strategies for imputing missing predictor variables when the analysis model is a cause-specific hazard when there were three different event types. We compared two MICE-based strategies that differed according to which cause-specific cumulative hazard functions were included in the imputation models (the three cause-specific cumulative hazard functions vs. only the cause-specific cumulative hazard function for the primary outcome) with the use of the substantive model compatible fully conditional specification (SMCFCS) algorithm. While no strategy had consistently superior performance compared to the other strategies, SMCFCS may be the preferred strategy. We illustrated the application of the strategies using a case study of patients hospitalized with AMI.

AN ADDITIVE SUBDISTRIBUTION HAZARDS MODEL FOR COMPETING RISKS DATA

Competing risk failure time data occur frequently in medical a number of methods have been proposed for the analysis of these data. The classic approach is to model all cause-specific hazards and then estimate the cumulative incidence curve based on these cause-specific hazards. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In this paper, we consider a more flexible model for the subdistribution. It is a combination of the additive model and the Cox model and allows one to perform a more detailed study of covariate effects. One advantage of this approach is that our regression modeling allows for non-proportional hazards. This leads to a new simple goodness-of-fit procedure for the proportional subdistribution hazards assumption that is very easy to use. We applied this method to melanoma data and estimated the cumulative death rate for those who died from melanoma after surgical removal of the tumor. It was found that two covariates had a time-varying effect and two other covariates had a constant effect in predicting the cumulative incidence curve in patients who died of melanoma following tumor removal surgery.

A comprehensive prognostic analysis of cause-specific mortality in patients with ovarian serous cystadenocarcinoma using a competing-risks model: a case study of the SEER database.

This retrospective study employed a competing-risks analysis utilizing the Surveillance, Epidemiology, and End Results (SEER) database to identify precise prognostic factors associated with ovarian serous cystadenocarcinoma (OSCC) in patients. Patients with OSCC during 2004-2015 were identified in the SEER database, and their clinicopathological, demographic, and survival data were examined. Univariate analysis using Gray's test and the cumulative incidence function was used to evaluate the prognoses of events of interest. The multivariate analysis involved several models, including the Cox proportional hazards, Fine-Gray, and cause-specific (CS) hazard function models, to estimate the hazard functions of competing risks. Hazard ratios were analyzed to identify the reliability of the prognostic factors. Among the 10,400 individuals diagnosed with OSCC, 5,713 died from the illness, and 1,125 died from other causes. The cumulative incidence rate of events of interest was found to be significant for ethnicity, age at diagnosis, histological grade, American Joint Committee on Cancer (AJCC) stage, chemotherapy and surgery status, tumor size, marital status, and local lymph node metastases (p<0.05). The multivariate analysis revealed that ethnicity, histological grade, surgery and chemotherapy status, age at diagnosis, AJCC stage, marital status, and distant metastases were independent prognostic factors in the Cox model (p<0.05). Finally, the Fine-Gray and CS models demonstrated that ethnicity, histological grade, surgery and chemotherapy status, age at diagnosis, AJCC stage, tumor size, marital status, and combination summary stage were all identified as independent prognostic factors (p<0.05). This study determined the risk factors for OSCC using a competing risk analysis model established by the SEER database. The findings can help clinicians understand OSCC better and provide more accurate medical support to affected patients.

Management of chordoma and chondrosarcoma with definitive dose-escalated single-fraction spine stereotactic radiosurgery.

The management of chordoma or chondrosarcoma involving the spine is often challenging due to adjacent critical structures and tumor radioresistance. Spine stereotactic radiosurgery (SSRS) has radiobiologic advantages compared with conventional radiotherapy, though there is limited evidence on SSRS in this population. We sought to characterize the long-term local control (LC) of patients treated with SSRS. We retrospectively reviewed patients with chordoma or chondrosarcoma treated with dose-escalated SSRS, defined as 24Gy in 1 fraction to the gross tumor volume. Overall survival (OS) was calculated by Kaplan-Meier functions. Competing risk analysis using the cause-specific hazard function estimated LC time. Fifteen patients, including 12 with chordoma and 3 with chondrosarcoma, with 22 lesions were included. SSRS intent was definitive, single-modality in 95% of cases (N = 21) and post-operative in 1 case (5%). After a median censored follow-up time of 5 years (IQR 4 to 8 years), median LC time was not reached (IQR 8 years to not reached), with LC rates of 100%, 100%, and 90% at 1 year, 2 years, and 5 years. The median OS was 8 years (IQR 3 years to not reached). Late grade 3 toxicity occurred after 23% of treatments (N = 5, fracture), all of which were managed successfully with stabilization. Definitive dose-escalated SSRS to 24Gy in 1 fraction appears to be a safe and effective treatment for achieving durable local control in chordoma or chondrosarcoma involving the spine, and may hold particular importance as a low-morbidity alternative to surgery in selected cases.

