On Generalized Log-Logistic Model for Censored Survival Data

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling cases where the hazard rate is non-monotonic. For such cases, log-logistic model is frequently used. However, due to the symmetric property of the log-logistic model, it may be poor for the cases where the hazard rate is skewed or heavily tailed. In this paper, we suggest a generalization of the log-logistic model by introducing a shape parameter. This generalized model is then applied to fit the lung cancer data of Prentice (1973). The results seem to improve over those obtained by using the log-logistic model.     

A Multivariate Permutation Test for the Analysis of Arbitrarily Censored Survival Data

The exact generalization of GEHAN's (1965) two-sample test for arbitrarily censored survival data has been overlooked by subsequent work on the multisample problem. We give this general covariance matrix and show how it may be used in test procedures. While this permutation test is less powerful than its competitors in cases where both apply, it may be used on types of data not previously discussed.     

Randomization Tests for Censored Survival Distributions

This paper discusses the application of randomization tests to censored survival distributions. The three types of censoring considered are those designated by MILLER (1981) as Type 1 (fixed time termination), Type 2 (termination of experiment at r-th failure), and random censoring. Examples utilize the Gehan scoring procedure. Randomization tests for which computer programs already exist can be applied to a variety of experimental designs, regardless of the presence of censored observations.     

Methods for Fitting the Right-Truncated Weibull Distribution to Life-Test and Survival Data

This paper develops mathematical and computational methods for fitting, by the method of maximum likelihood (ML), the two-parameter, right-truncated Weibull distribution (RTWD) to life-test or survival data. Some important statistical properties of the RTWD are derived and ML estimating equations for the scale and shape parameters of the RTWD are developed. The ML equations are used to express the scale parameter as an analytic function of the shape parameter and to establish a computationally useful lower bound on the ML estimate of the shape parameter. This bound is a function only of the sample observations and the (known) truncation point T. The ML equations are reducible to a single nonlinear, transcendental equation in the shape parameter, and a computationally efficient algorithm is described for solving this equation. The practical use of the methods is illustrated in two numerical examples.     

A Power Law Model for Survival Data Using GLIM

This paper proposes a regression model for the Weibull survival distribution of which the scale parameter is a power function of covariates. The estimation of parameters for partially censored data is pursued by using a statistical package called GLIM. Two sets of carcinogenic data are used to illustrate this procedure.     

A Test of Equality of Survival Distributions for Two Sample Censored Grouped Survival Data

A common testing problem for a life table or survival data is to test the equality of two survival distributions when the data is both grouped and censored. Several tests have been proposed in the literature which require various assumptions about the censoring distributions. It is shown that if these conditions are relaxed then the tests may no longer have the stated properties. The maximum likelihood test of equality when no assumptions are made about the censoring marginal distributions is derived. The properties of the test are found and it is compared to the existing tests. The fact that no assumptions are required about the censoring distributions make the test a useful initial testing procedure.     

Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.     

A Dynamic Logistic Regression Model for Multiple Spell Failure Time Data

The paper deals with discrete-time regression models to analyze multistate-multiepisode failure time data. The covariate process may include fixed and external as well as internal time dependent covariates. The effects of the covariates may differ among different kinds of failures and among successive episodes. A dynamic form of the logistic regression model is investigated and maximum likelihood estimation of the regression coefficients is discussed. In the last section we give an application of the model to the analysis of survival time after breast cancer operation.     

A Bayesian Decision Procedure for Selecting Prognostic Variables Associated with Survival for Data in which Censoring is Prevalent

A Bayesian procedure is developed for the selection of concomitant variables in survival models. The variables are selected in a step-up procedure according to the criterion of maximum expected likelihood, where the expectation is over the prior parameter space. Prior knowledge of the influence of these covariates on patient prognosis is incorporated into the analysis. The step-up procedure is stopped when the Bayes factor in favor of omitting the variable selected in a particular step exceeds a specified value. The resulting model with the selected variables is fitted using Bayes estimates of the coefficients. This technique is applied to Hodgkin's disease data from a large Cooperative Clinical Trial Group and the results are compared to the results from the classical likelihood selection procedure.     

A Generalization of the Intraclass Tau Correlation for Tied and Censored Data

Intraclass tau correlations and a corresponding asymptotic permutation test have already been derived by WHITFIELD (1949), though for continuous data only. WHITFIELD'S concepts are now generalized for use with tied and censored data and a suggestion is made for the application of the methods to arbitrary and varying group sizes. Special attention is given to their application to dichotomous data. Extensive simulations confirming the safe use of the asymptotic test even for samples of moderate size are reported and calculated examples with data from twin-births and kidney transplantations presented.     

