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Inference for a family of survival models encompassing the proportional hazards and proportional odds models.

For survival data regression, the Cox proportional hazards model is the most popular model, but in certain situations the Cox model is inappropriate. Various authors have proposed the proportional odds model as an alternative. Yang and Prentice recently presented a number of easily implemented estimators for the proportional odds model. Here we show how to extend the methods of Yang and Prentice to a family of survival models that includes the proportional hazards model and proportional odds model as special cases. The model is defined in terms of a Box-Cox transformation of the survival function, indexed by a transformation parameter rho. This model has been discussed by other authors, and is related to the Harrington-Fleming G(rho) family of tests and to frailty models. We discuss inference for the case where rho is known and the case where rho must be estimated. We present a simulation study of a pseudo-likelihood estimator and a martingale residual estimator. We find that the methods perform reasonably. We apply our model to a real data set.

Chlamydia Infections↗

Regression analysis of failure time data with informative interval censoring.

Interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed. Most existing approaches for analysing interval-censored failure time data assume that the censoring mechanism is independent of the true failure time. However, there are situations where this assumption may not hold. In this paper, we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed. The method makes use of the proportional hazards frailty model and an EM algorithm is presented for estimation. Finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an AIDS study.

Acquired Immunodeficiency Syndrome↗

Approaches in modelling long-term survival: an application to breast cancer.

Several modelling techniques have been proposed for non-proportional hazards. In this work we consider different models which can be classified into three wide categories: models with time-varying effects of the covariates; frailty models and cure rate models. We present those different extensions of the proportional hazards model on an application of 2433 breast cancer patients with a long follow-up. We comment on the differences and similarities among the models and evaluate their performance using survival and hazard plots, Brier scores and pseudo-observations.

Adult↗

The analysis of event history data: a review of progress and outstanding problems.

This paper reviews methods for the analysis of event history data by both parametric (exponential/Poisson) and semi-parametric methods. It identifies a need for software for handling the data structures of complex event histories and shows that, with such software, most Markov and semi-Markov models of event history data may be dealt with in the framework of generalized linear models. Finally, the emergent 'frailty' models for associated risks are discussed together with their implications for statistical software.

Data Interpretation, Statistical↗

Heterogeneity in survival analysis.

I discuss the impact of individual heterogeneity in survival analysis. It is well known that this phenomenon may distort what is observed. A general class of mixing (or frailty) distributions is applied, extending a model of Hougaard. The extension allows part of the population to be non-susceptible, and contains the traditional gamma distribution as a special case. I consider the mixing of both a constant and a Weibull individual rate, and also discuss the comparison of rates from two populations. A number of practical examples are mentioned. Finally, I analyse two data sets, the main one containing data from the Norwegian Cancer Registry on the survival of breast cancer patients. The statistical analysis is of necessity speculative, but may still provide some insight.

Actuarial Analysis↗

Analysis of dependent survival data applied to lifetimes of amalgam fillings.

When studying lifetimes of amalgam fillings, one is faced with the fact that each patient may contribute multiple survival data. This creates a dependence problem, and some methods for solving it are presented here. Analysis for individual patients with simple approaches for combining data is discussed first. Then a parametric frailty model is applied to analyse variation within and between patients. The results are presented in the form of an empirical Bayes estimate for each patient.

Adult↗

Analysis of recurrent failure times data: should the baseline hazard be stratified?

Over the past two decades, a variety of fruitful statistical methods for the analysis of recurrent events has been proposed for the estimation of covariates effect using the Cox proportional hazard model. Besides frailty modelling, two simple trends of modelling have been developed: the first one uses stratification on the rank of the event, whereas the second one, more closely related to Poisson processes theory, does not use stratification. Although they both take into account the correlation of the unit failure times, each of these approaches emphasizes a different aspect of the underlying point process and there is still an ongoing debate concerning the most appropriate method. The aim of this paper is to stress current interests and trends concerning these two approaches. For each model, main statistical methods for estimating the covariates effects are presented. Methods are illustrated and compared in two randomized clinical trials which involve recurrences of severe adverse events following chemotherapy in 938 patients with chronic lymphocytic leukaemia, and recurrences of infectious rhinitis episodes in 327 patients. The discussion, based on the previous examples and on the properties of underlying statistical inference, deals with the appropriateness of the model choice, which is closely related to the data structure.

Adjuvants, Immunologic↗

Poisson regression in mapping cancer mortality.

