Confidence intervals for the mean of diagnostic test charge data containing zeros

In this paper, we consider the problem of interval estimation for the mean of diagnostic test charges. Diagnostic test charge data may contain zero values, and the nonzero values can often be modeled by a log-normal distribution. Under such a model, we propose three different interval estimation procedures: a percentile-t bootstrap interval based on sufficient statistics and two likelihood-based confidence intervals. For theoretical properties, we show that the two likelihood-based one-sided confidence intervals are only first-order accurate and that the bootstrap-based one-sided confidence interval is second-order accurate. For two-sided confidence intervals, all three proposed methods are second-order accurate. A simulation study in finite-sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator (MVUE)-based interval except for the case of one-sided lower end-point intervals when the skewness is very small. Among the proposed one-sided intervals, the bootstrap interval has the best coverage accuracy. For the two-sided intervals, when the sample size is small, the bootstrap method still yields the best coverage accuracy unless the skewness is very small, in which case the bias-corrected ML method has the best accuracy. When the sample size is large, all three proposed intervals have similar coverage accuracy. Finally, we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression.     

Simultaneous inference for ratios of linear combinations of general linear model parameters

Consider a general linear model with p -dimensional parameter vector beta and i.i.d. normal errors. Let K(1), ..., K(k ), and L be linearly independent vectors of constants such that L(T)beta not equal 0. We describe exact simultaneous tests for hypotheses that Ki(T)beta/L(T)beta equal specified constants using one-sided and two-sided alternatives, and describe exact simultaneous confidence intervals for these ratios. In the case where the confidence set is a single bounded contiguous set, we describe what we claim are the best possible conservative simultaneous confidence intervals for these ratios - best in that they form the minimum k -dimensional hypercube enclosing the exact simultaneous confidence set. We show that in the case of k = 2, this "box" is defined by the minimum and maximum values for the two ratios in the simultaneous confidence set and that these values are obtained via one of two sources: either from the solutions to each of four systems of equations or at points along the boundary of the simultaneous confidence set where the correlation between two t variables is zero. We then verify that these intervals are narrower than those previously presented in the literature.     

A method to construct confidence interval for expected response to multi-trait selection

Summary Confidence intervals are constructed for the expected responses to three types of multi-trait selection. The influence of numbers of replicates and genotypes used in a progeny test experiment on the precision of response of multi-trait selection is discussed based on the structure of the established intervals. Special attention is paid to the characteristics of the intervals constructed for the conventional least square selection indices.     

Implementation of Rao's one-sample polynomial growth curve model using SAS

Longitudinal data are frequently treated with the classic analysis of variance and regression models. However, these models assume independence of observations. Hoel (1964) demonstrated that the use of least-squares methods on intercorrelated serial observations results in the rejection of the null hypothesis much too frequently. Although appropriate models for analyzing longitudinal data have been available for quite some time, they have remained inaccessible due to cumbersome matrix manipulations. We implement Rao's (1959) one-sample polynomial growth curve model using the programming capability and matrix language of SAS, which involves testing the goodness-of-fit and calculation of confidence bands for polynomial growth curves fit to data at equally spaced time points. Confidence intervals for the parameters themselves are also computed. The method and program (presented in the Appendix) are illustrated with examples involving mandibular ramus height in 12 young male rhesus monkeys. The data set, which spans a 4 year period (yearly observations), is fit adequately by a quadratic equation. The data spanning a 2 year period (half-year observations) are fit adequately by the linear equation. These examples illustrate the considerable widening of confidence bands that occurs when polynomial equations having more terms than are needed to meet the goodness-of-fit requirement are considered.     

