Search

In observational studies for the interaction between exposures on a dichotomous outcome of a certain population, usually one parameter of a regression model is used to describe the interaction, leading to one measure of the interaction. In this article we use the conditional risk of an outcome given exposures and covariates to describe the interaction and obtain five different measures of the interaction, that is, difference between the marginal risk differences, ratio of the marginal risk ratios, ratio of the marginal odds ratios, ratio of the conditional risk ratios, and ratio of the conditional odds ratios. These measures reflect different aspects of the interaction. By using only one regression model for the conditional risk, we obtain the maximum-likelihood (ML)-based point and interval estimates of these measures, which are most efficient due to the nature of ML. We use the ML estimates of the model parameters to obtain the ML estimates of these measures. We use the approximate normal distri...

In this paper, point and interval estimations for the parameters of the exponentiated exponential (EE) distribution are studied based on progressive first-failure-censored data. The Bayes estimates are computed based on squared error and Linex loss functions and using Markov Chain Monte Carlo (MCMC) algorithm. Also, based on this censoring scheme, approximate confidence intervals for the parameters of EE distribution are developed. Monte Carlo simulation study is carried out to compare the performances of the different methods by computing the estimated risks (ERs), as well as Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates. Finally, a real data set is introduced and analyzed using EE and Weibull distributions. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic to emphasize that the EE model fits the data with the same efficiency as the other model. Point and interval estimation of...

Interval-censored data are very common in the reliability and lifetime data analysis. This paper investigates the performance of different estimation procedures for a special type of interval-censored data, i.e. grouped data, from three widely used lifetime distributions. The approaches considered here include the maximum likelihood estimation, the minimum distance estimation based on chi-square criterion, the moment estimation based on imputation (IM) method and an ad hoc estimation procedure. Although IM-based techniques are extensively used recently, we show that this method is not always effective. It is found that the ad hoc estimation procedure is equivalent to the minimum distance estimation with another distance metric and more effective in the simulation. The procedures of different approaches are presented and their performances are investigated by Monte Carlo simulation for various combinations of sample sizes and parameter settings. The numerical results provide guidelines to analyse g...

Confidence interval (CI) is very useful for trend estimation in meta-analysis. It provides a type of interval estimate of the regression slope as well as an indicator of the reliability of the estimate. Thus a precise calculation of confidence interval at an expected level is important. It is always difficult to explicitly quantify the CIs when there is publication bias in meta-analysis. Various CIs have been proposed, including the most widely used DerSimonian–Laird CI and the recently proposed Henmi–Copas CI. The latter provides a robust solution when there are non-ignorable missing data due to publication bias. In this paper we extended the idea into meta-analysis for trend estimation. We applied the method in different scenarios and showed that this type of CI is more robust than the others.

Highly skewed and non-negative data can often be modeled by the delta-lognormal distribution in fisheries research. However, the coverage probabilities of extant interval estimation procedures are less satisfactory in small sample sizes and highly skewed data. We propose a heuristic method of estimating confidence intervals for the mean of the delta-lognormal distribution. This heuristic method is an estimation based on asymptotic generalized pivotal quantity to construct generalized confidence interval for the mean of the delta-lognormal distribution. Simulation results show that the proposed interval estimation procedure yields satisfactory coverage probabilities, expected interval lengths and reasonable relative biases. Finally, the proposed method is employed in red cod densities data for a demonstration.

In many clinical trials and epidemiological studies, comparing the mean count response of an exposed group to a control group is often of interest. This type of data is often over-dispersed with respect to Poisson variation, and previous studies usually compared groups using confidence intervals (CIs) of the difference between the two means. However, in some situations, especially when the means are small, interval estimation of the mean ratio (MR) is preferable. Moreover, Cox and Lewis [4] pointed out many other situations where the MR is more relevant than the difference of means. In this paper, we consider CI construction for the ratio of means between two treatments for over-dispersed Poisson data. We develop several CIs for the situation by hybridizing two separate CIs for two individual means. Extensive simulations show that all hybrid-based CIs perform reasonably well in terms of coverage. However, the CIs based on the delta method using the logarithmic transformation perform better than other inte...

