Cox Proportional Hazards Frailty Models Research Articles

Freedom from recurrent ventricular tachycardia after catheter ablation is associated with improved survival in patients with structural heart disease: An International VT Ablation Center Collaborative Group study

The impact of catheter ablation of ventricular tachycardia (VT) on all-cause mortality remains unknown. The purpose of this study was to examine the association between VT recurrence after ablation and survival in patients with scar-related VT. Analysis of 2061 patients with structural heart disease referred for catheter ablation of scar-related VT from 12 international centers was performed. Data on clinical and procedural variables, VT recurrence, and mortality were analyzed. Kaplan-Meier analysis was used to estimate freedom from recurrent VT, transplant, and death. Cox proportional hazards frailty models were used to analyze the effect of risk factors on VT recurrence and mortality. One-year freedom from VT recurrence was 70% (72% in ischemic and 68% in nonischemic cardiomyopathy). Fifty-seven patients (3%) underwent cardiac transplantation, and 216 (10%) died during follow-up. At 1 year, the estimated rate of transplant and/or mortality was 15% (same for ischemic and nonischemic cardiomyopathy). Transplant-free survival was significantly higher in patients without VT recurrence than in those with recurrence (90% vs 71%, P<.001). In multivariable analysis, recurrence of VT after ablation showed the highest risk for transplant and/or mortality [hazard ratio 6.9 (95% CI 5.3-9.0), P<.001]. In patients with ejection fraction <30% and across all New York Heart Association functional classes, improved transplant-free survival was seen in those without VT recurrence. Catheter ablation of VT in patients with structural heart disease results in 70% freedom from VT recurrence, with an overall transplant and/or mortality rate of 15% at 1 year. Freedom from VT recurrence is associated with improved transplant-free survival, independent of heart failure severity.

Intensive care in patients with lung cancer: a multinational study

Detailed information about lung cancer patients requiring admission to intensive care units (ICUs) is mostly restricted to single-center studies. Our aim was to evaluate the clinical characteristics and outcomes of lung cancer patients admitted to ICUs. Prospective multicenter study in 449 patients with lung cancer (small cell, n = 55; non-small cell, n = 394) admitted to 22 ICUs in six countries in Europe and South America during 2011. Multivariate Cox proportional hazards frailty models were built to identify characteristics associated with 30-day and 6-month mortality. Most of the patients (71%) had newly diagnosed cancer. Cancer-related complications occurred in 56% of patients; the most common was tumoral airway involvement (26%). Ventilatory support was required in 53% of patients. Overall hospital, 30-day, and 6-month mortality rates were 39%, 41%, and 55%, respectively. After adjustment for type of admission and early treatment-limitation decisions, determinants of mortality were organ dysfunction severity, poor performance status (PS), recurrent/progressive cancer, and cancer-related complications. Mortality rates were far lower in the patient subset with nonrecurrent/progressive cancer and a good PS, even those with sepsis, multiple organ dysfunctions, and need for ventilatory support. Mortality was also lower in high-volume centers. Poor PS predicted failure to receive the initially planned cancer treatment after hospital discharge. ICU admission was associated with meaningful survival in lung cancer patients with good PS and non-recurrent/progressive disease. Conversely, mortality rates were very high in patients not fit for anticancer treatment and poor PS. In this subgroup, palliative care may be the best option.

Predicting Clustered Dental Implant Survival Using Frailty Methods

The purpose of this study was to predict future implant survival using information on risk factors and on the survival status of an individual's existing implant(s). We considered a retrospective cohort study with 677 individuals having 2349 implants placed. We proposed to predict the survival probabilities using the Cox proportional hazards frailty model, with three important risk factors: smoking status, timing of placement, and implant staging. For a non-smoking individual with 2 implants placed, an immediate implant and in one stage, the marginal probability that 1 implant would survive 12 months was 85.8% (95%CI: 77%, 91.7%), and the predicted joint probability of surviving for 12 months was 75.1% (95%CI: 62.1%, 84.7%). If 1 implant was placed earlier and had survived for 12 months, then the second implant had an 87.5% (95%CI: 80.3%, 92.4%) chance of surviving 12 months. Such conditional and joint predictions can assist in clinical decision-making for individuals.

Bayesian Cure Rate Frailty Models with Application to a Root Canal Therapy Study

Due to natural or artificial clustering, multivariate survival data often arise in biomedical studies, for example, a dental study involving multiple teeth from each subject. A certain proportion of subjects in the population who are not expected to experience the event of interest are considered to be "cured" or insusceptible. To model correlated or clustered failure time data incorporating a surviving fraction, we propose two forms of cure rate frailty models. One model naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model. We formulate the likelihood functions based on piecewise constant hazards and derive the full conditional distributions for Gibbs sampling in the Bayesian paradigm. As opposed to the Cox frailty model, the proposed methods demonstrate great potential in modeling multivariate survival data with a cure fraction. We illustrate the cure rate frailty models with a root canal therapy data set.

Variable Selection for Cox's proportional Hazards Model and Frailty Model

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave penalized likelihood approach is extended further to the Cox proportional hazards model and the Cox proportional hazards frailty model, two commonly used semi-parametric models in survival analysis. As a result, new variable selection procedures for these two commonly-used models are proposed. It is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function. Further, with a proper choice of the regularization parameter and the penalty function, the proposed estimators possess an oracle property. Standard error formulae are derived and their accuracies are empirically tested. Simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection, and they reduce model complexity as effectively as the best subset variable selection. Compared with the LASSO, which is the penalized likelihood method with the $L_1$ -penalty, proposed by Tibshirani, the newly proposed approaches have better theoretic properties and finite sample performance.