Parametric and Nonparametric Analyses of Repeated Ordinal Categorical Data

We compare two models for the analysis of repeated ordinal categorical data: the classical parametric model for means of scores assigned to the categories of the response variable and a nonparametric model based on relative effects derived from the marginal distribution functions of the response. An example in the field of Dentistry is used to illustrate and to compare the models. We also consider a simulation study to evaluate the type‐I error rates and the power of tests under both models in a balanced design setup. The simulation results suggest that both approaches behave similarly for equally spaced scores but may perform differently otherwise. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonparametric Analysis of Ordered Categorical Data in Designs with Longitudinal Observations and Small Sample Sizes

For designs with longitudinal observations of ordered categorical data, a nonparametric model is considered where treatment effects and interactions are defined by means of the marginal distributions. These treatment effects are estimated consistently by ranking methods. The hypotheses in this nonparametric setup are formulated by means of the distribution functions. The asymptotic distribution of the estimators for the nonparametric effects are given under the hypotheses. For small samples, a rather accurate approximation is suggested. A clinical trial with ordered categorical data is used to motivate the ideas and to explain the procedures which are extensions of the Wilcoxon‐Mann‐Whitney test to factorial designs with longitudinal observations. The application of the procedures requires only some trivial regularity assumptions.     

Statistical Methods for Ordered Categorical Data Based on a Constrained Odds Model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann‐Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.     

A Coefficient of Agreement Adjusted for Bias in Paired Ordered Categorical Data

The quality of ordered categorical recordings is determined from repeated measurements on the same subject in order to assess the level of agreement between raters, scales or occasions. The presented rating-invariant method for ordered categorical data provides means of analysing the quality of single-item rating scales, irrespective of the number of possible response values and the marginal distributions. Marginal heterogeneity implies systematic disagreement, so-called bias. An augmented ranking approach is the basis for the separation of inter-rater disagreement into systematic and random components. Correlation between pairs of augmented rank values provides a measure of agreement to the best common ordering of paired classifications, given inter-rater bias. The essential differences in interpretation and applicability of the proposed coefficient of agreement and the Spearman rank-order correlation for ordered categorical data are discussed.     

A Multivariate Analysis of Variance of Categorical Data

Two methods of testing multivariate hypotheses in an IXJXK contingency table are presented. In one case, use is made of the trace of the matrix of sum of squares and sum of products while in the other, determinants of the matrices are used to construct test statistics. Asymptotic equivalence of the methods is shown.     

A Comparison between the LEHMACHER & WALL Rank Tests and Pyhel's Permutation Test for the Analysis of r Independent Samples of Response Curves

LEHMACHER & WALL'S (1978) example of the application of a rank test for the comparison of two independent samples of response curves is reanalyzed by PYHEL'S (1980) permutation test for the hypothesis of parallelism of response curves. This permutation test is part of a complete evaluation of effects for a split-plot design using the permutation test based procedure by WILLMES & PYHEL (1981). Differences in test decisions are discussed.     

Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.     

A comparative approach to examine competitive response of 48 wetland plant species

Abstract. Competitive ability can be separated into competitive effect (ability to suppress neighbours) and competitive response (ability to tolerate suppressive effect from neighbours), but little is known about the competitive response of plants. A screening trial was conducted in outdoor plant pots where competitive response was measured for 48 wetland species during four months grown with seven established sward species: Acorus calamus, Carex crinita, Eleocharis smallii, Lythrum salicaria, Penthorum sedoides, Scirpus acutus and Typha angustifolia. Competitive response was calculated as 100 (x₁–x₂)/x₁, where x₁ is the weight of the target plant grown alone and x₂ the weight of the target plant grown in the swards. Despite significant differences in biomass and survivorship of the target plants between the sward species, the correspondence, W, of the rank order of the competitive response of target plants grown in the seven sward species was 0.70 (P < 0.001). The competitive response values were not significantly correlated with independent measures of competitive effect, relative growth rate or functional classification. Published competitive effect values, however, were significantly positively correlated with RGR. The results suggest a different approach towards the study of competitive response, with a conceptual model including three different response types: (1) escape; (2) foraging; and (3) persistence.     

A Survey of Sample Size Formulas for Pairwise and Many‐one Multiple Comparisons in the Parametric,Nonparametric and Binomial Case

We present a survey of sample size formulas derived in other papers for pairwise comparisons of k treatments and for comparisons of k treatments with a control. We consider the calculation of sample sizes with preassigned per‐pair, any‐pair and all‐pairs power for tests that control either the comparisonwise or the experimentwise type I error rate. A comparison exhibits interesting similarities between the parametric, nonparametric and binomial case.     