Conditional Inference Following Group Sequential Testing

The work of Fisher (1959) and Buehler (1959) discuss the importance of conditioning on recognizable subsets of the sample space. The stopping time yields an easily identifiable partition of the sample space when considering group sequential testing. We first present confidence intervals that are correct when conditioning on the subset of data for which a trial stopped at a particular analysis. These intervals have very desirable properties for observations that are highly unusual (given any value of the mean). In addition, they provide insight into how information about the mean is distributed between the two sufficient statistics. We then use conditional coverage probabilities to compare the sample mean, stagewise, and repeated confidence intervals. We find that none of these intervals outperforms the others when conditioning on stopping time, and no interval is a uniformly acceptable performer.     

The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters

Summary Suppose that we are interested in making joint inferences about a set of constrained parameters. Confidence regions for these parameters are often constructed via a normal approximation of the distribution of a consistent estimator for a transformation of the parameters. In this article, we utilize the confidence distribution, a frequentist counterpart to the posterior distribution in Bayesian statistics, to obtain optimal confidence regions for the parameters. Members of such a region can be generated efficiently via a standard Markov chain Monte Carlo algorithm. We then apply this technique to draw inferences about the temporal profile of the survival function with censored observations. We illustrate the new proposal with the survival data from the well‐known Mayo primary biliary cirrhosis study and show that the volume of the new 0.95 confidence region is only one thirty‐fourth of that of the conventional confidence band.     

Test-based exact confidence intervals for the difference of two binomial proportions

Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.     

Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.     

Role of disc area and trabecular bone density on lumbar spinal column fracture risk curves under vertical impact

While studies have been conducted using human cadaver lumbar spines to understand injury biomechanics in terms of stability/energy to fracture, and physiological responses under pure-moment/follower loads, data are sparse for inferior-to-superior impacts. Injuries occur under this mode from underbody blasts. Objectives: determine role of age, disc area, and trabecular bone density on tolerances/risk curves under vertical loading from a controlled group of specimens. T12-S1 columns were obtained, pretest X-rays and CTs taken, load cells attached to both ends, impacts applied at S1-end using custom vertical accelerator device, and posttest X-ray, CT, and dissections done. BMD of L2-L4 vertebrae were obtained from QCT. Survival analysis-based Human Injury Probability Curves (HIPCs) were derived using proximal and distal forces. Age, area, and BMD were covariates. Forces were considered uncensored, representing the load carrying capacity. The Akaike Information Criterion was used to determine optimal distributions. The mean forces, ±95% confidence intervals, and Normalized Confidence Interval Size (NCIS) were computed. The Lognormal distribution was the optimal function for both forces. Age, area, and BMD were not significant (p > 0.05) covariates for distal forces, while only BMD was significant for proximal forces. The NCIS was the lowest for force-BMD covariate HIPC. The HIPCs for both genders at 35 and 45 years were based on population BMDs. These HIPCs serve as human tolerance criteria for automotive, military, and other applications. In this controlled group of samples, BMD is a better predictor-covariate that characterizes lumbar column injury under inferior-to-superior impacts.     

Spinal and sacroiliac assessment and treatment techniques used by osteopathic physicians in the United States

Background

Without systematic exposure to biomedical research concepts or applications, osteopathic medical students may be generally under-prepared to efficiently consume and effectively apply research and evidence-based medicine information in patient care. The academic literature suggests that although medical residents are increasingly expected to conduct research in their post graduate training specialties, they generally have limited understanding of research concepts. With grant support from the National Center for Complementary and Alternative Medicine, and a grant from the Osteopathic Heritage Foundation, the University of North Texas Health Science Center (UNTHSC) is incorporating research education in the osteopathic medical school curriculum. The first phase of this research education project involved a baseline assessment of students' understanding of targeted research concepts. This paper reports the results of that assessment and discusses implications for research education during medical school.

Methods

Using a novel set of research competencies supported by the literature as needed for understanding research information, we created a questionnaire to measure students' confidence and understanding of selected research concepts. Three matriculating medical school classes completed the on-line questionnaire. Data were analyzed for differences between groups using analysis of variance and t-tests. Correlation coefficients were computed for the confidence and applied understanding measures. We performed a principle component factor analysis of the confidence items, and used multiple regression analyses to explore how confidence might be related to the applied understanding.

