Generalized Survival Models Research Articles

The quick and the dead

The quick and the dead

A cure rate survival model under a hybrid latent activation scheme

In lifetimes studies, the occurrence of an event (such as tumor detection or death) might be caused by one of many competing causes. Moreover, both the number of causes and the time-to-event associated with each cause are not usually observable. The number of causes can be zero, corresponding to a cure fraction. In this article, we propose a method of estimating the numerical characteristics of unobservable stages (such as initiation, promotion and progression) of carcinogenesis from data on tumor size at detection in the presence of latent competing causes. To this end, a general survival model for spontaneous carcinogenesis under a hybrid latent activation scheme has been developed to allow for a simple pattern of the dynamics of tumor growth. It is assumed that a tumor becomes detectable when its size attains some threshold level (proliferation of tumorais cells (or descendants) generated by the malignant cell), which is treated as a random variable. We assume the number of initiated cells and the number of malignant cells (competing causes) both to follow weighted Poisson distributions. The advantage of this model is that it incorporates into the analysis characteristics of the stage of tumor progression as well as the proportion of initiated cells that had been 'promoted' to the malignant ones and the proportion of malignant cells that die before tumor induction. The lifetimes corresponding to each competing cause are assumed to follow a Weibull distribution. Parameter estimation of the proposed model is discussed through the maximum likelihood estimation method. A simulation study has been carried out in order to examine the coverage probabilities of the confidence intervals. Finally, we illustrate the usefulness of the proposed model by applying it to a real data involving malignant melanoma.

Consistent Estimation of the Expected Brier Score in General Survival Models with Right‐Censored Event Times

In survival analysis with censored data the mean squared error of prediction can be estimated by weighted averages of time-dependent residuals. Graf et al. (1999) suggested a robust weighting scheme based on the assumption that the censoring mechanism is independent of the covariates. We show consistency of the estimator. Furthermore, we show that a modified version of this estimator is consistent even when censoring and event times are only conditionally independent given the covariates. The modified estimators are derived on the basis of regression models for the censoring distribution. A simulation study and a real data example illustrate the results.

A Pseudo–Partial Likelihood Method for Semiparametric Survival Regression With Covariate Errors

This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive error model. It can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The estimator is shown to be consistent and asymptotically normal, and an estimate of the asymptotic covariance matrix is derived. Some extensions to general transformation survival models are indicated. Simulation studies are presented for a setup with a single error-prone binary covariate and a setup with a single error-prone normally distributed covariate. These simulation studies show that the method typically produces estimates with low bias and confidence intervals with accurate coverage rates. Efficiency results relative to fully parametric maximum likelihood are also presented. The method is applied to data from the Framingham Heart Study.

Estimation of the non-isothermal inactivation patterns of Bacillus sporothermodurans IC4 spores in soups from their isothermal survival data

The isothermal survival curves of the heat resistant spores of Bacillus sporothermodurans IC4, in the range of 117–125 °C, were determined in chicken, mushroom and pea soups by the capillary method. They were all non-linear with a noticeable upper concavity and could be described by the equation log 10 [ N( t)/ N 0]=− b( T) t n with a fixed power, n, of the order of 0.7–0.8. The temperature dependence of b( T) could be described by the equation b( T)=log e{1+exp[ k( T− T c)]}, where T c is the temperature where intensive inactivation starts and k is the slope of b( T) at temperatures well above T c. They were 121–123 °C and 0.2–0.4 °C −1, respectively, depending on the soup. These parameters were used to estimate the survival curves of the spores in two non-isothermal heat treatments using the procedure originally proposed by Peleg and Penchina [Crit. Rev. Food Sci. Nutr. 40 (2000) 159]. The results were compared with experimental survival curves, determined by the direct injection method, in another laboratory. There was a general agreement, although not perfect, between the predicted and experimentally observed survival ratios. Also, the isothermal survival parameters, estimated directly from the non-isothermal inactivation data using the model, were in general agreement with those calculated from the isothermal data. This suggests that the heat inactivation patterns of B. sporothermodurans IC4 spores in soups can be at least roughly estimated using the same general survival model, which has until now only been experimentally validated for vegetative bacterial cells.

Estimating mean body masses of marine mammals from maximum body lengths

Generalized survival models were applied to growth curves published for 17 species of cetaceans (5 mysticetes, 12 odontocetes) and 13 species of pinnipeds (1 odobenid, 4 otariids, 8 phocids). The mean mass of all individuals in the population was calculated and plotted against the maximum body length reported for each species. The data showed strong linearity (on logarithmic scales), with three distinct clusters of points corresponding to the mysticetes (baleen whales), odontocetes (toothed whales), and pinnipeds (seals, sea lions, and walruses). Exceptions to this pattern were the sperm whales, which appeared to be more closely related to the mysticetes than to the odontocetes. Regression equations were applied to the maximum lengths reported for 76 species of marine mammals without published growth curves. Estimates of mean body mass were thus derived for 106 living species of marine mammals.

Survival in wild‐living mice*

AbstractThe survival of a mouse in the wild depends on its reaction to the environment (food, climate, social conditions, cover, disease and predation), and this depends on the condition or ‘vigour’ of the animal itself. In general an animal increases in vigour until adulthood, and then begins to decrease, in House mice, at an age of approximately 100 days. These changes can be described as ageing; they lead to the characteristic U‐shaped mortality curves deduced from life‐tables in a wide variety of mammalian species. Another factor that has to be taken into consideration is genotype, since animals of different genotype may respond differently to environmental stresses. A large number of deaths in wild‐living House mouse populations in Britain are temperature‐dependent. Animals may respond to cold either physiologically or behaviourally, but it is possible to distinguish between winter survivors and non‐survivors with a fair degree of accuracy on the basis of physiological measurements made in the autumn (i.e. before the time of environmental stress). Nevertheless, any general survival model must incorporate environmental, ontogenetic, and genetic factors and their interactions. A simple model is proposed.Animals are not always struggling for existence. They spend most of their time doing nothing in particular. But when they do begin, they spend the greater part of their lives eating (Charles Elton).