Approximate confidence intervals for a ratio of two variance components

New approximate confidence intervals for the ratio of two variance components in an unbalanced mixed .linear model with a single set of random effects are proposed. Contrary to the confidence intervals known in the literature the new intervals preserve the confidence coefficient and cover the exact confidence interval which, however, is not easy to establish as it requires the solution of complicated nonlinear equations.     

A class of confidence intervals for sequential phase II clinical trials with binary outcome

The phase II clinical trials often use the binary outcome. Thus, accessing the success rate of the treatment is a primary objective for the phase II clinical trials. Reporting confidence intervals is a common practice for clinical trials. Due to the group sequence design and relatively small sample size, many existing confidence intervals for phase II trials are much conservative. In this paper, we propose a class of confidence intervals for binary outcomes. We also provide a general theory to assess the coverage of confidence intervals for discrete distributions, and hence make recommendations for choosing the parameter in calculating the confidence interval. The proposed method is applied to Simon's [14] optimal two-stage design with numerical studies. The proposed method can be viewed as an alternative approach for the confidence interval for discrete distributions in general.     

Approximate and generalized pivotal quantities for deriving confidence intervals for the offset between two clocks

Development of algorithms that estimate the offset between two clocks has received a lot of attention, with the motivating force being data networking applications that require synchronous communication protocols. Recently, statistical modeling techniques have been used to develop improved estimation algorithms with the focus being obtaining robust estimators in terms of mean squared error. In this paper, we extend the use of statistical modeling techniques to address the construction of confidence intervals for the offset parameter. We consider the case where the distributions of network delays are members of a scale family. Our results include an asymptotic confidence interval and a generalized confidence interval in the sense of [S. Weerahandi, Generalized confidence intervals, Journal of the American Statistical Association 88 (1993) 899–905. Correction in vol. 89, p. 726, 1994]. We compare and contrast the two approaches for obtaining a confidence interval, and illustrate specific applications using exponential, Rayleigh and heavy-tailed Weibull network delays as concrete examples.     

Comparing the overlapping of two independent confidence intervals with a single confidence interval for two normal population parameters

Two overlapping confidence intervals have been used in the past to conduct statistical inferences about two population means and proportions. Several authors have examined the shortcomings of Overlap procedure and have determined that such a method distorts the significance level of testing the null hypothesis of two population means and reduces the statistical power of the test. Nearly all results for small samples in Overlap literature have been obtained either by simulation or by formulas that may need refinement for small sample sizes, but accurate large sample information exists. Nevertheless, there are aspects of Overlap that have not been presented and compared against the standard statistical procedure. This article will present exact formulas for the maximum % overlap of two independent confidence intervals below which the null hypothesis of equality of two normal population means or variances must still be rejected for any sample sizes. Further, the impact of Overlap on the power of testing the null hypothesis of equality of two normal variances will be assessed. Finally, the noncentral t-distribution is used to assess the Overlap impact on type II error probability when testing equality of means for sample sizes larger than 1.     

Randomized confidence intervals of a parameter for a family of discrete exponential type distributions

For a family of one-parameter discrete exponential type distributions, the higher order approximation of randomized confidence intervals derived from the optimum test is discussed. Indeed, it is shown that they can be asymptotically constructed by means of the Edgeworth expansion. The usefulness is seen from the numerical results in the case of Poisson and binomial distributions.     

On exact confidence intervals in a competing risks model with generalized hybrid type-I censored exponential data

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints.     

Approximate confidence intervals for a linear combination of binomial proportions: A new variant

We propose a new adjustment for constructing an improved version of the Wald interval for linear combinations of binomial proportions, which addresses the presence of extremal samples. A comparative simulation study was carried out to investigate the performance of this new variant with respect to the exact coverage probability, expected interval length, and mesial and distal noncoverage probabilities. Additionally, we discuss the application of a criterion for interpreting interval location in the case of small samples and/or in situations in which extremal observations exist. The confidence intervals obtained from the new variant performed better for some evaluation measures.     

Convergence rates of sequential confidence intervals and tests for the mean of a u-statistic

Csenki(1980a) utilized the rate of convergence results of Landers and Rogge(1976b) for suitably normalized random means to obtain the rate of convergence of the coverage probability for Chow-Robbins'(1965) fixed-width confidence interval procedure. In this paper, we utilize the rate of convergence results of Ghosh and DasGupta(1980) for suitably normalized random U-statistics to derive the rate of convergence of the coverage probability for estimating the mean of a U-statistic through Sproule's(1969, 1974) procedure. We show that Csenki's(1980a) convergence rate can be achieved with a substantial economy on moment condition. We also propose a two-stage procedure for this pro-1970 AMS Classification: 60F05, 62L10, 62G10     

Group sequential analysis op a clinical trial with repeated measurements

Recently some work has been done in group sequential analysis for comparing two treatments with respect to the rate of change in a repeated measures design with staggered subject entries. We relax the involved assumption of linearity for the time-response curve and propose a group sequential procedure assuming multivariate normality with an ante-dependence structure for the repeated measurements obtained at protocol scheduled visits. The exit probabilities are determined through an a-spending function proposed by Lan and DeMets. A numerical example is given to illustrate the methodology.     