Results

Of 496 total incoming, first, and second year medical students, 354 (71.4%) completed the questionnaire. Incoming students expressed significantly more confidence than first or second year students (F = 7.198, df = 2, 351, P = 0.001) in their ability to understand the research concepts. Factor analyses of the confidence items yielded conceptually coherent groupings. Regression analysis confirmed a relationship between confidence and applied understanding referred to as knowledge. Confidence scores were important in explaining variability in knowledge scores of the respondents.

Conclusion

Medical students with limited understanding of research concepts may struggle to understand the medical literature. Assessing medical students' confidence to understand and objectively measured ability to interpret basic research concepts can be used to incorporate competency based research material into the existing curriculum.     

An Improvement of the Westlake Symmetric Confidence Interval

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST -LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one-sided t-tests. An (1-α)-confidence interval consistent with the two one-sided t-tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)-confidence interval of the t-test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one-sided confidence intervals.     

Normative cervical spine kinematics of a circumduction task

Neck pain is a prevalent condition and clinical examination techniques are limited and unable to assess out-of-plane motion. Recent works investigating cervical kinematics during neck circumduction (NC), a dynamic 3D task, has shown the ability to discern those with and without neck pain. The purposes of this study were to establish 1) confidence and prediction intervals of head-to-torso kinematics during NC in a healthy cohort, 2) a baseline summative metric to quantify the duration and magnitude of deviations outside the prediction interval, and 3) the reliability of NC. Thirty-nine participants (25.6 ± 6.3 years, 19F/20M) without neck pain completed left and right NC. A two-way smoothing spline analysis of variance was utilized to determine the mean-fitted values and 90% confidence and prediction intervals for NC. A standardized effect size was calculated and aggregated across all axes (Delta RMSD aggregate), as a summative metric of motion quality. Confidence and prediction intervals were comparable for left and right NC and demonstrated excellent reliability. The average sum of the Delta RMSD aggregate was 2.76 ± 0.55 for left NC and 2.74 ± 0.63 for right NC. The results of this study demonstrate the feasibility of utilizing normative intervals of a NC task to assess head-to-torso kinematics.     

Nonparametric confidence intervals for the one- and two-sample problems

Confidence intervals for the mean of one sample and the difference in means of two independent samples based on the ordinary-t statistic suffer deficiencies when samples come from skewed families. In this article we evaluate several existing techniques and propose new methods to improve coverage accuracy. The methods examined include the ordinary-t, the bootstrap-t, the biased-corrected acceleration and three new intervals based on transformation of the t-statistic. Our study shows that our new transformation intervals and the bootstrap-t intervals give best coverage accuracy for a variety of skewed distributions, and that our new transformation intervals have shorter interval lengths.     

Validation of a Demographic Model for Woodland Caribou

Abstract: Wildlife population models are potentially valuable for conservation planning. Validation is necessary to ensure that models are sufficiently robust for predicting management outcomes consistent with conservation objectives. Sorensen et al. (2008) produced a model of woodland caribou (Rangifer tarandus) population growth rate that was recently modified and used as a predictive tool at several scales. We computed confidence intervals and evaluated the performance of this model using novel data. Confidence intervals were wide, and results suggested that the model may have a positive bias, resulting in over-estimation of population growth rates, as well as low predictive power. Wide confidence intervals mean that current understanding of factors governing woodland caribou herd dynamics is not sufficient for wildlife managers to make reliable projections of responses to management.     

