Two-sample post-stratified or subgroup analysis with restricted randomization rules

In a clinical trial to compare two treatments, subjects may be allocated sequentially to treatment groups by a restricted randomization rule. Suppose that at the end of the trial, the investigator is interested in a post-stratified or subgroup analysis with respect to a particular demographic or clinical factor which was not selected prior to the trial for stratified randomization. Under a randomization model, large sample theory of two-sample post-stratified permutational tests is developed with a broad class of restricted randomization treatment allocation rules. The test procedures proposed here are illustrated with a real-life example. The results of this example indicate that it is not always possible to ignore the treatment rule used in the trial in the design-based analysis.     

Effects of unstratified and centre‐stratified randomization in multi‐centre clinical trials

This paper deals with the analysis of randomization effects in multi‐centre clinical trials. The two randomization schemes most often used in clinical trials are considered: unstratified and centre‐stratified block‐permuted randomization. The prediction of the number of patients randomized to different treatment arms in different regions during the recruitment period accounting for the stochastic nature of the recruitment and effects of multiple centres is investigated. A new analytic approach using a Poisson‐gamma patient recruitment model (patients arrive at different centres according to Poisson processes with rates sampled from a gamma distributed population) and its further extensions is proposed. Closed‐form expressions for corresponding distributions of the predicted number of the patients randomized in different regions are derived. In the case of two treatments, the properties of the total imbalance in the number of patients on treatment arms caused by using centre‐stratified randomization are investigated and for a large number of centres a normal approximation of imbalance is proved. The impact of imbalance on the power of the study is considered. It is shown that the loss of statistical power is practically negligible and can be compensated by a minor increase in sample size. The influence of patient dropout is also investigated. The impact of randomization on predicted drug supply overage is discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

A permutation‐based trend test for the analysis of a mechanistic animal migraine assay with a nonstandard design

The effect of a test compound on neurogenically induced vasodilation in marmosets was studied using a non‐standard experimental design with overlapping dosage groups and repeated measurements. In this study, the assumption that the data were normally distributed seemed inappropriate, so no traditional data analyses could be used. As an alternative, a new permutation trend test was designed based on the Jonckheere–Terpstra test statistic. This test protects the type I error without any further assumptions. Statistically significant differences in trend between treatment groups were detected. The effect of the compound was then shown across doses using subsequent Wilcoxon rank‐sum tests against ordered alternatives. In all, the permutation test proved quite useful in this context. This nonparametric approach to the analysis may easily be adapted to other applications. Copyright © 2005 John Wiley & Sons, Ltd.     

The pseudo‐GEE approach to the analysis of longitudinal surveys

Longitudinal surveys have emerged in recent years as an important data collection tool for population studies where the primary interest is to examine population changes over time at the individual level. Longitudinal data are often analyzed through the generalized estimating equations (GEE) approach. The vast majority of existing literature on the GEE method; however, is developed under non‐survey settings and are inappropriate for data collected through complex sampling designs. In this paper the authors develop a pseudo‐GEE approach for the analysis of survey data. They show that survey weights must and can be appropriately accounted in the GEE method under a joint randomization framework. The consistency of the resulting pseudo‐GEE estimators is established under the proposed framework. Linearization variance estimators are developed for the pseudo‐GEE estimators when the finite population sampling fractions are small or negligible, a scenario often held for large‐scale surveys. Finite sample performances of the proposed estimators are investigated through an extensive simulation study using data from the National Longitudinal Survey of Children and Youth. The results show that the pseudo‐GEE estimators and the linearization variance estimators perform well under several sampling designs and for both continuous and binary responses. The Canadian Journal of Statistics 38: 540–554; 2010 © 2010 Statistical Society of Canada     

Iterative algorithms for non-orthogonal analysis of variance

The normal equations for Analysis of Variance possess special properties which are not accounted by standard inversion methods.

The proportion of useful elements in the matrix XX may be very small, so that its storage requires much more computer place than necessary. The proposed iterative method extends to analysis of covarianee and is compared with other ones.     

Direct products: a powerful tool for the analysis of balanced data

This paper focuses attention on the use of direct (Kronecker) product techniques in the study of general balanced models. Direct products provide a powerful tool which facilitates the derivation of certain properties of these models. This is clearly demonstrated in determining the distribution of sums of squares in a balanced mixed-effects model under normality assumptions. Further evidence of its usefulness is also indicated.     

