Biostatistics Commons^™

Causal Inference Under Multiple Versions Of Treatment, Tyler J. Vanderweele, Miguel A. Hernan

COBRA Preprint Series

In this article we discuss the no-multiple-versions-of-treatment assumption and extend the potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which a treatment variable is dichotomized to …

Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel

COBRA Preprint Series

In order to functionally interpret differentially expressed genes or other discovered features, researchers seek to detect enrichment in the form of overrepresentation of discovered features associated with a biological process. Most enrichment methods treat the p-value as the measure of evidence using a statistical test such as the binomial test, Fisher's exact test or the hypergeometric test. However, the p-value is not interpretable as a measure of evidence apart from adjustments in light of the sample size. As a measure of evidence supporting one hypothesis over the other, the Bayes factor (BF) overcomes this drawback of the p-value but lacks …

Two-Stage Decompositions For The Analysis Of Functional Connectivity For Fmri With Application To Alzheimer's Disease Risk, Brian S. Caffo, Ciprian M. Crainiceanu, Guillermo Verduzco, Stewart H. Mostofsky, Susan Spear-Bassett, James J. Pekar

COBRA Preprint Series

Functional connectivity is the study of correlations in measured neurophysiological signals. Altered functional connectivity has been shown to be associated with numerous diseases including Alzheimer's disease and mild cognitive impairment. In this manuscript we use a two-stage application of the singular value decomposition to obtain data driven population-level measures of functional connectivity in functional magnetic resonance imaging (fMRI). The method is computationally simple and amenable to high dimensional fMRI data with large numbers of subjects. Simulation studies suggest the ability of the decomposition methods to recover population brain networks and their associated loadings. We further demonstrate the utility of these …

Composite Likelihood Em Algorithm With Applications To Multivariate Hidden Markov Model , Xin Gao, Peter Xuekun Song

COBRA Preprint Series

The method of composite likelihood is useful to deal with estimation and inference in parametric models with high-dimensional data, where the full likelihood approach renders to intractable computational complexity. We develop an extension of the EM algorithm in the framework of composite likelihood estimation in the presence of missing data or latent variables. We establish three key theoretical properties of the composite likelihood EM (CLEM) algorithm, including the ascent property, the algorithmic convergence and the convergence rate. The proposed method is applied to estimate the transition probabilities in multivariate hidden Markov model. Simulation studies are presented to demonstrate the empirical …

Simple, Defensible Sample Sizes Based On Cost Efficiency -- With Discussion And Rejoinder, Peter Bacchetti, Charles E. Mcculloch, Mark R. Segal, Richard Simon, Peter Muller, Gary L. Rosner, James A. Hanley, Stan Shapiro

COBRA Preprint Series

The conventional approach of choosing sample size to provide 80% or greater power ignores the cost implications of different sample size choices. Costs, however, are often impossible for investigators and funders to ignore in actual practice. Here, we propose and justify a new approach for choosing sample size based on cost efficiency, the ratio of a study’s projected scientific and/or practical value to its total cost. By showing that a study’s projected value exhibits diminishing marginal returns as a function of increasing sample size for a wide variety of definitions of study value, we are able to develop two simple …

Estimation Of Dose-Response Functions For Longitudinal Data, Erica E M Moodie, David A. Stephens

COBRA Preprint Series

In a longitudinal study of dose-response, the presence of confounding or non-compliance compromises the estimation of the true effect of a treatment. Standard regression methods cannot remove the bias introduced by patient-selected treatment level, that is, they do not permit the estimation of the causal effect of dose. Using an approach based on the Generalized Propensity Score (GPS), a generalization of the classical, binary treatment propensity score, it is possible to construct a balancing score that provides a more meaningful estimation procedure for the true (unconfounded) effect of dose. Previously, the GPS has been applied only in a single interval …

An Example Of How To Write The Statistical Section Of A Bioequivalence Study Protocol For Fda Review, William F. Mccarthy

COBRA Preprint Series

This paper provides a detailed example of how one should write the statistical section of a bioequivalence study protocol for FDA review. Three forms of bioequivalence are covered: average bioequivalence (ABE), population bioequivalence (PBE) and individual bioequivalence (IBE). The method of analysis is based on Jones and Kenward (2003) and a modification of their SAS Macro is provided.