#5365 T2DM MODIFIES THE RELATIONSHIP BETWEEN CAC AND ADVERSE KIDNEY OUTCOME IN PATIENTS WITH CKD

Abstract Background and Aims Kidney function decline faster in patients with type 2 diabetes mellitus (T2DM) than in those without. We previously showed that coronary artery calcification (CAC) is a strong risk of adverse kidney outcome. Here, we examined whether T2DM could modify the relationship between CAC and the progression of chronic kidney disease (CKD). Method 2067 participants from the KoreaN Cohort Study for Outcome in Patients With CKD were enrolled. The main exposures were T2DM and CAC. The primary outcome was CKD progression defined as a composite of a 50% decline in estimated glomerular filtration rate or kidney failure with replacement therapy. Multivariable cause-specific hazard function was employed to determine the association between the main exposures and the primary outcome. Results During 8633 person-years of follow-up, the primary outcome occurred in 565 (27.3%) participants. In the multivariable cause-specific hazard model, both T2DM and CAC Agatston score (CACS) &amp;gt;0 were associated with a 1.80- and a 1.41-fold increased risk of CKD progression compared with counterparts. There was a significant interaction between T2DM and CAC for the primary outcome. In patients without T2DM, CACS &amp;gt;0 was not associated with the primary outcome compared with CACS of 0. However, in patients with T2DM, CACS &amp;gt;0 was associated with a significantly higher risk of CKD progression (adjusted hazard ratio, 2.12; 95% confidence interval, 1.64-2.75). In addition, a 1-SD increase in CACS was associated with 1.11-fold higher risk of CKD progression. Notably, this association was also significant in patients with T2DM who had CACS of 0. The slope of eGFR decline was steeper in patients with T2DM and the magnitude of decline was greater when CACS &amp;gt;0. Conclusion CAC were more strongly associated with risk of CKD progression in patients with T2DM than in those without. Thus, clinical implication of CAC may differ depending on the presence of T2DM.

Cause of Death among Long-Term Cancer Survivors: The NANDE Study.

Survival information for Japanese patients with cancer is based only on survival status and the cause of death among these patients remains unclear. In this study, Osaka Cancer Registry data (1985-2014) and vital statistics data (1985-2016) were linked to create a database, permitting the extraction of data on the causes of death. In total, 522,566 subjects diagnosed with cancer between 1995 and 2011 were analyzed. Follow-up for vital status was conducted 5 and 10 years after cancer diagnosis. To evaluate the three causes of death (index cancer, non-index cancer, and non-cancer death), cause-specific hazard and cumulative incidence functions were estimated using a life table and Gray's methods. The number of deaths owing to any of the causes in the observation period (median: 3.51 years, mean: 4.90 years) was 394,146. The 5- and 10-year cancer-specific survival rate was 48.56% and 39.92%, respectively. Immediately after cancer onset, the hazard of index cancer death was high. The proportion of non-index cancer deaths was high in patients with mouth and pharynx cancers. The hazard of index cancer death remained constant for breast and liver cancers. In prostate, breast, and laryngeal cancers with good prognosis, the hazard of non-index cancer and non-cancer death constantly increased.

Additive subdistribution hazards regression for competing risks data in case-cohort studies.

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long-term follow-up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case-cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case-cohort studies involves the cause-specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case-cohort studies. We propose estimating equationsbased on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case-cohort dataset from the SisterStudy.

