Approximate Bootstrap Confidence Research Articles

Visualizing the quantile survival time difference curve.

The difference between the pth quantiles of 2 survival functions can be used to compare patients' survival between 2 therapies. Setting p = 0.5 yields the median survival time difference. Varying p between 0 and 1 defines the quantile survival time difference curve which can be straightforwardly estimated by the horizontal differences between 2 Kaplan‐Meier curves. The estimate's variability can be visualized by adding either a bundle of resampled bootstrap step functions or, alternatively, approximate bootstrap confidence bands. The user‐friendly SAS software macro %kmdiff enables the straightforward application of this exploratory graphical approach. The macro is described, and its application is exemplified with breast cancer data. The advantages and limitations of the approach are discussed.

Optimising the sampling effort in riparian surveys

Riparian condition is commonly measured as part of stream health monitoring programs as riparian vegetation provides an intricate linkage between the terrestrial and aquatic ecosystems. Field surveys of a riparian zone provide comprehensive riparian attribute data but can be considerably intensive and onerous on resources and workers. Our objective was to assess the impact of reducing the sampling effort on the variation in key riparian health indicators. Subsequently, we developed a non-parametric approach to calculate an information retained (IR) statistic for comparing several constrained systematic sampling schemes to the original survey. The IR statistic is used to select a scheme that reduces the time taken to undertake riparian surveys (and thus potentially the costs) whilst maximising the IR from the original survey. Approximate bootstrap confidence intervals were calculated to improve the inferential capability of the IR statistic. The approach is demonstrated using riparian vegetation indicators collected as part of an aquatic ecosystem health monitoring program in Queensland, Australia. Of the nine alternative sampling designs considered, the sampling design that reduced the sampling intensity per site by sixfold without significantly comprising the quality of the IR, results in halving the time taken to complete a riparian survey at a site. This approach could also be applied to reducing sampling effort involved in monitoring other ecosystem health indicators, where an intensive systematic sampling scheme was initially employed.

Confidence interval of intrinsic optimum temperature estimated using thermodynamic SSI model

The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecological and evolutional processes. The Sharpe-Schoolfield-Ikemoto (SSI) model succeeded in defining the temperature that can thermodynamically meet the condition that at a particular temperature the probability of an active enzyme reaching its maximum activity is realized. Previously, an algorithm was developed by Ikemoto (Tropical malaria does not mean hot environments. Journal of Medical Entomology, 45, 963-969) to estimate model parameters, but that program was computationally very time consuming. Now, investigators can use the SSI model more easily because a full automatic computer program was designed by Shi et al. (A modified program for estimating the parameters of the SSI model. Environmental Entomology, 40, 462-469). However, the statistical significance of the point estimate of the intrinsic optimum temperature for each ectotherm has not yet been determined. Here, we provided a new method for calculating the confidence interval of the estimated intrinsic optimum temperature by modifying the approximate bootstrap confidence intervals method. For this purpose, it was necessary to develop a new program for a faster estimation of the parameters in the SSI model, which we have also done.

Constructing second‐order accurate confidence intervals for communalities in factor analysis

In an effort to find accurate alternatives to the usual confidence intervals based on normal approximations, this paper compares four methods of generating second-order accurate confidence intervals for non-standardized and standardized communalities in exploratory factor analysis under the normality assumption. The methods to generate the intervals employ, respectively, the Cornish-Fisher expansion and the approximate bootstrap confidence (ABC), and the bootstrap-t and the bias-corrected and accelerated bootstrap (BC(a)). The former two are analytical and the latter two are numerical. Explicit expressions of the asymptotic bias and skewness of the communality estimators, used in the analytical methods, are derived. A Monte Carlo experiment reveals that the performance of central intervals based on normal approximations is a consequence of imbalance of miscoverage on the left- and right-hand sides. The second-order accurate intervals do not require symmetry around the point estimates of the usual intervals and achieve better balance, even when the sample size is not large. The behaviours of the second-order accurate intervals were similar to each other, particularly for large sample sizes, and no method performed consistently better than the others.

Confidence intervals for the 50 per cent response dose.

Confidence intervals for the 50 per cent response dose are usually computed using either the Delta method or Fieller's procedure. Recently, confidence intervals computed by inverting the asymptotic likelihood ratio test have also been recommended. There is some controversy as to which of these methods should be used. By means of an extensive simulation study we examine these methods as well as confidence intervals obtained by the approximate bootstrap confidence (ABC) procedure and an adjusted form of the likelihood ratio based confidence intervals.

Confidence intervals for directly standardized rates: a method based on the gamma distribution.

We offer an approximation to central confidence intervals for directly standardized rates, where we assume that the rates are distributed as a weighted sum of independent Poisson random variables. Like a recent method proposed by Dobson, Kuulasmaa, Eberle and Scherer, our method gives exact intervals whenever the standard population is proportional to the study population. In cases where the two populations differ non-proportionally, we show through simulation that our method is conservative while other methods (the Dobson et al. method and the approximate bootstrap confidence method) can be liberal.

Simple confidence intervals for standardized rates based on the approximate bootstrap method.

This paper presents simple expressions for the confidence intervals of indirect and direct standardized rates, based on the approximate bootstrap confidence (ABC) method of DiCiccio and Efron. For indirect rates, the ABC method compares favourably with the exact methods. An exact method is not available for direct standardized rates. I, therefore, compared the ABC to other simple procedures for confidence intervals, namely: the standard normal, log-normal, and a recent method proposed by Dobson et al. Simulation studies of the coverage properties of these methods for direct standardized rates show that the ABC method performs best, with balanced tail probabilities close to their expected values.