Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Assessing time-by-covariate interactions in Cox proportional hazards regression models using cubic spline functions

This dissertation develops and explores the methodology for the use of cubic spline functions in assessing time-by-covariate interactions in Cox proportional hazards regression models. These interactions indicate violations of the proportional hazards assumption of the Cox model. Use of cubic spline functions allows for the investigation of the shape of a possible covariate time-dependence without having to specify a particular functional form. Cubic spline functions yield both a graphical method and a formal test for the proportional hazards assumption as well as a test of the nonlinearity of the time-by-covariate interaction. Five existing methods for assessing violations of the proportional hazards assumption are reviewed and applied along with cubic splines to three well known two-sample datasets. An additional dataset with three covariates is used to explore the use of cubic spline functions in a more general setting. ^

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Seismic hazards of the Iberian Peninsula - evaluation with Kernel functions

The seismic hazard of the Iberian Peninsula is analysed using a nonparametric methodology based on statistical kernel functions; the activity rate is derived from the catalogue data, both its spatial dependence (without a seismogenetic zonation) and its magnitude dependence (without using Gutenberg–Richter's law). The catalogue is that of the Instituto Geográfico Nacional, supplemented with other catalogues around the periphery; the quantification of events has been homogenised and spatially or temporally interrelated events have been suppressed to assume a Poisson process. The activity rate is determined by the kernel function, the bandwidth and the effective periods. The resulting rate is compared with that produced using Gutenberg–Richter statistics and a zoned approach. Three attenuation laws have been employed, one for deep sources and two for shallower events, depending on whether their magnitude was above or below 5. The results are presented as seismic hazard maps for different spectral frequencies and for return periods of 475 and 2475 yr, which allows constructing uniform hazard spectra.

Invisible work, unseen hazards: the health of women immigrant household service workers in Spain

BACKGROUND: Household service work has been largely absent from occupational health studies. We examine the occupational hazards and health effects identified by immigrant women household service workers. METHODS: Exploratory, descriptive study of 46 documented and undocumented immigrant women in household services in Spain, using a phenomenological approach. Data were collected between September 2006 and May 2007 through focus groups and semi-structured individual interviews. Data were separated for analysis by documentation status and sorted using a mixed-generation process. In a second phase of analysis, data on psychosocial hazards were organized using the Copenhagen Psychosocial Questionnaire as a guide. RESULTS: Informants reported a number of environmental, ergonomic and psychosocial hazards and corresponding health effects. Psychosocial hazards were especially strongly present in data. Data on reported hazards were similar by documentation status and varied by several emerging categories: whether participants were primarily cleaners or carers and whether they lived in or outside of the homes of their employers. Documentation status was relevant in terms of empowerment and bargaining, but did not appear to influence work tasks or exposure to hazards directly. CONCLUSIONS: Female immigrant household service workers are exposed to a variety of health hazards that could be acted upon by improved legislation, enforcement, and preventive workplace measures, which are discussed.

Welfare state regimes and gender inequalities in the exposure to work-related psychosocial hazards

Background: Gender inequalities in the exposure to work-related psychosocial hazards are well established. However, little is known about how welfare state regimes influence these inequalities. Objectives: To examine the relationship between welfare state regimes and gender inequalities in the exposure to work-related psychosocial hazards in Europe, considering occupational social class. Methods: We used a sample of 27, 465 workers from 28 European countries. Dependent variables were high strain, iso-strain, and effort-reward imbalance, and the independent was gender. We calculated the prevalence and prevalence ratio separately for each welfare state regime and occupational social class, using multivariate logistic regression models. Results: More female than male managers/professionals were exposed to: high strain, iso-strain, and effort–reward imbalance in Scandinavian [adjusted prevalence ratio (aPR) = 2·26; 95% confidence interval (95% CI): 1·87–2·75; 2·12: 1·72–2·61; 1·41: 1·15–1·74; respectively] and Continental regimes (1·43: 1·23–1·54; 1·51: 1·23–1·84; 1·40: 1·17–1·67); and to high strain and iso-strain in Anglo-Saxon (1·92: 1·40–2·63; 1·85: 1·30–2·64; respectively), Southern (1·43: 1·14–1·79; 1·60: 1·18–2·18), and Eastern regimes (1·56: 1·35–1·81; 1·53: 1·28–1·83). Conclusion: Gender inequalities in the exposure to work-related psychosocial hazards were not lower in those welfare state regimes with higher levels of universal social protection policies.