Power and sample size estimation for the clustered wilcoxon test

The Wilcoxon rank sum test is widely used for two-group comparisons of nonnormal data. An assumption of this test is independence of sampling units both within and between groups, which will be violated in the clustered data setting such as in ophthalmological clinical trials, where the unit of randomization is the subject, but the unit of analysis is the individual eye. For this purpose, we have proposed the clustered Wilcoxon test to account for clustering among multiple subunits within the same cluster (Rosner, Glynn, and Lee, 2003, Biometrics 59, 1089-1098; 2006, Biometrics 62, 1251-1259). However, power estimation is needed to plan studies that use this analytic approach. We have recently published methods for estimating power and sample size for the ordinary Wilcoxon rank sum test (Rosner and Glynn, 2009, Biometrics 65, 188-197). In this article we present extensions of this approach to estimate power for the clustered Wilcoxon test. Simulation studies show a good agreement between estimated and empirical power. These methods are illustrated with examples from randomized trials in ophthalmology. Enhanced power is achieved with use of the subunit as the unit of analysis instead of the cluster using the ordinary Wilcoxon rank sum test.     

Sample size for case-control studies using Cochran's statistic

Sample size determination for case-control studies of chronic disease are often based on the simple 2 X 2 tabular cross-classification of exposure and disease, thereby ignoring stratification which may be considered in the analysis. One consequence of this approach is that the sample size may be inadequate to attain a specified power and size when performing a statistical analysis on J 2 X 2 tables using Cochran's (1954, Biometrics 10, 417-451) statistic or the Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748) statistic. A sample size formula is derived from Cochran's statistic and it is compared with the corresponding one derived when the data are treated as unstratified, and also with two other formulas proposed for stratified data analysis. The formula developed yields values slightly higher than one recently proposed by Mu?oz and Rosner (1984, Biometrics 40, 995-1004), which assumes that both margins of each 2 X 2 table are fixed, while the present study considers only the case-control margin to be fixed.     

Modeling concordance correlation via GEE to evaluate reproducibility

Clinical studies are often concerned with assessing whether different raters/methods produce similar values for measuring a quantitative variable. Use of the concordance correlation coefficient as a measure of reproducibility has gained popularity in practice since its introduction by Lin (1989, Biometrics 45, 255-268). Lin's method is applicable for studies evaluating two raters/two methods without replications. Chinchilli et al. (1996, Biometrics 52, 341-353) extended Lin's approach to repeated measures designs by using a weighted concordance correlation coefficient. However, the existing methods cannot easily accommodate covariate adjustment, especially when one needs to model agreement. In this article, we propose a generalized estimating equations (GEE) approach to model the concordance correlation coefficient via three sets of estimating equations. The proposed approach is flexible in that (1) it can accommodate more than two correlated readings and test for the equality of dependent concordant correlation estimates; (2) it can incorporate covariates predictive of the marginal distribution; (3) it can be used to identify covariates predictive of concordance correlation; and (4) it requires minimal distribution assumptions. A simulation study is conducted to evaluate the asymptotic properties of the proposed approach. The method is illustrated with data from two biomedical studies.     

Analysis of ordered categorical data: two score-independent approaches

SUMMARY: A trend test is often employed to analyze ordered categorical data, in which a set of increasing scores is assigned a priori. There is a drawback in this approach, because how to choose a set of scores is not clear. There have been debates on which scores should be used (e.g., Graubard and Korn, 1987, Biometrics 43, 471-476; Ivanova and Berger, 2001, Biometrics 57, 567-570; Senn, 2007, Biometrics 63, 296-298). Conflicting conclusions are often obtained with different sets of scores. Two approaches, which have been applied to genetic case-control studies, are appealing for ordered categorical data, because they take into account the natural order in the data, are score independent, and not contingent on asymptotic theory. These two approaches are applied to a prospective study for detecting association between maternal drinking and congenital malformations.     

Regression analysis of doubly censored failure time data using the additive hazards model

Doubly censored failure time data arise when the survival time of interest is the elapsed time between two related events and observations on occurrences of both events could be censored. Regression analysis of doubly censored data has recently attracted considerable attention and for this a few methods have been proposed (Kim et al., 1993, Biometrics 49, 13-22; Sun et al., 1999, Biometrics 55, 909-914; Pan, 2001, Biometrics 57, 1245-1250). However, all of the methods are based on the proportional hazards model and it is well known that the proportional hazards model may not fit failure time data well sometimes. This article investigates regression analysis of such data using the additive hazards model and an estimating equation approach is proposed for inference about regression parameters of interest. The proposed method can be easily implemented and the properties of the proposed estimates of regression parameters are established. The method is applied to a set of doubly censored data from an AIDS cohort study.     

Estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations

We present methods for the analysis of a K-variate binary measure for two independent groups where some observations may be incomplete, as in the case of K repeated measures in a comparative trial. For the K 2 X 2 tables, let theta = (theta 1,..., theta K) be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group (i = 1, 2; k = 1,..., K), such as the log odds ratio or log relative risk. The asymptotic distribution of the estimates theta = (theta 1,..., theta K) is derived. Under the assumption that theta k = theta for all k, we describe the maximally efficient linear estimator theta of the common parameter theta. Tests of contrasts on the theta are presented which provide a test of homogeneity Ha: theta k = theta l for all k not equal to l. We then present maximally efficient tests of aggregate association Hb: theta = theta 0, where theta 0 is a given value. It is shown that the test of aggregate association Hb is asymptotically independent of the preliminary test of homogeneity Ha. These methods generalize the efficient estimators of Gart (1962, Biometrics 18, 601-610), and the Cochran (1954, Biometrics 10, 417-451), Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748), and Radhakrishna (1965, Biometrics 21, 86-98) tests to nonindependent tables. The methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the National Cooperative Gallstone Study.     

Sample size determination for case-control studies and the comparison of stratified and unstratified analyses.

Woolson, Bean, and Rojas (1986, Biometrics 42, 927-932) present a simple approximation of sample size for Cochran's (1954, Biometrics 10, 417-451) test for detecting association between exposure and disease. It is useful in the design of case-control studies. We derive a sample size formula for Cochran's statistic with continuity correction which guarantees that the actual Type I error rate of the test does not exceed the nominal level. The corrected sample size is necessarily larger than the uncorrected one given by Woolson et al. and the relative difference between the two sample sizes is considerable. Allocation of equal number of cases and controls within each stratum is asymptotically optimal when the costs per case and control are the same. When any effect of stratification is absent, Cochran's stratified test, although valid, is less efficient than the unstratified one except for the important case of a balanced design.     

Reducing mean squared error in the analysis of stratified epidemiologic studies

Kalish (1990, Biometrics 46, 493-499) proposed an approximately optimal estimator of a common odds ratio for pair-matched case-control studies. His approach is easily extended to general stratified studies. For unmatched stratified studies, the form of the approximately optimal estimator is very simple, and may often correspond to no more than a small correction to the ordinary stratified estimator.     

Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies

This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.     

Virtual reality as a tool for evaluation of repetitive rhythmic movements in the elderly and Parkinson's disease patients

This work presents an immersive Virtual Reality (VR) system to evaluate, and potentially treat, the alterations in rhythmic hand movements seen in Parkinson's disease (PD) and the elderly (EC), by comparison with healthy young controls (YC). The system integrates the subjects into a VR environment by means of a Head Mounted Display, such that subjects perceive themselves in a virtual world consisting of a table within a room. In this experiment, subjects are presented in 1(st) person perspective, so that the avatar reproduces finger tapping movements performed by the subjects. The task, known as the finger tapping test (FT), was performed by all three subject groups, PD, EC and YC. FT was carried out by each subject on two different days (sessions), one week apart. In each FT session all subjects performed FT in the real world (FT(REAL)) and in the VR (FT(VR)); each mode was repeated three times in randomized order. During FT both the tapping frequency and the coefficient of variation of inter-tap interval were registered. FT(VR) was a valid test to detect differences in rhythm formation between the three groups. Intra-class correlation coefficients (ICC) and mean difference between days for FT(VR) (for each group) showed reliable results. Finally, the analysis of ICC and mean difference between FT(VR) vs FT(REAL), for each variable and group, also showed high reliability. This shows that FT evaluation in VR environments is valid as real world alternative, as VR evaluation did not distort movement execution and detects alteration in rhythm formation. These results support the use of VR as a promising tool to study alterations and the control of movement in different subject groups in unusual environments, such as during fMRI or other imaging studies.     

