Analysis of Survival Data with Two Dependent Competing Risks

Here we consider a competing risks model where the two risks of interest are not independent. The dependence is due to the additive effect of an independent contaminating risk on two initially independent risks. The problem is identifiable when the three risks fllow independent exponential distributions and also when the two initial risks follow proportional hazards model. Procedures are suggested for estimation and testing hypotheses regarding the parameters of the three exponentials in the first can and the constant of proportionality in the second case, when the information available consists of the times to death and the causes of death of the individuals.     

Relating Cox's Proportional Hazard Model to the Exponential Model for Survival

An approximate representation is given for the partial likelihood estimate of the regression coefficient in Cox's proportional hazard model which indicates how it measures the association between survival time and covariate. The case of a single covariate is concentrated on. The representation is closely related to the first step of a Newton-Raphson iteration, i.e. to the score test. A similar representation for the Feigl-Zelen exponential model shows that a similar type of association is being measured, if observed lifetimes are interpreted as expected lifetimes of ordered exponentials. Necessary and sufficient conditions for the existence of Cox's estimate in the simple case are also written down.     

Application of the Principal Components Method and the Proportional Hazards Regression Model to Analysis of Survival Data

One of factor analysis techniques, viz. the principal components method, and the proportional hazards regression model (Cox, 1972) are applied in this work to study the significance of various factors characterizing the patient, the disease, and the method of treatment in the survival. The application of these methods to analysis of survival data for cervical cancer patients has shown, in particular, the tumor growth rate to be the crucial factor in distribution of the patients survival time and to be even more important than the therapy characteristics.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

植物种群具有常收获率的一类植物-食植者微分模型

讨论植物种群具有常收获率的一类植物－－食植者微分方程模型。分析了此系统当对植物种群的常收获率逐渐增大的过程中,在第一象限内轨线拓扑结构的变化规律,从而获知对植物种群不同程度的常收获率将对食植生态环境所产生影响的程度。     

两种群均具有常收获率或常投放率的Lotka-Volterra系统可以存在三个极限环

证明了两种群均具有常收获率或常投放率的Lotka-Volterra系统可以存在三个极限环。     

Hazard rates and causes of death in a captive group of crab-eating monkeys (Macaca fascicularis)

In an attempt to examine possible associations between stages of agespecific mortality and various causes of death, vital records of 159 male and 192 female crab-eating monkeys (Macaca fascicularis), housed as a single group, were analyzed. Survival and hazard rates associated with each of five distinct categories of causes of death were estimated for males and females, using the nonparametric kernel method. The obtained overall survival and hazard functions were similar to those reported previously for rhesus monkeys. Among two stages identified in age-specific mortality, the first stage, characterized by rapidly decreasing hazard rates up to about 1.5–2 years of age, was discriminated by the occurrence of deaths due to unfitness for postnatal life. The second stage lasted up to the age of 10–15 years and was largely characterized by a high incidence of violent deaths. The respective hazard rates in males and females attained peaks during the early reproductive period of life and markedly decreased thereafter. This pattern was interpreted to indicate that second stage mortality is unlikely related to senescence, but rather, seems to depend on extrinsic environmental factors. Thus, when considering overall hazard rates in Macaca fascicularis, the onset of senescence, as a result of the specific aspects of simian reproduction, may be hidden from view, and mortality due to aging may only be appreciable after 10 to 15 years of age. © 1993 Wiley-Liss, Inc.     

Assessment of Carcinogenic Risk and Non-Carcinogenic Health Hazard from Exposure to Toxicants in Water from the Southwestern Coastal River System in Ghana

This study evaluated cancer risk and non-cancer human health hazard from exposure to the toxicants such as As, Cu, Pb, Zn, Mn, and CN in water from a southwestern river system in Ghana that drains through gold mining areas, using 108 water samples collected with random sampling techniques and analyzed in accordance with standard methods of chemical analysis outlined by the U.S. Environmental Protection Agency (USEPA). The concentrations of Cu and Zn were within World Health Organization and USEPA guideline values; Mn, free cyanide, As, and Pb values in most cases either exceeded USEPA and WHO values or both. The concentrations of the toxicants were used as input parameters in the cancer and non-cancer study that was conducted in line with USEPA risk assessment guidelines. The results of As cancer health risk revealed higher risk cases in two locations (Potroase and Dominase); non-cancer health risk for As was higher in 10 of the 14 locations, with other metals being of health concern at few locations in the study area. In conclusion, the findings of this study hold several policy implications as residents of mining communities still depend on these water bodies as their source of drinking water.     