Improving equity in kidney transplant allocation policies through a novel genetic metric: The Matched Donor Potential

The demand for donors’ kidneys continues to increase amid a shortage of available donors. Managing policies to thoughtfully allocate this scarce resource is a complex process. Although human leukocyte antigen (HLA) matching has been shown to prolong graft survival, its relative contribution to allocation schemes is empirically compromised owing to competing priorities. We explored using a new metric, Matched Donor Potential (MDP), to facilitate improved HLA matching while promoting equity. We interrogated all active kidney waitlist patients (N = 164 427), their corresponding unacceptable antigen files, and all effective donors in the Scientific Registry of Transplant Recipients (January 1, 2016-December 31, 2017). Cause-specific hazard functions were evaluated to assess the potential impact of the MDP metric on deceased donor transplant access rates for all candidates.Access was affected by ethnicity, blood group type, and calculated Panel Reactive Antibody (cPRA). Importantly, we show that access to transplantation is influenced by the patient’s own HLA makeup regardless of their ethnicity and by the HLA makeup of effective donors. The MDP metric demonstrates a high association with access to transplantation. Adjusting Cox models to include this new metric resulted in improved access to kidney transplantation for waitlist candidates of minority heritage while significantly promoting HLA matching. Thus, the MDP metric accounts for balanced, equitable organ allocation algorithms.

Hazard Function Analysis of Recurrence in Patients with Curatively Resected Lung Cancer: Results from the Japanese Lung Cancer Registry in 2010.

Simple SummaryTo optimize postoperative surveillance of lung cancer patients, we investigated the hazard function of tumor recurrence in patients with completely resected lung cancer. Using the records of the 2010 Japanese Joint Committee of Lung Cancer Registry, the risk of postoperative recurrence was analyzed using a cause-specific hazard function in patients who underwent lobectomy to completely resect pathological stage I–III lung cancer. The hazard function for recurrence exhibited a peak at approximately 9 months after surgery, followed by a tapered plateau-like tail extending to 60 months. The peak risk for intrathoracic recurrence was approximately two-fold higher compared with that of extrathoracic recurrence. When considered together with the results of the subgroup analysis, the characteristics of the postoperative tumor recurrence hazard in a large cohort of lung cancer patients may be useful for improving stage-related management of postoperative surveillance.To optimize postoperative surveillance of lung cancer patients, we investigated the hazard function of tumor recurrence in patients with completely resected lung cancer. We analyzed the records of 12,897 patients in the 2010 Japanese Joint Committee of Lung Cancer Registry who underwent lobectomy to completely resect pathological stage I–III lung cancer. The risk of postoperative recurrence was determined using a cause-specific hazard function. The hazard function for recurrence exhibited a peak at approximately 9 months after surgery, followed by a tapered plateau-like tail extending to 60 months. The peak risk for intrathoracic recurrence was approximately two-fold higher compared with that of extrathoracic recurrence. Subgroup analysis showed that patients with stage IIIA adenocarcinoma had a continuously higher risk of recurrence compared with patients with earlier-stage disease. However, the risk of recurrence in patients with squamous cell carcinoma was not significantly different compared with that more than 24 months after surgery, regardless of pathological stage. In conclusion, the characteristics of postoperative tumor recurrence hazard in a large cohort of lung cancer patients may be useful for determining the time after surgery at which patients are at the highest risk of tumor recurrence. This information may improve stage-related management of postoperative surveillance.

Mobitz type I 2nd degree atrioventricular (Wenckebach) block and cardiovascular death using 978,901 12 lead ECGs recordings