A sequential design for a clinical trial with a linear prognostic factor

We study a randomized adaptive design to assign one of the L$L$ treatments to patients who arrive sequentially by means of an urn model. At each stage n$n$, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?_Yn?1$0?Y_n?1$, and 1-_Yn$1-Y_n$ is distributed among the other treatments according to their performance until stage n-1$n-1$. Patients can be classified in K+1$K+1$ levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1$n-1$.     

Construction of fixed width confidence intervals for a Bernoulli success probability using sequential sampling: a simulation study

This article considers the construction of level 1?α fixed width 2d confidence intervals for a Bernoulli success probability p, assuming no prior knowledge about p and so p can be anywhere in the interval [0, 1]. It is shown that some fixed width 2d confidence intervals that combine sequential sampling of Hall [Asymptotic theory of triple sampling for sequential estimation of a mean, Ann. Stat. 9 (1981), pp. 1229–1238] and fixed-sample-size confidence intervals of Agresti and Coull [Approximate is better than ‘exact’ for interval estimation of binomial proportions, Am. Stat. 52 (1998), pp. 119–126], Wilson [Probable inference, the law of succession, and statistical inference, J. Am. Stat. Assoc. 22 (1927), pp. 209–212] and Brown et al. [Interval estimation for binomial proportion (with discussion), Stat. Sci. 16 (2001), pp. 101–133] have close to 1?α confidence level. These sequential confidence intervals require a much smaller sample size than a fixed-sample-size confidence interval. For the coin jamming example considered, a fixed-sample-size confidence interval requires a sample size of 9457, while a sequential confidence interval requires a sample size that rarely exceeds 2042.     

An alternative to confidence intervals constructed after a Hausman pretest in panel data

Consider panel data modelled by a linear random intercept model that includes a time‐varying covariate. Suppose that our aim is to construct a confidence interval for the slope parameter. Commonly, a Hausman pretest is used to decide whether this confidence interval is constructed using the random effects model or the fixed effects model. This post‐model‐selection confidence interval has the attractive features that it (a) is relatively short when the random effects model is correct and (b) reduces to the confidence interval based on the fixed effects model when the data and the random effects model are highly discordant. However, this confidence interval has the drawbacks that (i) its endpoints are discontinuous functions of the data and (ii) its minimum coverage can be far below its nominal coverage probability. We construct a new confidence interval that possesses these attractive features, but does not suffer from these drawbacks. This new confidence interval provides an intermediate between the post‐model‐selection confidence interval and the confidence interval obtained by always using the fixed effects model. The endpoints of the new confidence interval are smooth functions of the Hausman test statistic, whereas the endpoints of the post‐model‐selection confidence interval are discontinuous functions of this statistic.     

Evaluation of a method for setting confidence intervals on the common mean of two normal populations

Let X₁, , X₂, …, X be distributed N(µ, σ² _x), let Y₁, Y₂, …, Y"_n be distributed N(µ, σ² _y), and let X , X , … X_m, Y₁, Y₂, …, Y_n be mutually independent. In this paper a method for setting confidence intervals on the common mean µ is proposed and evaluated.     

A comparison of two large sample confidence intervals for a proportion: A Monte Carlo simulation

SUMMARY Two pairs of confidence intervals for a proportion, similar to that of Larson, are compared. It can be shown through computer simulation experiments that, for certain values of p, the confidence interval obtained by the approximation is superior.     

Planning the duration of a survival group sequential trial with a fixed follow-up time for all subjects

To explore the operation characteristics of survival group sequential trials with a fixed follow-up period, the accrual time and total trial duration to ensure power and type I error rate requirements are explained and investigated for hazard ratios ranging from 1.3 to 3.0, with slow or high accrual rate, and in the presence or absence of censoring. Impacts of hazard rate, accrual rate, and competitive censoring on accrual time and subsequently on total trial duration are carefully illustrated. Real time for interim analyses, needed number of events, and recruited number of subjects at time of interim analyses are also tabulated.     

Adaptive sequential procedures for comparing new treatments with a standard

In this paper we propose and study two sequential elimination procedures for selecting all new treatments better than a standard or control treatment. These procedures differ from those previously proposed in that we assume variances are unequal and unknown. Expressions for asymptotic expected sample sizes are given. Confidence intervals associated with the procedures are also discussed.