A Statistical Issue About a Phase III Multi-regional Trial for the Survival Data under Accelerated Failure Time Model with Unrecognized Heterogeneity

For the time-to-event outcome, current methods for sample size determination are based on the proportional hazard model. However, if the proportionality assumption fails to capture the relationship between the hazard time and covariates, the proportional hazard model is not suitable to analyze survival data. The accelerated failure time model is an alternative method to deal with survival data. In this article, we address the issue that the relationship between the hazard time and the treatment effect is satisfied with the accelerated failure time model to design a multi-regional trial for a phase III clinical trial. The log-rank test is employed to deal with the heterogeneous effect size among regions. The test statistic for the overall treatment effect is used to determine the total sample size for a multi-regional trial and the consistent trend is used to rationalize partition sample size to each region.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Tolerance regions for random vectors and best linear predictors

In the case that vectors X and Y have a joint multivariate normal distribution, tolerance regions are found for the best linear predictor of Y using X if samples are used to estimate the regression coeffierante. Tolerance regions are also found for Y. In addition, simultaneous tolerance intervals for all linear functions of Y or of the best linear predictor of Y using X are found.     

A two-stage procedure for selecting the best of k exponential distributions

The problem of selecting the best of k exponential distributions with different guarantee times and the same unknown variance is considered. A two-stage procedure, similar to the one considered by Bechhofer, Dunnett and Sobel (1954), is given. Some specific guidelines for selecting the first-stage sample size are also given.     

Confidence sets based on sequential Tests

For given (small) a and β a sequential confidence set that covers the true parameter point with probability at least 1 - a and one or more specified false parameter points with probability at most β can be generated by a family of sequen-tial tests. Several situations are described where this approach would be a natural one. The following example is studied in some detail: obtain an upper (1 - α)-confidence interval for a normal mean μ (variance known) with β-protection at μ - δ(μ), where δ(.) is not bounded away from 0 so that a truly sequential procedure is mandatory. Some numerical results are presented for intervals generated by (1) sequential probability ratio tests (SPRT's), and (2) generalized sequential probability ratio tests (GSPRT's). These results indicate the superiority of the GSPRT-generated intervals over the SPRT-generated ones if expected sample size is taken as performance criterion     

A four-moment approach and other practical solutions to the behrens-f1sher problem

Fixed sample size approximately similar tests for the Behrens-Fisher problem are studied and compared with various other tests suggested in current sttistical methodelogy texts. Several fourmoment approxiamtely similar tests are developed and offered as alternatives. These tests are shown to be good practical solutions which are easily implemented in practice.     

A method of power assessment for tests comparing several treatments with a control

A method of power assessment for the problem of comparing several treatments with a control is considered. Power assessment is based on the power function of a two-sided hypothesis test that none of the treatment is different from the control. Normally distributed data and binary response data are considered. Minimum power levels are found under certain easily interpretable range conditions on the treatment and control means or success probabilities. Expressions are provided allowing simple computer evaluation of minimum guaranteed power levels, and some illustrative tables of power levels are given.     

Use of ranks in probability propoetional to size sampling

Use of ranks in unequal probability sampling is examined for sample selection, stratification as well as determining the strata boundaries. A few sampling schemes are proposed and investigated, For samples of size two, two sampling schemes and their 1PPS versions are discussed, An extension of these schemes to general sample sizes is outlined. Nonnegative unbiased variance estimators are proposed in each case, An empirical comparison is included.     

Estimation of Laspeyres Price Indexes Using the Prediction Approach for Finite Population Sampling

Estimators of chain and fixed-base Laspeyres price indexes are studied using the prediction approach to finite population sampling. The estimators include some that are based on those used in several U.S. government index programs and others derived from prediction models. Biases and variances of the estimators are studied for a case in which the reference period index weights are unknown for nonsample items. Under a model for a one-period price change in which items have common within-stratum means, unbiased estimators can be constructed, but under a more general regression model, special sample balance conditions are needed for unbiasedness of those estimators. The theory for the estimators of fixed-base indexes is illustrated in an empirical study using a population of items priced for the U.S. Consumer Price Index.