Abstract Background Mobitz type I 2nd degree atrioventricular (AV) block (Wenckebach) is usually considered benign. Guidelines recommend permanent cardiac pacing for patients with Mobitz type II second degree AV block (Mobitz II), but for patients with Wenckebach, permanent pacing is only indicated if the AV block causes symptoms or if the conductions delay occurs below the bundle of His. However, these guidelines are based on evidence of modest quality and a consensus amongst experts (1). Purpose This study aims to investigate if Wenckebach really is benign by comparing the risk of cardiovascular death for patients with Wenckebach to patients with normal ECGs. Methods This retrospective cohort study included 978,901 ECGs obtained from general practitioners in Denmark from 01/02/2001 to 31/10/2014. Index date was the day of the ECG recording and the patients were followed until death or end of follow up at December 2019. The association between Wenckebach and cardiovascular death was analyzed using: 1) multivariate Cox models adjusted for age and comorbidities, 2) cause-specific Cox models and 3) cumulative risk and cause-specific hazard function plots, compared to matched controls. Information about comorbidities, pacemaker, indications, and death was retrieved from Danish nationwide registries. Results From the 978,901 ECG recordings, we found 262 patients with Wenckebach, 131 patients with Mobitz II, and 229,056 patients with normal ECGs. In Wenckebach, Mobitz II, and normal ECG the median age was 76, 80, and 50 years, 76%, 63%, and 41% were male, 25%, 16%, and 3% had diabetes, 35%, 30%, and 8% had hypertension, respectively. During a mean follow-up of 11.2 years, cardiovascular death occurred in a total of 11,301 patients: 77 (29%) patients with Wenckebach, 40 (31%) patients with Mobitz II, and 11,184 (5%) patients with normal ECGs. In a matched cohort 262 Wenckebach patients were matched with 520 controls with normal ECGs. In the multivariate Cox model, Wenckebach was associated with cardiovascular death (HR: 2.14 [95% CI: 1.46–3.13], P&amp;lt;0.001). Furthermore, in multivariate cause-specific Cox analysis with non-cardiovascular death and pacemaker as competing risk, Wenckebach was still associated with cardiovascular death (HR: 2.27 [95% CI: 1.37–3.75], P=0.001). Furthermore, the results showed that 43% of the Wenckebach patients received pacemaker with a median time to pacemaker from ECG recording being 252 days. The vast majority of the Wenckebach patients who received pacemaker had a higher degree AV block than Wenckebach as indication for the implantation. Conclusion Wenckebach on routine ECG was associated with a significant higher hazard rate of cardiovascular death compared to matched controls with normal ECGs. Funding Acknowledgement Type of funding sources: Foundation. Main funding source(s): The Danish Heart Association

Prognostic factors for squamous cervical carcinoma identified by competing-risks analysis: A study based on the SEER database.

Cervical cancer has a high incidence of malignant tumors and a high mortality rate, with squamous cervical carcinoma (SCC) accounting for 80% of cases. A competing-risks model is recommended as being more feasible for evaluating the prognosis and guiding clinical practice in the future compared to Cox regression. Data originating from the Surveillance, epidemiology, and end results (SEER) database during 2004 to 2013 were analyzed. Univariate analysis with the cumulative incidence function was performed to assess the potential risk of each covariate. Significant covariates (P < .05) were extracted for inclusion in a Cox regression analysis and a competing-risks model that included a cause-specific (CS) hazard function model and a sub-distribution (SD) hazard function model. A total of 5591 SCC patients met the inclusion criteria. The three methods (Cox regression analysis, CS analysis, and SD analysis) showed that age, metastasis, American Joint Committee on Cancer stage, surgery, chemotherapy, radiation sequence with surgery, lymph node dissection, tumor size, and tumor grade were prognostic factors affecting survival in patients with SCC. In contrast, race and radiation status were prognostic factors affecting survival in the Cox regression and CS analysis, but the results were different in the SD analysis. Being separated, divorced, or widowed was an independent prognostic factor in the Cox regression analysis, but the results were different in the CS and SD analyses. A competing-risks model was used as a new statistical method to more accurately identify prognostic factors than conventional Cox regression analysis leading to bias in the results. This study found that the SD model may be better suited to estimate the clinical prognosis of a patient, and that the results of an SD model analysis were close to those of a CS analysis.

Competing risks predictions with different time scales under the additive risk model.

In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

Hiding in plain sight: The magnitude of unused disease modifying therapies in multiple sclerosis and strategies for reducing the economic burden of care