The odds ratio (OR) has been recommended elsewhere to measure the relative treatment efficacy in a randomized clinical trial (RCT), because it possesses a few desirable statistical properties. In practice, it is not uncommon to come across an RCT in which there are patients who do not comply with their assigned treatments and patients whose outcomes are missing. Under the compound exclusion restriction, latent ignorable and monotonicity assumptions, we derive the maximum likelihood estimator (MLE) of the OR and apply Monte Carlo simulation to compare its performance with those of the other two commonly used estimators for missing completely at random (MCAR) and for the intention-to-treat (ITT) analysis based on patients with known outcomes, respectively. We note that both estimators for MCAR and the ITT analysis may produce a misleading inference of the OR even when the relative treatment effect is equal. We further derive three asymptotic interval estimators for the OR, including the interval estimator u...

On the basis of a negative binomial sampling scheme, we consider a uniformly most accurate upper confidence limit for a small but unknown proportion, such as the proportion of defectives in a manufacturing process. The optimal stopping rule, with reference to the twin criteria of the expected length of the confidence interval and the expected sample size, is investigated. The proposed confidence interval has also been compared with several others that have received attention in the recent literature.

When working with a single random variable, the simplest and most obvious approach when estimating a 1 − γ prediction interval, is to estimate the γ/2 and 1 − γ/2 quantiles. The paper compares the small-sample properties of several methods aimed at estimating an interval that contains the 1 − γ prediction interval with probability 1 − α. In effect, the goal is to compute a 1 − α confidence interval for the true 1 − γ prediction interval. The only successful method when the sample size is small is based in part on an adaptive kernel estimate of the underlying density. Some simulation results are reported on how an extension to non-parametric regression performs, based on a so-called running interval smoother.

Interval estimation of the x th effective dose (ED x ), where x is a prespecified percentage, has been the focus of interest of a number of recent studies, the majority of which have considered the case in which a logistic dose-response curve is correctly assumed. In this paper, we focus our attention upon the 90% effective dose (ED 90 ) and consider the situation in which the assumption of a logistic dose-response curve is incorrect. Specifically, we consider three classes of true model: the probit, the cubic logistic and the asymmetric Aranda-Ordaz models. We investigate the robustness of four large sample parametric methods of interval construction and four methods based upon bootstrap resampling.

Existing models for ring recovery and recapture data analysis treat temporal variations in annual survival probability (S) as fixed effects. Often there is no explainable structure to the temporal variation in S 1 , … , S k ; random effects can then be a useful model: Si = E(S) + k i . Here, the temporal variation in survival probability is treated as random with average value E( k 2 ) = † 2 . This random effects model can now be fit in program MARK. Resultant inferences include point and interval estimation for process variation, † 2 , estimation of E(S) and var(E(S)) where the latter includes a component for † 2 as well as the traditional component for v ar(S|S). Furthermore, the random effects model leads to shrinkage estimates, S i , as improved (in mean square error) estimators of Si compared to the MLE, S i , from the unrestricted time-effects model. Appropriate confidence intervals based on the S i are also provided. In addition, AIC has been generalized to random effects models. This paper present...

Efficient reliability industrial experiments consist of submitting items to accelerated life tests. It is of interest to obtain measures of the realiability of the devices under the usual working conditions, represented here by the mean lifetime. A practical problem refers to the accuracy of interval estimation of the parameter of interest when the sample size is small or moderate. In this paper, we describe the effect of several reparametrizations on the accuracy of the interval estimation. We propose a reparametrization that leads to accuracy while allowing orthogonality between the parameters. The idea is to consider a logarithmic reparametrization on orthogonal parameters in order to have independent maximum likelihood estimates with good asymptotic normal approximation. The study is illustrated by a data set on an accelerated life test at pressurized containers of Kevlan/Epoxy 49.

