More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

Objective Bayesian Analysis of an Exponential Regression Model with Constrained Parameters Applied to Animal Digestibility

In animal digestibility the proportion of degraded food along the time has usually been modeled as a normal random variable with mean a function of the time and the following three parameters: the proportion of degraded food almost instantaneously, remaining proportion of food to be degraded, and velocity of degradation. The estimation of these parameters has been carried out mainly from a frequentist viewpoint by using the asymptotic distribution of the maximum likelihood estimator. This may give inadmissible estimates, such as values outside of the range of the parameters. This drawback could not appear if a Bayesian approach were adopted. In this article an objective Bayesian analysis is developed and illustrated on real and simulated data.     

A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.     

A New Method for Testing Interaction in Unreplicated Two-Way Analysis of Variance

For a two-way ANOVA table, with a single observation per cell, the standard approach is to assume that interaction between the two factors is negligible, and to base inferences about the main factors on the model without interaction. But there is no totally satisfactory method for testing if interaction can be ignored. The classical approach is to specify a functional form for the interaction terms, involving a small number of parameters, and then use an appropriate test. But, such tests have low power if the functional form is inappropriate. This has led researchers to propose tests which do not assume a specific form for the interactions. In this article, we present a new approach for testing interaction which also does not assume a specific form for the interaction. This approach is fairly simple and flexible, and its usefulness is illustrated with several examples. We also present a general result which shows that there is no test of interaction with good power properties against all types of interaction.     

Parameter Estimation for the Discrete Stable Family

The discrete stable family constitutes an interesting two-parameter model of distributions on the non-negative integers with a Paretian tail. The practical use of the discrete stable distribution is inhibited by the lack of an explicit expression for its probability function. Moreover, the distribution does not possess moments of any order. Therefore, the usual tools—such as the maximum-likelihood method or even the moment method—are not feasible for parameter estimation. However, the probability generating function of the discrete stable distribution is available in a simple form. Hence, we initially explore the application of some existing estimation procedures based on the empirical probability generating function. Subsequently, we propose a new estimation method by minimizing a suitable weighted L ²-distance between the empirical and the theoretical probability generating functions. In addition, we provide a goodness-of-fit statistic based on the same distance.     

Shannon Information Properties of the Endpoints of Record Coverage

This paper addresses the largest and the smallest observations, at the times when a new record of either kind (upper or lower) occurs, which are it called the current upper and lower record, respectively. We examine the entropy properties of these statistics, especially the difference between entropy of upper and lower bounds of record coverage. The results are presented for some common parametric families of distributions. Several upper and lower bounds, in terms of the entropy of parent distribution, for the entropy of current records are obtained. It is shown that mutual information, as well as Kullback–Leibler distance between the endpoints of record coverage, Kullback–Leibler distance between data distribution, and current records, are all distribution-free.     

Presmoothed Estimation with Left-Truncated and Right-Censored Data

We propose a new method to estimate the cumulative hazard function and the corresponding distribution function of survival times under randomly left-truncated and right-censored observations (LTRC). The new estimators are based on presmoothing ideas, the estimation of the conditional expectation m of the censoring indicator. An almost sure representation for both estimators is established, from which a strong consistency rate and asymptotic normality are derived. It is shown that the presmoothed modification leads to a gain in terms of asymptotic mean squared error. This efficiency with respect to the classical estimators is also shown in a simulation study. Finally, an application to a real data set is provided.     

The 3 F 2 with Complex Parameters as Generating Function of Discrete Distribution

A new discrete family of probability distributions that are generated by the ₃ F ₂ function with complex parameters is presented. Some of the properties of this new family are studied as well as methods of estimation for its parameters. It affords considerable flexibility of shape which turns the distribution into an appropriate candidate for modeling data that cannot be adequately fitted by classical families with fewer parameters. Finally, three examples in the fields of Agriculture and Education are included in order to show the versatility and utility of this distribution.     

Comparing Equal-Tail Probability and Unbiased Confidence Intervals for the Intraclass Correlation Coefficient

The conventional confidence interval for the intraclass correlation coefficient assumes equal-tail probabilities. In general, the equal-tail probability interval is biased and other interval procedures should be considered. Unbiased confidence intervals for the intraclass correlation coefficient are readily available. The equal-tail probability and unbiased intervals have exact coverage as they are constructed using the pivotal quantity method. In this article, confidence intervals for the intraclass correlation coefficient are built using balanced and unbalanced one-way random effects models. The expected length of confidence intervals serves as a tool to compare the two procedures. The unbiased confidence interval outperforms the equal-tail probability interval if the intraclass correlation coefficient is small and the equal-tail probability interval outperforms the unbiased interval if the intraclass correlation coefficient is large.