The aim of this study was to map standardized mortality ratios (SMRs) of specific cancers in Argentina and to examine some ecological relationships using Poisson regression, Poisson regression with frailties, and empirical Bayes estimates. Mortality data for lung cancer, nonmelanoma skin cancer, melanoma, and stomach cancer were obtained from national registers for the period 1989-1993. Overcrowding and unsatisfied basic needs (UBN) were used as indicators of socioeconomic status and people working permanently on farms as an indicator of rural activity. Empirical Bayes estimates provided a good solution for mapping rare causes of cancer when random fluctuations of observed deaths are important, as in the case of nonmelanoma skin cancer (NMSC) and melanoma. In the case of lung and stomach cancers the main improvement was the attenuation of confidence intervals. Lung cancer rates (males and females) were higher in jurisdictions with better socioeconomic status. When the variable UBN was categorized in tertiles (<20, 20-27, and 28% and higher) the rate ratios of lung cancer in men fell to 0.82 IC 95% (0. 78-0.85) in those with UNB index among 20-27% with respect to the reference level and to 0.56 IC 95% (0.54-0.59) in those with more than 28%. In contrast, stomach cancer rates were associated with worse economic conditions. NMSC and melanoma showed different patterns. The former was associated with working on farms, while the latter was not. Neither NMSC nor melanoma was increased in areas affected by Antarctica's ozone hole. Research appears to be warranted to further investigate associations of lung cancer with smoking and behavior in women living in southern Argentinean provinces. Public education must continue to promote personal responsibility in the intervention process to reduce the morbidity and mortality associated with cancers, such as lung and skin cancer, which are partially avoidable through behavioral changes.

Age Factors↗

Modelling conditional distributions in bivariate survival.

Conditional distributions for bivariate survival can be obtained via a model for the joint distribution, or, as has sometimes been suggested, by modelling the conditioned variable directly, with the conditioning variable included as a covariate. A quantitative comparison of estimated covariate effects and predictive distributions under the two approaches is given. The results are illustrated in a novel frailty application.

Humans↗

The effects of health histories on stochastic process models of aging and mortality.

A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in "fixed frailty" population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95+) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.

Aging↗

Unexpected consequences of deinstitutionalization of the mentally disabled elderly.

An unexpected consequence of the rapid deinstitutionalization of state mental hospital patients has been a sharp rise in posttransfer mortality among the elderly. Considerable evidence suggests that outcome is mediated by two factors. Elderly patients with certain characteristics - especially physical frailty and severe cognitive impairement - comprise a high-risk subgroup for whom relocation is likely to be fatal. Among other elderly persons, environmental, personality and personality-environment congruence are associated with posttransfer prognosis. The studies reviewed indicate that the therapeutic value of deinstitutionalization for mentally disabled elderly persons is problematic.

Aged↗

Modeling unemployment duration in a dependent competing risks framework: identification and estimation.

Three Mixed Proportional Hazard models for estimation of unemployment duration when attrition is present are considered. The virtue of these models is that they take account of dependence between failure times in a multivariate failure time distribution context. However, identification in dependent competing risks models is not straightforward. We show that these models, independently derived, are special cases of a general frailty model. It is also demonstrated that the three models are identified by means of identification of the general model. An empirical example illustrates the approach to model dependent failure times.

Humans↗

Fitting Weibull duration models with random effects.

Duration time models often should include correlated failure times, due to clustered data. These random effects hierarchical models sometimes are called "frailty models" when used for survival analyses. The data analyzed here involve such correlations because patient level outcomes (the times until graft failure following kidney transplantation) are observed, but patients are clustered in different transplant centers. We describe fitting such models by combining two kinds of software, one for parametric survival regression models, and the other for doing Poisson regression in a hierarchical setting. The latter is implemented by using PRIMM (Poisson Regression and Interactive Multilevel Modeling) methods and software (Christiansen & Morris, 1994a). An illustrative example for profiling data is included with k = 11 kidney transplant centers and N = 412 patients.

Graft Survival↗

Score test of homogeneity for survival data.

If follow-up is made for subjects which are grouped into units, such as familial or spatial units then it may be interesting to test whether the groups are homogeneous (or independent for given explanatory variables). The effect of the groups is modelled as random and we consider a frailty proportional hazards model which allows to adjust for explanatory variables. We derive the score test of homogeneity from the marginal partial likelihood and it turns out to be the sum of a pairwise correlation term of martingale residuals and an overdispersion term. In the particular case where the sizes of the groups are equal to one, this statistic can be used for testing overdispersion. The asymptotic variance of this statistic is derived using counting process arguments. An extension to the case of several strata is given. The resulting test is computationally simple; its use is illustrated using both stimulated and real data. In addition a decomposition of the score statistic is proposed as a sum of a pairwise correlation term and an overdispersion term. The pairwise correlation term can be used for constructing a statistic more robust to departure from the proportional hazard model, and the overdispersion term for constructing a test of fit of the proportional hazard model.

Graft Rejection↗

Ileostomy options. Asking the right questions.

The patient requiring ileostomy may have the opportunity to choose from four options. The Brooke ileostomy has afforded thousands of patients a secure, comfortable life. Appliances adhere well, and complications are few. The continent ileostomy or Kock pouch permits a patient to forego the wearing of an appliance. It is about 90 per cent successful but has a significant complication rate. Crohn's disease and physical frailties preclude its use. In "endorectal pull-through," the colon and rectal mucous membrane are removed to cure polyposis or ulcerative colitis. The ileum is led through the rectal muscular cylinder and anastomosed to the anus. The operation is tedious and not uniformly successful. A period of training must follow. It is unfit for people with Crohn's disease. Ileal anastomosis to a rectal segment is simpler but leaves disease behind. It may be used in Crohn's disease but may expose the patient to the hazard of recurrent disease or cancer. We must understand and ask the right questions if we are to give our patients the right answers.