A Two Sample CRAMÉR-VON MISES Test for Randomly Censored Data

A CRAMÉR-VON MISES type statistic is introduced for testing the equality of the underlying survival distributions of two populations when observations are subject to arbitrary right censorship. The statistic is appropriate in testing problems where a two-sided alternative is of interest. The asymptotic distribution of the statistic is found; under certain circumstances, the limiting distribution coincides with that of a one sample CRAMÉR-VON MISES type statistic for randomly censored data investigated previously. Approximations to the asymptotic distribution are discussed; an example is given.     

Tests for Equality of Several Binomial Populations Against an Order Restricted Alternative and Model Selection for One-Dimensional Multinomials

The problem of testing the equality of several binomial population against an order restricted alternative and model selection for one-dimensional multinomials is studied. Test procedures are proposed. The asymptotic distribution of the test statistics are obtained. Comparisons are made with other test statistics including the likelihood ratio test for stochastic ordering. Also alternatives which does not depend on the distribution of test statistic is proposed.     

A Model for the Censoring Process in Incomplete Repeated Measurement Experiments

Premature terminations or dropouts occur often in repeated measurement experiments. A number of methods have been proposed to analyze such data but most of them assume that the censoring mechanism is, within each group, unaffected by the mechanism generating the response variables. In this paper, we propose a model for the censoring mechanism that generates dropouts. We then show how this model can be used to check whether the censoring mechanism is affected by the response variables and other covariates. Finally, the methods of the paper are applied to the “Halothane” data set.     

Gamma frailty model for linkage analysis with application to interval-censored migraine data

For many diseases, it seems that the age at onset is geneticallyinfluenced. Therefore, the age-at-onset data are often collectedin order to map the disease gene(s). The ages are often (right)censored or truncated, and therefore, many standard techniquesfor linkage analysis cannot be used. In this paper, we presenta correlated frailty model for censored survival data of siblings.The model is used for testing heritability for the age at onsetand linkage between the loci and the gene(s) that influence(s)the survival time. The model is applied to interval-censoredmigraine twin data. Heritability (obtained from the frailtiesrather than actual onset times) was estimated as 0.42; thisvalue was highly significant. The highest lod score, a scoreof 1.9, was found at the end of chromosome 19.     

A Mixed Model for Binary Data: The Modified X2-test

In this paper, a statistical model for clinical trials is presented for the special situation that a varying and unstructered number of binary responses is obtained from each subject. The assumptions of the model are the following: 1.) For each subject there is a (constant) individual Bernoulli parameter determining the distribution of the binary responses of this subject. 2.) The Bernoulli parameters associated with the subjects are realizations of independent random variables with distributions P_g in treatment group g(g = 1, 2, …, G). 3.) Given the value of the Bernoulli parameter, the observations are stochastically independent within each subject. Under these assumptions, a test statistic is derived to test the hypothesis H₀:E(P₁) = E(P₂) = … = E(P_G). It is proven and demonstrated by simulations, that the test statistic asymptotically (i.e. for a large number of subjects) follows the X²-distribution.     

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.     

A potentially functional polymorphism in the regulatory region of let-7a-2 is associated with an increased risk for diabetic nephropathy

Diabetic nephropathy (DN) is a major diabetic complication. However, the initiating molecular events triggering DN are unknown. MicroRNAs (miRNAs) have recently been identified as regulators that modulate the target gene expression and are involved in DN. However, the evidence of the mechanism is still insufficient in human samples. In this study, microRNA microarray assay was used to study gene differential expression profiles in DN and diabetes mellitus (DM) patients. One of the specific differentially expressed microRNAs, let-7a, was down-expressed in DN. Additionally, the expression of let-7a was also decreased in DN by real-time RT PCR in the patients' samples. Moreover, single nucleotide polymorphism (SNP) analysis was used to evaluate the relationship between three SNPs in the regulatory region of let-7a-2 gene and the risk of DN in the Chinese Han population by means of PCR-restriction fragment length polymorphism (RFLP-PCR). Also, the genotype and allele frequencies of let-7a-2 polymorphism were tested in 274 individuals, including 108 DN, 104 DM patients and 62 health control individuals (CON). It was found that a variant rs1143770 and the distributions of CT/TT genotypes were significantly different in three groups, and the CT + TT genotypes frequencies were significantly higher in DN and DM groups than that in CON group. In conclusion, let-7a-2 might participate in the regulation of the occurrence of DN, and a potential variant rs1143770 was significantly associated with the increased risk for DN.