Leave-one-out and 632 bootstrap are popular data-based methods of estimating the true error rate of a classification rule, but practical applications almost exclusively quote only point estimates. Interval estimation would provide better assessment of the future performance of the rule, but little has been published on this topic. We first review general-purpose jackknife and bootstrap methodology that can be used in conjunction with leave-one-out estimates to provide prediction intervals for true error rates of classification rules. Monte Carlo simulation is then used to investigate coverage rates of the resulting intervals for normal data, but the results are disappointing; standard intervals show considerable overinclusion, intervals based on Edgeworth approximations or random weighting do not perform well, and while a bootstrap approach provides intervals with coverage rates closer to the nominal ones there is still marked underinclusion. We then turn to intervals constructed from 632 bootstrap estima...

Virtually all models for the utility of personnel selection are based on the average criterion score of the predictor selected applicants. This paper indicates how standard results from the theory on order statistics can be used to determine the expected value, the standard error and the sampling distribution of the average criterion score statistic when a finite number of employees is selected. Exact as well as approximate results are derived and it is shown how these results can be used to construct intervals that will contain, with a given probability 1 - f , the average criterion score associated with a particular implementation of the personnel selection. These interval estimates are particularly helpful to the selection practitioner because they can be used to state the confidence level with which the selection payoff will be above a specific value. In addition, for most realistic selection scenarios, it is found that the corresponding utility interval estimate is quite large. For situations in whic...

A number of recent studies have looked at the coverage probabilities of various common parametric methods of interval estimation of the median effective dose (ED 50 ) for a logistic dose-response curve. There has been comparatively little work done on more extreme effective doses. In this paper, the interval estimation of the 90% effective dose (ED 90 ) will be of principal interest. We provide a comparison of four parametric methods of interval construction with four methods based on bootstrap resampling.

In 1986, Williams showed how, assuming a logistic dose-response curve, one can construct a confidence interval for the median effective dose from the asymptotic likelihood ratio test. He gave reasons for preferring this likelihood ratio interval to the established interval calculated by applying Fieller's theorem to the maximum-likelihood estimates. Here, we assess the impact of applying a Bartlett adjustment to the likelihood ratio statistic and introduce the score test as an alternative approach for constructing a confidence interval for the median effective dose.

Process capability indexes are widely used in the manufacturing industries and by supplier companies in process assessments and in the evaluation of purchasing decisions. One concern about using the process capability indexes is the assumption of the mutual independence of the process data, because, in process industries, process data are often autocorrelated. This paper discusses the use of the process capability indexes Cp and Cpk when the process data are autocorrelated. Interval estimation procedures for Cp and Cpk are proposed and their properties are studied.

Interval estimation of a well-known measure of heterogeneity or diversity is approached by fitting a distribution by the method of moments. Exact expressions for the moments of the distribution are derived and evaluated using a computer algebra package.

When a published statistical model is also distributed as computer software, it will usually be desirable to present the outputs as interval, as well as point, estimates. The present paper compares three methods for approximate interval estimation about a model output, for use when the model form does not permit an exact interval estimate. The methods considered are first-order asymptotics, using second derivatives of the log-likelihood to estimate variance information; higher-order asymptotics based on the signed-root transformation; and the non-parametric bootstrap. The signed-root method is Bayesian, and uses an approximation for posterior moments that has not previously been tested in a real-world application. Use of the three methods is illustrated with reference to a software project arising in medical decision-making, the UKPDS Risk Engine. Intervals from the first-order and signed-root methods are near-identical, and typically 1% wider to 7% narrower than those from the non-parametric bootstrap. The asymptotic methods are markedly faster than the bootstrap method.

An extension of Monte Carlo methods to confidence interval estimation, using the bootstrap technique, is investigated. The approach may have considerable potential for parameters that have estimators with complicated analytic properties but with probability distribution that can be simulated. Potential fields of application include ratio estimation, compound distribution and estimation of probabilities.