Parabolic flight reveals independent binocular control of otolith-induced eye torsion

To examine otolith-governed ocular torsion in hyper- and hypogravity, eight subjects, including two astronauts, underwent parabolic flight while seated upright with head fixed. A mask fitted with two video cameras provided synchronized images of both eyes at a rate of 25/sec during 15 parabolas, the individual parabolas separated by a few minutes of level 1 G flight. Three main findings emerged: 1) After the first parabola, most subjects showed differential torsional offset of the two eyes in the 1 G portions between parabolas, compared to the conjugate baseline position of the eyes prior to the first parabola. 2) Changes in binocular torsion in the 0 G and 1.8 G portions of parabolic flight revealed in most subjects systematic reversal of direction. The reversal was consistent within, but not across subjects. 3) Disconjugacy defined as the moment-to-moment difference in the movements of the two eyes, and evaluated without the contribution of the differential offset, found two subjects with relatively high disconjugacy scores, and the remaining six with low scores. On the basis of prior studies (9, 20), we would predict the first two would be subject to SMS, the remainder not. The two astronauts, who did not have SMS on their space missions, fell into the low scoring group. We propose that the disconjugacies may be due to intrinsic asymmetries in the otolith receptors on the two sides of the head, which appear to be independently linked to the extraocular muscles of the two eyes, a phenomenon masked in normal 1 G states by adaptation. The apparently independent control of the two sides cannot be detected by the simpler and more common monocular studies.     

Modeling repeated count data subject to informative dropout

In certain diseases, outcome is the number of morbid events over the course of follow-up. In epilepsy, e.g., daily seizure counts are often used to reflect disease severity. Follow-up of patients in clinical trials of such diseases is often subject to censoring due to patients dying or dropping out. If the sicker patients tend to be censored in such trials, estimates of the treatment effect that do not incorporate the censoring process may be misleading. We extend the shared random effects approach of Wu and Carroll (1988, Biometrics 44, 175-188) to the setting of repeated counts of events. Three strategies are developed. The first is a likelihood-based approach for jointly modeling the count and censoring processes. A shared random effect is incorporated to introduce dependence between the two processes. The second is a likelihood-based approach that conditions on the dropout times in adjusting for informative dropout. The third is a generalized estimating equations (GEE) approach, which also conditions on the dropout times but makes fewer assumptions about the distribution of the count process. Estimation procedures for each of the approaches are discussed, and the approaches are applied to data from an epilepsy clinical trial. A simulation study is also conducted to compare the various approaches. Through analyses and simulations, we demonstrate the flexibility of the likelihood-based conditional model for analyzing data from the epilepsy trial.     

Modeling Healthcare Processes Using Commitments: An Empirical Evaluation

The two primary objectives of this paper are: (a) to demonstrate how Comma, a business modeling methodology based on commitments, can be applied in healthcare process modeling, and (b) to evaluate the effectiveness of such an approach in producing healthcare process models. We apply the Comma approach on a breast cancer diagnosis process adapted from an HHS committee report, and presents the results of an empirical study that compares Comma with a traditional approach based on the HL7 Messaging Standard (Traditional-HL7). Our empirical study involved 47 subjects, and two phases. In the first phase, we partitioned the subjects into two approximately equal groups. We gave each group the same requirements based on a process scenario for breast cancer diagnosis. Members of one group first applied Traditional-HL7 and then Comma whereas members of the second group first applied Comma and then Traditional-HL7—each on the above-mentioned requirements. Thus, each subject produced two models, each model being a set of UML Sequence Diagrams. In the second phase, we repartitioned the subjects into two groups with approximately equal distributions from both original groups. We developed exemplar Traditional-HL7 and Comma models; we gave one repartitioned group our Traditional-HL7 model and the other repartitioned group our Comma model. We provided the same changed set of requirements to all subjects and asked them to modify the provided exemplar model to satisfy the new requirements. We assessed solutions produced by subjects in both phases with respect to measures of flexibility, time, difficulty, objective quality, and subjective quality. Our study found that Comma is superior to Traditional-HL7 in flexibility and objective quality as validated via Student’s t-test to the 10% level of significance. Comma is a promising new approach for modeling healthcare processes. Further gains could be made through improved tooling and enhanced training of modeling personnel.     

Biomechanics of the Cornea Evaluated by Spectral Analysis of Waveforms from Ocular Response Analyzer and Corvis-ST

Purpose

In this study, spectral analysis of the deformation signal from Corvis-ST (CoST) and reflected light intensity from ocular response analyzer (ORA) was performed to evaluate biomechanical concordance with each other.

