Confidence Intervals for the Relative Risk Ratio Parameter from Survival Data Under a Random Censorship Model in Biomedical and Epidemiologic Studies (By Simulation)

The present paper reports the results of a Monte Carlo simulation study to examine the performance of several approximate confidence intervals for the Relative Risk Ratio (RRR) parameter in an epidemiologic study, involving two groups of individuals. The first group consists of n₁ individuals, called the experimental group, who are exposed to some carcinogen, say radiation, whose effect on the incidence of some form of cancer, say skin cancer, is being investigated. The second group consists of n₂ individuals (called the control group) who are not exposed to the carcinogen. Two cases are considered in which the life times (or time to cancer) in the two groups follow (i) the exponential and (ii) the Weibull distributions. The case when the life times follow a Rayleigh distribution follows as a particular case. A general random censorship model is considered in which the life times of the individuals are censored on the right by random censoring times following (i) the exponential and (ii) the Weibull distributions. The Relative Risk Ratio parameter in the study is defined as the ratio of the hazard rates in the two distributions of the times to cancer. Approximate confidence intervals are constructed for the RRR parameter using its maximum likelihood estimator (m.l.e) and several other methods, including a method due to FIELLER. SPROTT'S (1973) and Cox's (1953) suggestions, as well as the Box-Cox (1964) transformation, are also utilized to construct approximate confidence intervals. The performance of these confidence intervals in small samples is investigated by means of some Monte Carlo simulations based on 500 random samples. Our simulation study indicates that many of these confidence intervals perform quite well in samples of size 10 and 15, in terms of the coverage probability and expected length of the interval.     

New Better than Used and Other Concepts for a Class of Life Distributions

It is well-known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed. As a simple application of the result proved in the paper, the life expectancy of an organism at age γ₀ involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.     

A Variation of the Method of Translation to Generate Bivariate and Multivariate Survival Distributions with Competing Risk or Reliability Applications

In the present paper, a variation of the methode of translation is discussed to generate bivariate or multivariate survival distributions starting a given bivariate or multivariate distribution which is not necessarily a life distribution. The new distribution has been called the dual of the given distribution. The duals of several bivariate and multivariate famílies of distributions are obtained, such as FRECHET'S , FARLIE -GUMBEL -MORGENSTERN'S , MARDIA'S and PLACKETT'S , among others. A necessary and sufficient condition is given for a bivariate distribution to be its own dual. Thus the present paper generates several survival distributions in addition to what are already available in the literature. These have important applications in competing risk theory or reliability of engineering systems.     

On a Statistical Model of Mortality in Chicken

In this paper a statistical model for analysing mortality pattern among chicken is developed. The model is used to infer the mortality characteristics in four strains of white leghorn birds.     

Nearest Neighbor Classification Rule for Mixtures of Discrete and Continuous Random Variables

In this paper very simple nonparametric classification rule for mixtures of discrete and continuous random variables is described. It is based on the method of nearest neighbor proposed by Cover and Hart (1967). The bounds on the limit of the nearest neighbor rule risks are given. Both lower and upper bound depend on the Bayes risk and the loss function. Finally the method is compared with other existing methods on some practical data set.     

Effects of Hydration on Steric and Electric Charge-Induced Interstitial Volume Exclusion—a Model

The presence of collagen and charged macromolecules like glycosaminoglycans (GAGs) in the interstitial space limits the space available for plasma proteins and other macromolecules. This phenomenon, known as interstitial exclusion, is of importance for interstitial fluid volume regulation. Physical/mathematical models are presented for calculating the exclusion of electrically charged and neutral macromolecules that equilibrate in the interstitium under various degrees of hydration. Here, a central hypothesis is that the swelling of highly electrically charged GAGs with increased hydration shields parts of the neutral collagen of the interstitial matrix from interacting with electrically charged macromolecules, such that exclusion of charged macromolecules exhibits change due to steric and charge effects. GAGs are also thought to allow relatively small neutral, but also charged macromolecules neutralized by a very high ionic strength, diffuse into the interior of GAGs, whereas larger macromolecules may not. Thus, in the model, relatively small electrically charged macromolecules, such as human serum albumin, and larger neutral macromolecules such as IgG, will have quite similar total volume exclusion properties in the interstitium. Our results are in agreement with ex vivo and in vivo experiments, and suggest that the charge of GAGs or macromolecular drugs may be targeted to increase the tissue uptake of macromolecular therapeutic agents.     

Cryopreservation of cornea: a low cooling rate improves functional survival of endothelium after freezing and thawing

AIM: To investigate the influence of low cooling rates on endothelial function and morphology of corneas frozen with propane-1,2-diol (PROH). METHODS: Rabbit corneas, mounted on support rings, were exposed to 1.4mol/l (10% v/v) PROH, seeded to initiate freezing, and cooled at 0.2 or 1 degrees C/min to -80 degrees C. Corneas were frozen immersed in liquid or suspended in air. After being held overnight in liquid nitrogen, corneas were warmed at 1 or 20 degrees C/min. After stepwise removal of the cryoprotectant, the ability of the endothelium actively to control corneal hydration was monitored during normothermic perfusion. Morphology was assessed after staining with trypan blue and alizarin red S, and by specular microscopy during perfusion. RESULTS: Functional survival was achieved only after slow cooling (0.2 degrees C/min) with the cornea immersed in the cryoprotectant medium, and rapid warming (20 degrees C/min). These conditions also gave the best morphology after freezing and thawing. CONCLUSION: Cooling rates lower than those typically applied to cornea improved functional survival of the endothelium. This result is in accord with previous observations showing the benefit of low cooling rates for cell monolayers [CryoLetters 17 (1996) 213-218].