An Examination of the Relationship Between Resting Heart Rate Variability and Heart Rate Reactivity to a Mental Arithmetic Stressor

Resting heart rate variability can be an index of sympathetic or parasympathetic dominance, according to the frequency of the variability studied. Sympathetic dominance of this system has been linked to increased risk of cardiovascular disease (CVD). Similarly, rapid and dramatic increases in heart rate reactivity to a stressor task have also been suggested as indicating increased risk of CVD via atherogenesis. Although both of these variables have been related to the development of cardiovascular disease, and both may be related to increased sympathetic activity or parasympathetic withdrawal, most research studies have tended to focus on either variable independently of the other. In order to investigate whether these two indices of stressor reactivity were related in relatively young and healthy subjects, resting heart rate variability data were collected from 80 volunteers for 20 minutes. In addition, heart rate reactivity data were collected during a 2-minute mental arithmetic stressor, which has been previously shown to induce significant increases in heart rate. After classifying subjects according to whether their heart rate variability data were above or below the mean for their gender, heart rate reactivity data were examined via MANOVA to detect significant differences between subject groups. Females showed significant effects, and males showed nonsignificant trends, but these two sets of data were in different directions, suggesting that gender may be a confounding factor in the relationship between heart rate reactivity and heart rate variability.     

A solution to the problem of monotone likelihood in Cox regression

The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.     

Modelling Survival Data to Examine Length of Treatment Effectiveness in a Clinical Trial

In some clinical trials where the experimental treatment is found to be effective in increasing survival, an important question is how long should the patient remain under treatment. Although the trial may not be designed to specifically answer this question, comparisons of the hazard curves among the treatment groups can yield some useful information. The survival data may be modelled using a flexible set of hazard functions and specific models are then chosen for further examination. This paper illustrates the approach using data from the Beta-Blocker Heart Attack Trial. Parametric and semi-parametric models are fitted and likelihood methods are used to assess length of treatment effectiveness.     

gfp-Tagged Cells as a Useful Tool to Study the Survival of Escherichia coli in the Presence of the River Microbial Community

We have used an Escherichia coli strain DH5a containing pGreenTIR to study the survival of this bacterium in river water. As green fluorescence was maintained throughout survival both in dark and illuminated conditions, gfp-tagged E. coli cells were clearly distinguished from the microbial community of the river Butrón. gfp-tagged E. coli cells were monitored to estimate total density as well as the density of the culturable and viable (active electron transport system, CTC+) cells. Our results indicate that autochthonous bacteria and introduced E. coli are predated by flagellates. The autochthonous bacterial community behaves as predation-escaping prey, showing a tendency to cellular miniaturization and so maintaining the density of the population. In contrast, introduced E. coli behaves as predation-non-escaping prey, so E. coli was eliminated from the system. When comparing the elimination by predation of heat-treated and non-heated gfp-tagged E. coli cells we deduce that the flagellates do not discriminate between live and heat-treated cells. Finally, in the presence of the river microbial community, the E. coli cells appeared to be ingested before cellular deterioration could occur. Thus predation reduces the quantitative importance of the viable but nonculturable (VBNC) population of E. coli in the aquatic systems.     

Linear and Non Linear Competition Plots in the Deoxyribose Assay for Determination of Rate Constants for Reaction of non Steroidal Antiinflammatory Drugs with Hydroxyl Radicals

Performing the deoxyribose (DR) assay for determination of the rate constants for reaction of non steroidal antiinflammatory drugs with hydroxyl radicals led to some unusual competition plots. The molecules from the arylpropionic family of drugs: ibuprofen, flurbiprofen, ketoprofen and naproxen produced the linear relationship. However, acemetacin, diclofenac Na, flufenamic acid, indometacin, niflumic acid, tolmetin Na and sulindac presented non linear competition plots manifesting at relatively low drug concentrations. This effect was corrected by increasing DR concentrations from 2.8 mM to 15 mM. The modification did not affect rate constants values for those derivatives which already presented a linear plot at 2.8 mM, but allowed to calculate rate constants for other compounds. It is suggested that the experimental conditions have to be adapted particularly for those derivatives with a relatively high. rate constant for reaction with the radical species. The oxicam derivatives (tenoxicam and piroxicam) presented another kind of deviation that revealed a prooxidant effect in this system: non linear plots were also observed at relatively low drug concentrations, but in the opposite direction than for the other molecules. This last effect was independent of DR concentration but could be corrected by increasing ascorbate concentration in the system.     

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.     

Testing the Equality of the Intra‐Subject Treatment Covariance Matrices in a Crossover Study

In a 2 × 2 crossover bioavailability study, the sets of estimates of the pharmacokinetic parameters quite often have a symmetric covariance structure between the two treatments. For testing the equality of the intra‐subject covariance matrices for the two treatments in such studies, we suggest in this paper some statistical tests. When the response vectors are bivariate, we propose an exact test. Since the statistical procedures depend on the assumption of a symmetric covariance structure between the two treatments, we put forth some statistical tests for this assumption. We then apply the discussed tests to real data from a crossover bioavailability trial.     

The Role of the Metabolic Status of the Donor and the Recipient in Survival of a Skin Graft according to Histological Data

The role of the metabolic status of the donor and the recipient in graft survival was studied with skin grafting between genetically different mouse strains (BALB/C, C3HA, DBA/2, and C57Bl/6). It was concluded that the donor must have a lower metabolic rate than the recipient when the involvement of structural elements of the graft is required for healing in skin plastic surgery. In contrast, when it is necessary to strongly biologically stimulate the reparative processes of the recipient, the donor must have a higher metabolic rate than the recipient.