Summary.-The parametric statistical models discussed include all those which have previously been described in the literature (Boag, 1948-lognormal; Berkson and Gage, 1952-negative exponential; Haybittle, 1959-extrapolated actuarial) and the basic data used to test the models comprised some 3000 case histories of patients treated between 1945 and 1962. The histories were followed up during the period 1969-71 and thus provided adequate information to validate long-term survival fractions predicted using short-term follow-up data. The results with the lognormal model showed that for series of staged carcinoma cervix patients treated during a 5-year period, satisfactory estimates of long-term survival fractions could be predicted after a minimum waiting period of 3 years for stages I and II, and 2 years for stage III. The model should be used with a value assumed for the lognormal paramater S in the range S = 0-35 to S = 0 40. Although alternative models often gave adequate predictions, the lognormal proved to be the most consistent model. This model may therefore now be used with more confidence for prospective studies on carcinoma cervix series and can provide good estimates of long-term

Summary.-In an experiment consisting of the continuous constant application of various carcinogenic regimens to a pure strain of experimental animals for a long period, the cancer incidence rates so caused may be studied and compared by the fit of an appropriate class of statistical distributions. In this paper we show that a Weibull distribution in which the age-specific cancer incidence rate rises as a power of time since first risk is more appropriate than a lognormal distribution. If the Weibull family of distributions is used, more information can be extracted from the data, and differences of toxicity between various regimens will not bias the comparison of their carcinogenic forces. CARCINOGENESIS produced by continued application of a carcinogen to mouse skin is becoming an increasingly common technique of assay of the carcinogenic forces of various substances. It has been pointed out (Pike and Roe, 1963) that a simple count of the number of cancers induced in a particular group is not a satisfactory measure of carcinogenic force, since cancers commonly occur late in life and a toxic treatment, although highly carcinogenic, may produce only a small number of cancers if it kills off a substantial fraction of the animals before the main cancer-susceptible age range is reached. Allowance for the effects of intercurrent deaths on the numbers of cancers produced is therefore necessary before treatments can be compared. The method of Pike and Roe allows the unbiased estimation of the proportion of animals which would still be alive at a particular time if all causes of death other than cancer were eliminated, and the authors suggest that a plot of this estimated proportion against time gives the best description possible of the carcinogenic effects of a treatment. Although

Cure rate estimation is an important issue in clinical trials for diseases such as lymphoma and breast cancer and mixture models are the main statistical methods. In the last decade, mixture models under different distributions, such as exponential, Weibull, log-normal and Gompertz, have been discussed and used. However, these models involve stronger distributional assumptions than is desirable and inferences may not be robust to departures from these assumptions. In this paper, a mixture model is proposed using the generalized F distribution family. Although this family is seldom used because of computational difficulties, it has the advantage of being very flexible and including many commonly used distributions as special cases. The generalised F mixture model can relax the usual stronger distributional assumptions and allow the analyst to uncover structure in the data that might otherwise have been missed. This is illustrated by fitting the model to data from large-scale clinical trials with long follow-up of lymphoma patients. Computational problems with the model and model selection methods are discussed. Comparison of maximum likelihood estimates with those obtained from mixture models under other distributions are included. � 1998 John Wiley & Sons, Ltd. 1.

Econometric duration analysis has become an important part of methodology in econometrics, bringing forth a plenty of applications. The probability distribution of the duration of a time span is modeled through its conditional hazard rate given the covariates. When some of the covariates are unobservable, the duration, given the observable covariates, has a mixture distribution. The paper surveys and discusses...

The National Institute of Mental Health (NIMH) Collaborative Study of Long-Term Maintenance Drug Therapy in Recurrent Affective Illness was a multicenter randomized controlled clinical trial designed to determine the efficacy of a pharmacotherapy for the prevention of the recurrence of unipolar affective disorders. The outcome of interest in this study was the time until the recurrence of a depressive episode. The data show much heterogeneity between centers for the placebo group. The aim of this paper is to use Bayesian hierarchical survival models to investigate the heterogeneity of placebo effects among centers in the NIMH study. This heterogeneity is explored in terms of the marginal posterior distributions of parameters of interest and predictive distributions of future observations. The Gibbs sampling algorithm is used to approximate posterior and predictive distributions. Sensitivity of results to the assumption of a constant hazard survival distribution at the first stage of th...

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Simultaneous discrimination among various parametric lifetime models is an important step in the parametric analysis of survival data. We consider a plot of the skewness versus the coefficient of variation for the purpose of discriminating among parametric survival models. We extend the method of Cox & Oakes from complete to censored data by developing an algorithm based on a competing risks model and kernel function estimation. A by-product of this algorithm is a nonparametric survival function estimate.

We consider the problem of modelling the failure-time distribution, where failure is due to two distinct causes. One approach is to adopt a two-component mixture model where the components correspond to the two different causes of failure. However, routine application of this approach with typical parametric forms for the component densities proves to be inadequate in modelling the time to a re-replacement operation or death after the initial replacement of the aortic valve in the heart by a prosthesis, such as a xenograft valve. Hence we consider modifications to the usual mixture model approach to handle situations where there exists a strong dependency between the failure times of the distinct causes. With these modifications, a suitable model is able to be provided for the distribution of the time to a re-replacement operation conditional on the age of the patient at the time of the initial replacement operation. The estimate so obtained by the probability that a patient of a given age will undergo a re-replacement operation provides a useful guide to heart surgeons on the type of valve to be used in view of the patient's age.