Unconditional Exact Tests for Equivalence or Noninferiority for Paired Binary Endpoints

Problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between correlated proportions. When the sample size is small, the asymptotic tests may not be reliable. This article proposes an unconditional exact test procedure to assess equivalence or noninferiority. Two statistics, a sample-based test statistic and a restricted maximum likelihood estimation (RMLE)-based test statistic, to define the rejection region of the exact test are considered. We show the p-value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis. Assessment of equivalence is often based on a comparison of the confidence limits with the equivalence limits. We also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics. A typical data set of comparing two diagnostic procedures is analyzed using the proposed unconditional exact and asymptotic methods. The p-value from the unconditional exact tests is generally larger than the p-value from the asymptotic tests. In other words, an exact confidence interval is generally wider than the confidence interval obtained from an asymptotic test.     

Symmetric Intervals and Confidence Intervals

We show that the symmetric “confidence intervals” of WESTLAKE (1972, 1976), widely used and referred to in bioequivalence studies, are not confidence intervals in any accepted sense. Nevertheless, meaningful symmetric intervals can be constructed in the context of Bayesian or fiducial inference.     

Nonparametric statistical methods for cost-effectiveness analyses

Two measures often used in a cost-effectiveness analysis are the incremental cost-effectiveness ratio (ICER) and the net health benefit (NHB). Inferences on these two quantities are often hindered by highly skewed cost data. In this article, we derive the Edgeworth expansions for the studentized t-statistics for the two measures and show how they could be used to guide inferences. In particular, we use the expansions to study the theoretical performance of existing confidence intervals based on normal theory and to derive new confidence intervals for the ICER and the NHB. We conduct a simulation study to compare our new intervals with several existing methods. The methods evaluated include Taylor's interval, Fieller's interval, the bootstrap percentile interval, and the bootstrap bias-corrected acceleration interval. We found that our new intervals give good coverage accuracy and are narrower compared to the current recommended intervals.     

A study on confidence intervals for incremental cost-effectiveness ratios

In health policy and economics studies, the incremental cost-effectiveness ratio (ICER) has long been used to compare the economic consequences relative to the health benefits of therapies. Due to the skewed distributions of the costs and ICERs, much research has been done on how to obtain confidence intervals of ICERs, using either parametric or nonparametric methods, with or without the presence of censoring. In this paper, we will examine and compare the finite sample performance of many approaches via simulation studies. For the special situation when the health effect of the treatment is not statistically significant, we will propose a new bootstrapping approach to improve upon the bootstrap percentile method that is currently available. The most efficient way of constructing confidence intervals will be identified and extended to the censored data case. Finally, a data example from a cardiovascular clinical trial is used to demonstrate the application of these methods.     

The empirical coverage of confidence intervals: Point estimates and confidence intervals for confidence levels

Many confidence intervals calculated in practice are potentially not exact, either because the requirements for the interval estimator to be exact are known to be violated, or because the (exact) distribution of the data is unknown. If a confidence interval is approximate, the crucial question is how well its true coverage probability approximates its intended coverage probability. In this paper we propose to use the bootstrap to calculate an empirical estimate for the (true) coverage probability of a confidence interval. In the first instance, the empirical coverage can be used to assess whether a given type of confidence interval is adequate for the data at hand. More generally, when planning the statistical analysis of future trials based on existing data pools, the empirical coverage can be used to study the coverage properties of confidence intervals as a function of type of data, sample size, and analysis scale, and thus inform the statistical analysis plan for the future trial. In this sense, the paper proposes an alternative to the problematic pretest of the data for normality, followed by selection of the analysis method based on the results of the pretest. We apply the methodology to a data pool of bioequivalence studies, and in the selection of covariance patterns for repeated measures data.     

Confidence Intervals and Tests of Hypotheses on Variance Components in an Unbalanced Two-fold Nested Design

Confidence intervals and tests of hypotheses on variance components are required in studies that employ a random effects design. The unbalanced random two-fold nested design is considered in this paper and confidence intervals are proposed for the variance components σ2/A and σ2/B. Computer simulation is used to show that even in very unbalanced designs, these intervals generally maintain the stated confidence coefficient. The hypothesis test for σ2/A based on the lower bound of the recommended confidence interval is shown to be better than previously proposed approximate tests.