BackgroundThe rising costs associated with multiple sclerosis (MS) disease modifying therapies (DMTs) creates challenges for patients and the healthcare system in the United States (U.S.). Within a specialty medicine waste project, we quantified the magnitude of unused medications and corresponding value, the primary factors driving treatment switches, and explored reasons for discontinuations by race and ethnicity. MethodsOver one calendar year, MS DMTs were recovered from new and existing patients from a single neuroimmunologist within a tertiary MS care center. Baseline demographic and clinical information, including reasons for medication discontinuation or transitions were captured. Patients were stratified into three treatment transition categories: (i) non-medical, (ii) medical, or (iii) tolerability reasons. Cause-specific Cox proportional hazard functions were fit for possible causes for treatment changes. ResultsA total of 422 patients (female: 73.2%, median age at diagnosis: 32.9 years (y)) comprised of 86.3% Whites, 11.6% Black or African Americans, 1.4% Asians, and 0.7% Native Americans were included, representing 23% of patients evaluated within 2018, with a mean disease duration of 12.8 years (y) (standard deviation (SD): 8.2) and treatment duration of 2.9y (3.4). Women were more likely to switch due to injection fatigue or desire for an oral DMT when compared to men (95% CI [0.26, 0.78], p = 0.01). Being Black or African American people with MS increased the hazard of switching treatment due to injection fatigue and desire for an oral medication relative to White patients with MS by 91% (95% CI [1.07, 3.42], p = 0.03) and switching to a new DMT based on the subjective report of a perceived lack of efficacy was 221% greater (95% CI [1.04, 4.70], p = 0.04), but not in relation to side effects, being 50% less likely to switch (95% CI [0.28, 0.90], p = 0.02). In the passive recruitment phase over a single calendar year, DMTs with a retail value of $5.2 million (Average Wholesale Price (AWP)) were recovered. In the 1-month active recruitment phase within the same year involving 49 people with MS, unused MS DMTs of $1.1 million (AWP) were acquired. Of the 471 patients studied, 56.2% reported transitions in DMTs for reasons other than adequate disease control and tolerability at one point in their treatment history, underscoring the need for individualized therapy selections that enhance persistence and increase the likelihood of reducing further neurological disability. ConclusionThe magnitude of unused and wasted MS DMTs is staggering and these findings allude to a larger, more pervasive problem within the healthcare system with financial resources being applied to therapies that go unused.

Graphical calibration curves and the integrated calibration index (ICI) for competing risk models

BackgroundAssessing calibration—the agreement between estimated risk and observed proportions—is an important component of deriving and validating clinical prediction models. Methods for assessing the calibration of prognostic models for use with competing risk data have received little attention.MethodsWe propose a method for graphically assessing the calibration of competing risk regression models. Our proposed method can be used to assess the calibration of any model for estimating incidence in the presence of competing risk (e.g., a Fine-Gray subdistribution hazard model; a combination of cause-specific hazard functions; or a random survival forest). Our method is based on using the Fine-Gray subdistribution hazard model to regress the cumulative incidence function of the cause-specific outcome of interest on the predicted outcome risk of the model whose calibration we want to assess. We provide modifications of the integrated calibration index (ICI), of E50 and of E90, which are numerical calibration metrics, for use with competing risk data. We conducted a series of Monte Carlo simulations to evaluate the performance of these calibration measures when the underlying model has been correctly specified and when the model was mis-specified and when the incidence of the cause-specific outcome differed between the derivation and validation samples. We illustrated the usefulness of calibration curves and the numerical calibration metrics by comparing the calibration of a Fine-Gray subdistribution hazards regression model with that of random survival forests for predicting cardiovascular mortality in patients hospitalized with heart failure.ResultsThe simulations indicated that the method for constructing graphical calibration curves and the associated calibration metrics performed as desired. We also demonstrated that the numerical calibration metrics can be used as optimization criteria when tuning machine learning methods for competing risk outcomes.ConclusionsThe calibration curves and numeric calibration metrics permit a comprehensive comparison of the calibration of different competing risk models.

Event‐specific win ratios for inference with terminal and non‐terminal events

For semi-competing risks data involving a non-terminal event and a terminal event we derive the asymptotic distributions of the event-specific win ratios under proportional hazards (PH) assumptions for the relevant cause-specific hazard functions of the non-terminal and terminal event, respectively. The win ratios converge to the respective hazard ratios under the PH assumptions and therefore are censoring-free, whether or not the censoring distributions in the two treatment arms are the same. With the asymptotic bivariate normal distributions of the win ratios, confidence intervals and testing procedures are obtained. Through extensive simulation studies and data analysis, we identified proper transformations of the win ratios that yield good control of the type one error rate for various testing procedures while maintaining competitive power. The confidence intervals also have good coverage probabilities. Furthermore, a test for the PH assumptions and a test of equal hazard ratios are developed. The new procedures are illustrated in the clinical trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function, which evaluated the effects of spironolactone in patients with heart failure and a preserved left ventricular ejection fraction.

Estimation of separable direct and indirect effects in continuous time.

Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause-specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause-specific hazard functions. We describe the asymptotic properties of these estimators and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we reanalyze the prostate cancer trial from Stensrud etal. (2020).