Methods

The study was non-interventional, observational, cross-sectional and involved 188 eyes from 94 normal subjects. Three measurements were made on each eye with ORA and CoST each and then averaged for each device. The deformation signal from CoST and reflected light intensity (applanation) signal from ORA was compiled for all the eyes. The ORA signal was inverted about a line joining the two applanation peaks. All the signals were analyzed with Fourier series. The area under the signal curves (AUC), root mean square (RMS) of all the harmonics, lower order (LO included 1^st and 2^nd order harmonic), higher order (HO up to 6^th harmonic), CoST deformation amplitude (DA), corneal hysteresis (CH) and corneal resistance factor (CRF) were analyzed.

Results

The device variables and those calculated by Fourier transform were statistically significantly different between CoST and ORA. These variables also differed between the eyes of the same subject. There was also statistically significant influence of eyes (left vs. right) on the differences in a sub-set of RMS variables only. CH and CRF differed statistically significantly between the eyes of subject (p<0.001) but not DA (p = 0.65).

Conclusions

CoST was statistically significantly different from ORA. CoST may be useful in delineating true biomechanical differences between the eyes of a subject as it reports deformation.     

Post blocking gone too far! Recovery of information and spatial analysis in field experiments

Federer (1998, Biometrics 54, 471-481) presents two analyses of field data in which high-order polynomials are fitted as random regressions to remove spatial variation. We challenge the justification of this approach and suggest some alternatives.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.     

Testing for linear trends in proportions using correlated otolaryngology or ophthalmology data

This paper is concerned with the issue of testing for trend with correlated binary data. We consider the problem where one has either one or two ears (or eyes) available for analysis at baseline and one wishes to look at changes over time in a dichotomous outcome taking into account the correlation between responses from two ears. A reparameterization of Rosner's (1982, Biometrics 38, 105-114) correlated binary data model is presented and applied to a test for trend where the stratifying variable is age (or any other subject-specific variable). Observed and expected values are calculated for the trend statistic separately for both unilateral and bilateral cases and are then summed to obtain an overall summary statistic. The proposed method is illustrated by a reanalysis of data presented in a published study of the efficacy of antibiotics for the treatment of otitis media.     

On the use of historical control data for trend test in carcinogenicity studies

Historical control data are often available in carcinogenicity studies and are included for testing dose effects in current studies. A new method is developed for incorporating the historical control information into a dose effect test. The method generalizes the test procedures proposed by Tarone (1982, Biometrics 38, 215-220) and Ibrahim and Ryan (1996, Biometrics 52, 1478-1485) by taking into account the variation resulting from parameter estimation based on historical data. Two examples are discussed for illustrating the proposed method.     

Procedures for two-sample comparisons with multiple endpoints controlling the experimentwise error rate

Clinical trials are often concerned with the comparison of two treatment groups with multiple endpoints. As alternatives to the commonly used methods, the T2 test and the Bonferroni method, O'Brien (1984, Biometrics 40, 1079-1087) proposes tests based on statistics that are simple or weighted sums of the single endpoints. This approach turns out to be powerful if all treatment differences are in the same direction [compare Pocock, Geller, and Tsiatis (1987, Biometrics 43, 487-498)]. The disadvantage of these multivariate methods is that they are suitable only for demonstrating a global difference, whereas the clinician is further interested in which specific endpoints or sets of endpoints actually caused this difference. It is shown here that all tests are suitable for the construction of a closed multiple test procedure where, after the rejection of the global hypothesis, all lower-dimensional marginal hypotheses and finally the single hypotheses are tested step by step. This procedure controls the experimentwise error rate. It is just as powerful as the multivariate test and, in addition, it is possible to detect significant differences between the endpoints or sets of endpoints.     

Weighted least-squares approach for comparing correlated kappa

In the medical sciences, studies are often designed to assess the agreement between different raters or different instruments. The kappa coefficient is a popular index of agreement for binary and categorical ratings. Here we focus on testing for the equality of two dependent kappa coefficients. We use the weighted least-squares (WLS) approach of Koch et al. (1977, Biometrics 33, 133-158) to take into account the correlation between the estimated kappa statistics. We demonstrate how the SAS PROC CATMOD can be used to test for the equality of dependent Cohen's kappa coefficients and dependent intraclass kappa coefficients with nominal categorical ratings. We also test for the equality of dependent Cohen's kappa and dependent weighted kappa with ordinal ratings. The major advantage of the WLS approach is that it allows the data analyst a way of testing dependent kappa with popular SAS software. The WLS approach can handle any number of categories. Analyses of three biomedical studies are used for illustration.