A cautionary note on the analysis of randomized block designs with a few missing values

The randomized block design is routinely employed in the social and biopharmaceutical sciences. With no missing values, analysis of variance (AOV) can be used to analyze such experiments. However, if some data are missing, the AOV formulae are no longer applicable, and iterative methods such as restricted maximum likelihood (REML) are recommended, assuming block effects are treated as random. Despite the well-known advantages of REML, methods like AOV based on complete cases (blocks) only (CC-AOV) continue to be used by researchers, particularly in situations where routinely only a few missing values are encountered. Reasons for this appear to include a natural proclivity for non-iterative, summary-statistic-based methods, and a presumption that CC-AOV is only trivially less efficient than REML with only a few missing values (say≤10%). The purpose of this note is two-fold. First, to caution that CC-AOV can be considerably less powerful than REML even with only a few missing values. Second, to offer a summary-statistic-based, pairwise-available-case-estimation (PACE) alternative to CC-AOV. PACE, which is identical to AOV (and REML) with no missing values, outperforms CC-AOV in terms of statistical power. However, it is recommended in lieu of REMLonly if software to implement the latter is unavailable, or the use of a “transparent” formula-based approach is deemed necessary. An example using real data is provided for illustration.     

An efficient analysis of covariance model for crossover thorough QT studies with period‐specific pre‐dose baselines

Baseline adjustment is an important consideration in thorough QT studies for non‐antiarrhythmic drugs. For crossover studies with period‐specific pre‐dose baselines, we propose a by‐time‐point analysis of covariance model with change from pre‐dose baseline as response, treatment as a fixed effect, pre‐dose baseline for current treatment and pre‐dose baseline averaged across treatments as covariates, and subject as a random effect. Additional factors such as period and sex should be included in the model as appropriate. Multiple pre‐dose measurements can be averaged to obtain a pre‐dose‐averaged baseline and used in the model. We provide conditions under which the proposed model is more efficient than other models. We demonstrate the efficiency and robustness of the proposed model both analytically and through simulation studies. The advantage of the proposed model is also illustrated using the data from a real clinical trial. Copyright © 2014 John Wiley & Sons, Ltd.     

Tree-structured subgroup analysis for censored survival data: Validation of computationally inexpensive model selection criteria

The performance of computationally inexpensive model selection criteria in the context of tree-structured subgroup analysis is investigated. It is shown through simulation that no single model selection criterion exhibits a uniformly superior performance over a wide range of scenarios. Therefore, a two-stage approach for model selection is proposed and shown to perform satisfactorily. Applied example of subgroup analysis is presented. Problems associated with tree-structured subgroup analysis are discussed and practical solutions are suggested.     

A nonparametric method for analysis of variance

A nonparametric method for analyzing analysis of variance models is introduced which is highly resistant to outliers, computationally simple, and comprehensible to anyone with a rudimentary knowledge of classical analysis of variance. The methodology is based on Mood's median test and is highly useful as an exploratory technique.     

Analysis of means approach for random factor analysis

Analysis of means (ANOM) is a powerful tool for comparing means and variances in fixed-effects models. The graphical exhibit of ANOM is considered as a great advantage because of its interpretability and its ability to evaluate the practical significance of the mean effects. However, the presence of random factors may be problematic for the ANOM method. In this paper, we propose an ANOM approach that can be applied to test random effects in many different balanced statistical models including fixed-, random- and mixed-effects models. The proposed approach utilizes the range of the treatment averages for identifying the dispersions of the underlying populations. The power performance of the proposed procedure is compared to the analysis of variance (ANOVA) approach in a wide range of situations via a Monte Carlo simulation study. Illustrative examples are used to demonstrate the usefulness of the proposed approach and its graphical exhibits, provide meaningful interpretations, and discuss the statistical and practical significance of factor effects.     

A tow-stage procedure for testing homogeneity of means against ordered alternatives in analysis of variance with unequal variances

In this paper we present a two-stage sampling procedure for testing the equality of normal means against ordered alternatives in one-way analysis of variance with unequal unknown variances. A table of approximated percentiles needed for implementation is provided. Some Monte Carlo results for estimating the power of the proposed test statistic are presented.     

On correlation analysis of many‐to‐many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study

Correlation studies are an important hypothesis‐generating and testing tool, and have a wide range of applications in many scientific fields. In ecological studies in particular, multiple environmental variables are often measured in an attempt to determine relationships between chemical, physical and biological factors. For example, one may wish to know whether and how soil properties correlate with plant physiology. Although correlation coefficients are widely used, their properties and limitations are often imperfectly understood. This is especially the case when one is interested in correlations between, say, trace element content in sediments and in marine organisms, where no one‐to‐one correspondence exists. We show that evaluating Pearson's correlation coefficient for either site‐specific means or composite samples results in biased estimates, and we propose an alternative estimator. We use simulation studies to demonstrate that our estimator generally has a much smaller bias and mean squared error. We further illustrate its use in a case study of the correlation between trace element content in sediments and in mussels in Lyttelton Harbour, New Zealand.     

Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe

Abstract. In geophysical and environmental problems, it is common to have multiple variables of interest measured at the same location and time. These multiple variables typically have dependence over space (and/or time). As a consequence, there is a growing interest in developing models for multivariate spatial processes, in particular, the cross‐covariance models. On the other hand, many data sets these days cover a large portion of the Earth such as satellite data, which require valid covariance models on a globe. We present a class of parametric covariance models for multivariate processes on a globe. The covariance models are flexible in capturing non‐stationarity in the data yet computationally feasible and require moderate numbers of parameters. We apply our covariance model to surface temperature and precipitation data from an NCAR climate model output. We compare our model to the multivariate version of the Matérn cross‐covariance function and models based on coregionalization and demonstrate the superior performance of our model in terms of AIC (and/or maximum loglikelihood values) and predictive skill. We also present some challenges in modelling the cross‐covariance structure of the temperature and precipitation data. Based on the fitted results using full data, we give the estimated cross‐correlation structure between the two variables.     

Estimation of discrete survival function for error‐prone diagnostic tests

The product limit or Kaplan‐Meier (KM) estimator is commonly used to estimate the survival function in the presence of incomplete time to event. Application of this method assumes inherently that the occurrence of an event is known with certainty. However, the clinical diagnosis of an event is often subject to misclassification due to assay error or adjudication error, by which the event is assessed with some uncertainty. In the presence of such errors, the true distribution of the time to first event would not be estimated accurately using the KM method. We develop a method to estimate the true survival distribution by incorporating negative predictive values and positive predictive values, into a KM‐like method of estimation. This allows us to quantify the bias in the KM survival estimates due to the presence of misclassified events in the observed data. We present an unbiased estimator of the true survival function and its variance. Asymptotic properties of the proposed estimators are provided, and these properties are examined through simulations. We demonstrate our methods using data from the Viral Resistance to Antiviral Therapy of Hepatitis C study.     

Linear Regression With Nested Errors Using Probability‐Linked Data

Probabilistic matching of records is widely used to create linked data sets for use in health science, epidemiological, economic, demographic and sociological research. Clearly, this type of matching can lead to linkage errors, which in turn can lead to bias and increased variability when standard statistical estimation techniques are used with the linked data. In this paper we develop unbiased regression parameter estimates to be used when fitting a linear model with nested errors to probabilistically linked data. Since estimation of variance components is typically an important objective when fitting such a model, we also develop appropriate modifications to standard methods of variance components estimation in order to account for linkage error. In particular, we focus on three widely used methods of variance components estimation: analysis of variance, maximum likelihood and restricted maximum likelihood. Simulation results show that our estimators perform reasonably well when compared to standard estimation methods that ignore linkage errors.     

Robustness of a multiple ranking procedure: a monte carlo experiment illustrating design and analysis techniques

This case study demonstrates statistical design and analysis techniques applicable to any Monte Carlo or simulation experiment, namely a 2^7?3 experimental design, antithetic variates, sample size determination, analysis of variance, regression analysis, and simultaneous inference. The example is a Monte Carlo investigation of the robustness of Bechhofer and Blumenthal’s multiple ranking procedure (MRP). The investigation shows that their procedure works often, but not always. Factors that make it break down, are identified.     

A calibrated imputation method for secondary data analysis of survey data

In practical survey sampling, missing data are unavoidable due to nonresponse, rejected observations by editing, disclosure control, or outlier suppression. We propose a calibrated imputation approach so that valid point and variance estimates of the population (or domain) totals can be computed by the secondary users using simple complete‐sample formulae. This is especially helpful for variance estimation, which generally require additional information and tools that are unavailable to the secondary users. Our approach is natural for continuous variables, where the estimation may be either based on reweighting or imputation, including possibly their outlier‐robust extensions. We also propose a multivariate procedure to accommodate the estimation of the covariance matrix between estimated population totals, which facilitates variance estimation of the ratios or differences among the estimated totals. We illustrate the proposed approach using simulation data in supplementary materials that are available online.     

Mixture and mixture–process variable experiments for pharmaceutical applications

Many experiments in research and development in the pharmaceutical industry involve mixture components. These are experiments in which the experimental factors are the ingredients of a mixture and the response variable is a function of the relative proportion of each ingredient, not its absolute amount. Thus the mixture ingredients cannot be varied independently. A common variation of the mixture experiment occurs when there are also one or more process factors that can be varied independently of each other and of the mixture components, leading to a mixture–process variable experiment. We discuss the design and analysis of these types of experiments, using tablet formulation as an example. Our objective is to encourage greater utilization of these techniques in pharmaceutical research and development. Copyright © 2004 John Wiley & Sons Ltd.