Competing risks in patients with primary prevention implantable cardioverter-defibrillators: Global Electrical Heterogeneity and Clinical Outcomes study

Global electrical heterogeneity (GEH) is associated with sudden cardiac death in the general population. Its utility in patients with systolic heart failure who are candidates for primary prevention (PP) implantable cardioverter-defibrillators (ICDs) is unclear. The purpose of this study was to investigate whether GEH is associated with sustained ventricular tachycardia/ventricular fibrillation leading to appropriate ICD therapies in patients with heart failure and PP ICDs. We conducted a multicenter retrospective cohort study. GEH was measured by spatial ventricular gradient (SVG) direction (azimuth and elevation) and magnitude, QRS-T angle, and sum absolute QRST integral on preimplant 12-lead electrocardiograms. Survival analysis using cause-specific hazard functions compared the strength of associations with 2 competing outcomes: sustained ventricular tachycardia/ventricular fibrillation leading to appropriate ICD therapies and all-cause death without appropriate ICD therapies. We analyzed 2668 patients (mean age 63 ± 12 years; 624 (23%) female; 78% white; 43% nonischemic cardiomyopathy; left ventricular ejection fraction 28% ± 11% from 6 academic medical centers). After adjustment for demographic, clinical, device, andtraditional electrocardiographic characteristics, SVG elevation (hazard ratio [HR] per 1SD 1.14; 95% confidence interval [CI] 1.04-1.25; P = .004), SVG azimuth (HR per 1SD 1.12; 95% CI 1.01-1.24; P = .039), SVG magnitude (HR per 1SD 0.75; 95% CI0.66-0.85; P < .0001), and QRS-T angle (HR per 1SD 1.21; 95% CI 1.08-1.36; P = .001) were associated with appropriate ICD therapies. Sum absolute QRST integral had different associations in infarct-related cardiomyopathy (HR 1.29; 95% CI 1.04-1.60) and nonischemic cardiomyopathy (HR 0.78; 95% CI 0.62-0.96) (Pinteraction = .022). In patients with PP ICDs, GEH is independently associated with appropriate ICD therapies. The SVG vector points in distinctly different directions in patients with 2 competing outcomes.

Cause-specific hazard regression estimation for modified Weibull distribution under a class of non-informative priors

ABSTRACT In time to event analysis, the situation of competing risks arises when the individual (or subject) may experience p mutually exclusive causes of death (failure), where cause-specific hazard function is of great importance in this framework. For instance, in malignancy-related death, colorectal cancer is one of the leading causes of the death in the world and death due to other causes considered as competing causes. We include prognostic variables in the model through parametric Cox proportional hazards model. Mostly, in literature exponential, Weibull, etc. distributions have been used for parametric modelling of cause-specific hazard function but they are incapable to accommodate non-monotone failure rate. Therefore, in this article, we consider a modified Weibull distribution which is capable to model survival data with non-monotonic behaviour of hazard rate. For estimating the cumulative cause-specific hazard function, we utilized maximum likelihood and Bayesian methods. A class of non-informative types of prior (uniform, Jeffrey’s and half-t) is introduced for Bayes estimation under squared error (symmetric) as well as LINEX (asymmetric) loss functions. A simulation study is performed for a comprehensive comparison of Bayes and maximum likelihood estimators of cumulative cause-specific hazard function. Real data on colorectal cancer is used to demonstrate the proposed model.

Competing risks joint models using R-INLA

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

Cause-specific quantile regression on inactivity time.

In time-to-event analysis, the traditional summary measures have been based on the hazard function, survival function, quantile event time, restricted mean event time, and residual lifetime. Under competing risks, furthermore, typical summary measures have been the cause-specific hazard function and cumulative incidence function. Recently inactivity time has recaptured attention in the literature, being interpreted as life lost. In this paper, we further interpret it as quality of life reduced and time period after transition to a drug, and propose a quantile regression model to associate the inactivity time with potential predictors under competing risks. We define the proper cumulative distribution function of the inactivity time distribution for each specific event type among those subjects who experience the same type of events during a follow-up period. A score function-type estimating equation is developed and asymptotic properties of the regression coefficient estimators are derived by assuming that competing events are censored at their occurrence times as in the cause-specific hazard analysis. The proposed approach reduces to a regular quantile regression on the inactivity time without competing risks when all types of competing events are collapsed into the same type. Due to difficulty in estimating the improper probability density function of the cause-specific inactivity distribution to evaluate the variance of the quantiles, a computationally efficient perturbation method is adopted to infer the regression coefficients. Simulation results show that our proposed method works well under the assumed finite sample settings. The proposed method is illustrated with a real dataset from a breast cancer study.