Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Confidence Intervals for Selected Parameters

Abstract: Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported uncertainties deceptively optimistic: confidence intervals that ignore selection generally have less than their nominal coverage probability. Controlling the probability that one or more intervals for selected parameters do not cover---the ``simultaneous over the selected'' (SoS) error rate---is crucial in many scientific problems. Intervals that control the SoS error rate can be constructed in ways that take advantage of knowledge of the selection rule. We construct SoS-controlling confidence intervals for parameters deemed the most ``important'' $k$ of $m$ shift parameters because they are estimated (by independent estimators) to be the largest. The new intervals improve substantially over Sidak intervals when $k$ is small compared to $m$, and approach the standard Bonferroni-corrected intervals when $k \approx m$. Standard, unadjusted confidence intervals for location parameters have the correct coverage probability for $k=1$, $m=2$ if, when the true parameters are zero, the estimators are exchangeable and symmetric.

Interval estimation of the proportion ratio under multiple matching.

Abstract: The discussions on interval estimation of the proportion ratio (PR) of responses or the relative risk (RR) of a disease for multiple matching have been generally focused on the odds ratio (OR) based on the assumption that the latter can approximate the former well. When the underlying proportion of outcomes is not rare, however, the results for the OR would be inadequate for use if the PR or RR was the parameter of our interest. In this paper, we develop five asymptotic interval estimators of the common PR (or RR) for multiple matching. To evaluate and compare the finite sample performance of these estimators, we apply Monte Carlo simulation to calculate the coverage probability and the average length of the resulting confidence intervals in a variety of situations. We note that when we have a constant number of matching, the interval estimator using the logarithmic transformation of the Mantel-Haenszel estimator, the interval estimator derived from the quadratic inequality given in this paper, and the interval estimator using the logarithmic transformation of the ratio estimator can consistently perform well. When the number of matching varies between matched sets, we find that the interval estimator using the logarithmic transformation of the ratio estimator is probably the best among the five interval estimators considered here in the case of a small number (=20) of matched sets. To illustrate the use of these interval estimators, we employ the data studying the supplemental ascorbate in the supportive treatment of terminal cancer patients.

Covariates-dependent confidence intervals for the difference or ratio of two median survival times.

Abstract: In this paper, we are concerned with the estimation of the discrepancy between two treatments when right-censored survival data are accompanied with covariates. Conditional confidence intervals given the available covariates are constructed for the difference between or ratio of two median survival times under the unstratified and stratified Cox proportional hazards models, respectively. The proposed confidence intervals provide the information about the difference in survivorship for patients with common covariates but in different treatments. The results of a simulation study investigation of the coverage probability and expected length of the confidence intervals suggest the one designed for the stratified Cox model when data fit reasonably with the model. When the stratified Cox model is not feasible, however, the one designed for the unstratified Cox model is recommended. The use of the confidence intervals is finally illustrated with a HIV+ data set.

Generalized inference for the common mean of several lognormal populations

Abstract: A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are exact and can be used without restriction on sample sizes, number of populations, or difference hypotheses. A simulation study for coverage probability, size and power shown that the new methods are better than the existing methods. A numerical example is given with some real medical data.