Effects of unmeasured heterogeneity in the linear transformation model for censored data

We investigate the effect of unobserved heterogeneity in the context of the linear transformation model for censored survival data in the clinical trials setting. The unobserved heterogeneity is represented by a frailty term, with unknown distribution, in the linear transformation model. The bias of the estimate under the assumption of no unobserved heterogeneity when it truly is present is obtained. We also derive the asymptotic relative efficiency of the estimate of treatment effect under the incorrect assumption of no unobserved heterogeneity. Additionally we investigate the loss of power for clinical trials that are designed assuming the model without frailty when, in fact, the model with frailty is true. Numerical studies under a proportional odds model show that the loss of efficiency and the loss of power can be substantial when the heterogeneity, as embodied by a frailty, is ignored. An erratum to this article can be found at     

The meaning of frailty according to Dutch older frail and non-frail persons

Frailty is a term often used by researchers and clinicians to describe a state in which older persons are at risk for adverse outcomes such as falls, disability, institutionalization and mortality. However, no study so far examined what frailty means to older persons. Therefore the aim of this study was to describe the meaning that older community-dwelling persons attach to frailty. Twenty-five semi-structured interviews were conducted. The interviews were analyzed using the grounded theory method. Frailty was described as being in poor health, having walking difficulties, feeling down, being anxious, having few social contacts and not being able to do the things one likes to do. Men described in more detail the physical dimension whereas women elaborated in more depth on the psychological and social component. Existing definitions of frailty should be adjusted to better reflect the meaning of frailty for older persons.     

中国老年人虚弱指数与死亡风险及队列差异

利用中国老年人健康长寿影响因素调查（ CLHLS ）2002－2011年跟踪调查数据,通过多种健康指标构建中国老年人虚弱指数,运用增长曲线模型和Cox等比例风险函数的研究方法,对中国老年人虚弱指数和死亡风险及其队列差异进行了深入分析。研究发现,女性虚弱指数比男性高,增长速度也比男性快,但是死亡风险比男性低;出生较晚的队列与出生早的队列相比,虚弱指数会更高,他们的增长程度更快;受教育程度高的老年人虚弱指数低,但是其增长速度却比受教育程度低的老年人要高。     

Association of the modified frailty index with adverse outcomes after penile prosthesis implantation

Objectives: To investigate frailty as a predictor of surgical outcome in elderly patients undergoing penile prosthesis implantation.

Material and methods: A total of 54 elderly patients, above 60 years of age, underwent penile prosthesis implantation between 2012 and 2014. Their data were collected and retrospectively analyzed. A modified frailty index (mFI) was calculated for each patient based on 11 risk factors from the Canadian Study of Health and Aging Frailty Index. The 1-year adverse outcomes were correlated with mFI, patients’ and procedure’s risk factors.

Results: Mean age was 64.9?±?5.2 years. No mortality was reported in our patients, however, one-year adverse outcomes were encountered in 43 (79.6%) patients. Among all studied variables, the 1-year adverse outcomes was not significantly association with mFI, but with preoperative glycosylated hemoglobin A1c (HbA1c) (p?=?0.031) and associated Peyronie’s disease (PD) (p?=?0.000). HbA1c, dyslipidemia, hypertension, PD and duration of the procedure were predictive of infection complications (p?Conclusions: mFI is not a predictive of post-penile prosthesis implantation adverse outcomes in elderly patients with impotence. Degree of diabetic control and association with PD was associated with the 1-year adverse outcomes and infection complications.     

Robust Poisson likelihood estimation for frailty Cox models: A simulation study

Frailty models can be fit as mixed-effects Poisson models after transforming time-to-event data to the Poisson model framework. We assess, through simulations, the robustness of Poisson likelihood estimation for Cox proportional hazards models with log-normal frailties under misspecified frailty distribution. The log-gamma and Laplace distributions were used as true distributions for frailties on a natural log scale. Factors such as the magnitude of heterogeneity, censoring rate, number and sizes of groups were explored. In the simulations, the Poisson modeling approach that assumes log-normally distributed frailties provided accurate estimates of within- and between-group fixed effects even under a misspecified frailty distribution. Non-robust estimation of variance components was observed in the situations of substantial heterogeneity, large event rates, or high data dimensions.     

Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing

This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family. This assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified. Another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution. As a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately. This paper therefore proposes a Bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates' effect on the distribution of the mixed effects.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

The Protective Impact of a Covariate on Competing Failures with an Example from a Bone Marrow Transplantation Study

Starting from an applied Bone Marrow Transplantation(BMT) study, the problem of “unexpected protectivity” in competing risks models is introduced, which occurs when one covariate shows a protective impact not expected from a medical perspective. Current explanations found in the statistical literature suggest that unexpected protectivity might be due to the lack of independence between the competing failures. Actually, in the presence of dependence, the Kaplan-Meier curves are not interpretable. Conversely, the cumulative incidence curves remain interpretable, and therefore seem to be a candidate for solving the problem. We discuss the particular nature of dependence in a competing risks framework and illustrate how this dependence may be created via a common frailty factor. A Monte Carlo experiment is set up which accounts also for the association between the observable covariates and the frailty factor. The aim of the experiment is to understand whether and how the bias showed by the estimates could be related to the omitted frailty variable. The results show that dependence alone does not cause false protectivity, and that the cumulative incidence curves suffer the same bias as the survival curves and therefore do not seem to be a solution to false protectivity. Conversely, false protectivity may occur according to the magnitude and the sign of the dependence between the frailty factor and the covariate. The paper ends with some suggestions for empirical research. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimating the association parameter for copula models under dependent censoring

Summary. Many biomedical studies involve the analysis of multiple events. The dependence between the times to these end points is often of scientific interest. We investigate a situation when one end point is subject to censoring by the other. The model assumptions of Day and co-workers and Fine and co-workers are extended to more general structures where the level of association may vary with time. Two types of estimating function are proposed. Asymptotic properties of the proposed estimators are derived. Their finite sample performance is studied via simulations. The inference procedures are applied to two real data sets for illustration.     

A Frailty Model in Crossover Studies with Time-to-Event Response Variable

In this article, we develop a model to study treatment, period, carryover, and other applicable effects in a crossover design with a time-to-event response variable. Because time-to-event outcomes on different treatment regimens within the crossover design are correlated for an individual, we adopt a proportional hazards frailty model. If the frailty is assumed to have a gamma distribution, and the hazard rates are piecewise constant, then the likelihood function can be determined via closed-form expressions. We illustrate the methodology via an application to a data set from an asthma clinical trial and run simulations that investigate sensitivity of the model to data generated from different distributions.