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After the completion of many studies, experimental results are reported in terms of distribution-free confidence intervals that may involve pairs of order statistics. This article considers a meta-analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution. Data synthesis is made under both fixed-effect and random-effect meta-analysis models. We show that mean square error (MSE) of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator. We also show that the coverage probability of the meta-analysis confidence interval is quite close to the nominal confidence level. The random-effect meta-analysis model yields a better coverage probability and smaller MSE than the fixed-effect meta-analysis model. The meta-analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in China to provide an illustration of the proposed methodology.

Conventionally a confidence interval (CI) for the standardized mortality ratio is set using the conservative CI for a Poisson expectation, mu. Employing the mid-P argument we present alternative CIs that are shorter than the conventional ones. The mid-P intervals do not guarantee the nominal confidence level, but the true coverage probability is only lower than the nominal level for a few short ranges of mu. The implications for mid-P confidence intervals of various proposed definitions of two-sided tests for discrete data are discussed.

I propose a new confidence interval for the difference between two binomial probabilities that requires only the solution of a quadratic equation. The procedure is based on estimating the variance of the observed difference at the boundaries of the confidence interval, and uses least squares estimation rather than maximum likelihood as previously suggested. The proposed procedure is non-iterative, agrees with the conventional test of equality of two binomial probabilities, and, even for fairly small sample sizes, appears to yields actual 95 per cent confidence intervals with mean or median probabilities of coverage very close to 0⋅95. The Yates continuity correction appears to generate confidence intervals with the conditional probability of coverage at least equal to nominal levels. © 1997 by John Wiley & Sons, Ltd.

A linear relative risk form for the Cox model is sometimes more appropriate than the usual exponential form. The usual asymptotic confidence interval may not have the appropriate coverage, however, due to flatness of the likelihood in the neighbourhood of beta. For a single continuous covariate, we derive bootstrapped confidence intervals with use of two resampling methods. The first resamples the original data and yields both one-step and fully iterated estimates of beta. The second resamples the score and information quantities at each failure time to yield a one-step estimate. We computed the bootstrapped confidence intervals by three different methods and compared these intervals to one based on the asymptotic standard error and to a likelihood-based interval. The bootstrapped intervals did not perform well and underestimated the true coverage in most cases.

We examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities. We compare the effective sample sizes of Cutler and Ederer and Peto et al., as well as a modified Cutler-Ederer effective sample size. We investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time. We note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric. We recommend the use of the Cutler-Ederer effective sample size in construction of upper confidence intervals and the Peto effective sample size in construction of lower confidence intervals. Two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes. This study also illustrates the need for caution in the application of simulation studies to real problems.