实验兔脚皮炎与相对湿度的相关性及对热原筛选实验的影响分析

目的分析实验兔脚皮炎发病率与相对湿度的相关性及脚皮炎实验兔对热原筛选实验合格率的影响。方法将2006、2007年实验室相对湿度记录、实验兔脚皮炎记录及热原筛选实验记录进行汇总统计,并对数据进行生物学分析。结果实验室相对湿度超过70％时,可导致实验兔脚皮炎发病率的升高,二者存在显著相关性（P〈0．01）;有脚皮炎的实验兔可降低筛选实验的合格率,二者存在显著相关性（P〈0．01）;实验兔基础体温的高低,对筛选合格率有显著影响（P〈0．0001）。结论实验兔的脚皮炎发病率与环境相对湿度有显著的正相关性,当实验室相对湿度超过实验兔适宜湿度范围时,可导致其脚皮炎的发病率上升;有脚皮炎的实验兔与无脚皮炎的实验免相比,可显著降低热原筛选实验的合格率。     

Multiple Imputation Approaches for the Analysis of Dichotomized Responses in Longitudinal Studies with Missing Data

Summary Often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value. In the event that the underlying continuous measurements are from a longitudinal study, one can use the repeated‐measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status. Standard Bayesian multiple imputation techniques ( Rubin, 1987 , in Multiple Imputation for Nonresponse in Surveys) that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within‐ and between‐imputation variances are found to be conservative. The frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of Robins and Wang (2000, Biometrika 87, 113–124) is shown to be more efficient. We propose to apply ( Kenward and Roger, 1997 , Biometrics 53, 983–997) degrees of freedom to account for the uncertainty associated with variance–covariance parameter estimates for the repeated measures model.     

A New Nonparametric Approach to the Comparison of K Independent Samples of Response Curves

Two simultaneous distribution free test procedures to test the homogeneity of K samples of response curves measured at T points of time each are proposed which react upon the shape of the response curve. One procedure is based on the comparison of K T-tupels of FRIEDMAN-rank sums, the other on the comparison of K T × T-incidence tables, which first were introduced by KANNEMANN (1976). The application of the two procedures is illustrated by a numerical example. In the discussion the tests are compared with each other and with concurring tests.     

A Generalization of the Intraclass Tau Correlation for Tied and Censored Data

Intraclass tau correlations and a corresponding asymptotic permutation test have already been derived by WHITFIELD (1949), though for continuous data only. WHITFIELD'S concepts are now generalized for use with tied and censored data and a suggestion is made for the application of the methods to arbitrary and varying group sizes. Special attention is given to their application to dichotomous data. Extensive simulations confirming the safe use of the asymptotic test even for samples of moderate size are reported and calculated examples with data from twin-births and kidney transplantations presented.     

A Structure Comparison of two Approaches to LCA Inventory Data, Based on the MIET and ETH Databases (10 pp)

Goal and Scope This study compared two different approaches to general inventory data in LCA, one involving the process-based ETH 96 database and the other an environmentally extended Input-Output table for the US, referring to MIET (Missing Inventory Estimation Tool) 2.0. The purpose of the present paper is to highlight and explain some of the differences between the two approaches, in order to give LCA practitioners a clearer idea of the advantages and limitations of using Input-Output analysis combined with process LCA. Methods The comparison was made despite substantial differences between the two approaches, through a reduction and reclassification of the ETH process technology matrix to fit the Input-Output classification scheme and by concentrating on the structure of the processes rather than their absolute values. The structure is described in terms of the percentage of the CO2 contribution to the total emission by all processes involved in the supply chain. An input and output structure comparison was carried out between ETH 96 and MIET 2.0, to extract information about their structures. Results and Discussion The results of the study show that, despite their methodological differences, MIET 2.0 and ETH 96 show substantial similarities in their overall structures. There are also differences in the structure of the two databases, and most of them have occurred randomly, while, for certain particular sectors, the differences are rather persistent. Especially the contributions by capital goods are constantly lower in ETH 96 database and vice versa. The results imply possible systematic truncation in process LCA databases, especially for a few sectors such as capital goods. Recommendation and Perspective Hybrid analysis can overcome the problem of incompleteness in process LCA, while avoiding such disadvantages of IOA as aggregation problem.     

Complementary Log–Log Regression for the Estimation of Covariate‐Adjusted Prevalence Ratios in the Analysis of Data from Cross‐Sectional Studies

We assessed complementary log–log (CLL) regression as an alternative statistical model for estimating multivariable‐adjusted prevalence ratios (PR) and their confidence intervals. Using the delta method, we derived an expression for approximating the variance of the PR estimated using CLL regression. Then, using simulated data, we examined the performance of CLL regression in terms of the accuracy of the PR estimates, the width of the confidence intervals, and the empirical coverage probability, and compared it with results obtained from log–binomial regression and stratified Mantel–Haenszel analysis. Within the range of values of our simulated data, CLL regression performed well, with only slight bias of point estimates of the PR and good confidence interval coverage. In addition, and importantly, the computational algorithm did not have the convergence problems occasionally exhibited by log–binomial regression. The technique is easy to implement in SAS (SAS Institute, Cary, NC), and it does not have the theoretical and practical issues associated with competing approaches. CLL regression is an alternative method of binomial regression that warrants further assessment.     

Use of Generalised Linear Mixed Models for the Analysis of Clustered Survival Data

Data from a litter matched tumorigenesis experiment are analysed using a generalised linear mixed model (GLMM) approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same litter. Maximum likelihood (ML) and residual maximum likelihood (REML) estimates of risk variable parameters, variance component parameters and the prediction of random effects are given. Estimation of treatment effect parameter (carcinogen effect) has good agreement with previous analyses obtained in the literature though the dependence structure within a litter is modelled in different ways. The variance component estimation provides the estimated dispersion of the random effects. The prediction of random effects, is useful, for instance, in identifying high risk litters and individuals. The present analysis illustrates its wider application to detecting increased risk of occurrence of disease in particular families of a study population.