Colitis, Ulcerative↗

Multidimensional assessment and risk factors for prolonged hospitalization in the elderly.

BACKGROUND AND AIMS: Frailty, multiple pathologies, functional impairment and socioeconomic conditions can prolong the length of hospitalization in the elderly. The aim of our study was to analyze risk factors for prolonged hospitalization. METHODS: Our sample included 1054 patients consecutively admitted to the University Department of Geriatric Medicine of Torino, Italy. We examined some demographic variables (age, sex, socioeconomic conditions), affective, cognitive and functional status, main pathologies, and blood pressure and some hematological parameters (hemoglobin, creatinine, albumin, sodium). RESULTS: The number of functions lost to IADL and ADL, DMI (Dependent Medical Index) dependence, high levels of creatinine and low blood levels of albumin and sodium were associated with longer hospitalization, as also were the following clinical diagnoses: tumor, chronic obstructive pulmonary disease (COPD), hip fractures, peripheral arterial disease (PAD), and pressure sores. Independent predictors of prolonged hospitalization were: the number of functions lost to the ADL index, pressure sores, hip fracture, peripheral arterial disease with critical ischemia, and low levels of sodium. CONCLUSIONS: Multidimensional assessment is essential to identify medical, functional and socioeconomic problems, and can highlight risk factors for prolonged hospitalization.

Aged↗

Informed consent for research participation in frail older persons.

Informed consent has been the most scrutinized and controversial aspect of clinical research ethics. Institutional review boards (IRBs), government regulatory agencies, and the threat of litigation have all contributed to increasingly detailed consent documents that hope to ensure that subjects are not misled or coerced. Unfortunately, the growing regulatory burden on researchers has not succeeded in protecting subjects, but has rather made the consent process less effective and has discouraged research on vulnerable populations. As a matter of fact, investigators and ethicists continue to identify failures of the consenting process, particularly concerning participation in research of older individuals. The challenges involved in ensuring appropriate consent from the elderly include physical frailty, reduced autonomy and privacy, and impaired decision-making capacity due to dementia, delirium, or other neuropsychiatric illnesses. Ageism among investigators also contributes to failure of informed consent. The evaluation and continuing re-evaluation of an individual's decision-making capacity is critical but difficult. In the most extreme cases, the older adult's ability to participate in the consent process is clearly impaired. However, in many instances, the decision-making capacity is only partially impaired but declines during the course of a research project. Implementing methods of effective communication may enable many frail elderly individuals to make informed decisions. Special challenges are posed by research on end-of-life care, which typically involves frail, older subjects who are uniquely vulnerable, and research is conducted in institutional settings where subtle violations of autonomy are routine. Clearly, the frail elderly represent a vulnerable population that deserves special attention when developing and evaluating an informed consent process. Two important ethical conflicts should be kept in mind. First, although vulnerable older patients must be protected, protection should not prevent research on this important population. Similarly, because informed consent documents are often written to prevent legal jeopardy, these technical documents, expressed in language sometimes difficult to understand, can prevent comprehension of basic issues, defeating the ethical purpose of human protection.

Aged↗

Combined measurement of serum albumin and high-density lipoprotein cholesterol strongly predicts mortality in frail older nursing-home residents.

BACKGROUND AND AIMS: The aim of this study was to verify the hypothesis that a combined measurement of albumin and HDL-C might predict total mortality in institutionalized frail older residents. METHODS: Participants were 344 older subjects (272 F, 72 M), living in the "Istituto Riposo Anziani" (I.R.A.), a nursing-home located in Padova, North-east Italy. Functional status, comorbidity, and clinical chemistry parameters were evaluated at entry. All-cause mortality was evaluated after 2 and 4 years. The sample was divided into 4 groups by using the 50 degrees percentile of albumin and HDL-C as cut-off value. The mortality odds ratio (OR) was estimated by multivariate logistic regression analysis. RESULTS: Total mortality was 36.8% after 2 years and 51.8% after four years. A trend toward an increase in mortality from group 1 to 4 was observed (p for trend: 0.01). The OR for 2 and 4 years mortality was 3.83 (95% CI 1.86-7.58) and 2.66 (95% CI 1.37-5.17), respectively, in group 4 compared with group 1, after adjustment for age, gender, number of chronic diseases, functional status, BMI, diabetes, dementia, stroke, CHD, CHF, hypertension, depression, COPD, and total cholesterol levels. CONCLUSIONS: Among frail older nursing-home residents, simple measurement of serum albumin and HDL-C levels may be useful in identifying varying degrees of frailty.

Aged↗