Estimation of a relative potency of two preparations with correlated responses

Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new tuberculins with respect to some international standards tested in experiments on guinea-pigs.     

Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling

The maximum likelihood estimator (MLE) and the likelihood ratio test (LRT) will be considered for making inference about the scale parameter of the exponential distribution in case of moving extreme ranked set sampling (MERSS). The MLE and LRT can not be written in closed form. Therefore, a modification of the MLE using the technique suggested by Maharota and Nanda (Biometrika 61:601–606, 1974) will be considered and this modified estimator will be used to modify the LRT to get a test in closed form for testing a simple hypothesis against one sided alternatives. The same idea will be used to modify the most powerful test (MPT) for testing a simple hypothesis versus a simple hypothesis to get a test in closed form for testing a simple hypothesis against one sided alternatives. Then it appears that the modified estimator is a good competitor of the MLE and the modified tests are good competitors of the LRT using MERSS and simple random sampling (SRS).     

Consistency of minimizing a penalized density power divergence estimator for mixing distribution

In this paper, we study the MDPDE (minimizing a density power divergence estimator), proposed by Basu et al. (Biometrika 85:549–559, 1998), for mixing distributions whose component densities are members of some known parametric family. As with the ordinary MDPDE, we also consider a penalized version of the estimator, and show that they are consistent in the sense of weak convergence. A simulation result is provided to illustrate the robustness. Finally, we apply the penalized method to analyzing the red blood cell SLC data presented in Roeder (J Am Stat Assoc 89:487–495, 1994). This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.     

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

Link-tracing sampling with an initial sequential sample of sites: Estimating the size of a hidden human population

We proposed a modification to the variant of link-tracing sampling suggested by Félix-Medina and Thompson [M.H. Félix-Medina, S.K. Thompson, Combining cluster sampling and link-tracing sampling to estimate the size of hidden populations, Journal of Official Statistics 20 (2004) 19–38] that allows the researcher to have certain control of the final sample size, precision of the estimates or other characteristics of the sample that the researcher is interested in controlling. We achieve this goal by selecting an initial sequential sample of sites instead of an initial simple random sample of sites as those authors suggested. We estimate the population size by means of the maximum likelihood estimators suggested by the above-mentioned authors or by the Bayesian estimators proposed by Félix-Medina and Monjardin [M.H. Félix-Medina, P.E. Monjardin, Combining link-tracing sampling and cluster sampling to estimate the size of hidden populations: A Bayesian-assisted approach, Survey Methodology 32 (2006) 187–195]. Variances are estimated by means of jackknife and bootstrap estimators as well as by the delta estimators proposed in the two above-mentioned papers. Interval estimates of the population size are obtained by means of Wald and bootstrap confidence intervals. The results of an exploratory simulation study indicate good performance of the proposed sampling strategy.     

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model. The authors would like to thank the editor and referees for their helpful comments. This work was supported by CNPq, Brazil.