Adjustment To The Mcnemar’S Test For The Analysis Of Clustered Matched-Pair Data, William F. Mccarthy

COBRA Preprint Series

This paper presents how one can adjust the McNemar’s test for the analysis of clustered matched-pair data. A McNemar’s-like table for K clusters of matched-pair data is used.

Assessment Of Sample Size And Power For The Analysis Of Clustered Matched-Pair Data, William F. Mccarthy

COBRA Preprint Series

This paper outlines how one can determined the sample size or power of a study design that is based on clustered matched-pair data. Detailed examples are provided.

Lachenbruch’S Method For Determining The Sample Size Required For Testing Interactions: How It Compares To Nquery Advisor And O’Brien’S Sas Unifypow., William F. Mccarthy

COBRA Preprint Series

Lachenbruch (1988) proposed a simple method based on the use of orthogonal contrasts to determine the sample size or power for testing main effects and interactions, and uses the normal distribution instead of the non-central F distribution. This method can be used for factorial designs of various size. The example illustrated in this paper considers a 2 x 2 factorial design. This paper will determine both sample size and power of a particular study design with anticipated (assumed) means for each cell of the 2 x 2 factorial design. Lachenbruch’s method will be compared to nQuery Advisor 6.0 (2005) and …

The Existence Of Maximum Likelihood Estimates For The Binary Response Logistic Regression Model, William F. Mccarthy

COBRA Preprint Series

The existence of maximum likelihood estimates for the binary response logistic regression model depends on the configuration of the data points in your data set. There are three mutually exclusive and exhaustive categories for the configuration of data points in a data set: Complete Separation, Quasi-Complete Separation, and Overlap. For this paper, a binary response logistic regression model is considered. A 2 x 2 tabular presentation of the data set to be modeled is provided for each of the three categories mentioned above. In addition, the paper will present an example of a data set whose data points have a …

The Assessment Of The Degree Of Concordance Between The Observed Values And The Predicted Values Of A Mixed-Effect Model Using “Method Of Comparison” Techniques, William F. Mccarthy, Nan Guo

COBRA Preprint Series

In this paper, we present a methodology for determining the degree of concordance between observed and model-based predicted values of a mixed-effect model. In particular, we will compare the degree to which observed and model-based predicted values agree by using ‘method of comparison’ techniques. We will also present the results of the concordance correlation coefficient (CCC).

The Analysis Of Pixel Intensity (Myocardial Signal Density) Data: The Quantification Of Myocardial Perfusion By Imaging Methods., William F. Mccarthy, Douglas R. Thompson

COBRA Preprint Series

This paper described a number of important issues in the analysis of pixel intensity data, as well as approaches for dealing with these. We particularly emphasized the issue of clustering, which may be ubiquitous in studies of pixel intensity data. Clustering can take many forms, e.g., measurements of different sections of a heart or repeated measurements of the same research participant. Clustering typically has the effect of increasing variance estimates. When one fails to account for clustering, variance estimates may be unrealistically small, resulting in spurious significance. We illustrated several possible approaches to account for clustering, including adjusting standard errors …

A Flexible Semi-Parametric Approach To Estimating A Dose-Response Relationship: The Treatment Of Childhood Amblyopia. , David A. Stephens, Erica E M Moodie

COBRA Preprint Series

In a study of a dose-response relationship, flexibility in modelling is essential to capturing the treatment effect when the mean effect of other covariates is not fully understood, so that observed treatment effect is not due to the imposition of a rigid model for the relationship between response, treatment, and other variables. A semiparametric additive linear mixed (SPALM) model (Ruppert et al. 2003) provides a tractable and flexible approach to modelling the influence of potentially confounding variables. In this paper, we present pure likelihood and Bayesian versions of the SPALM model. Both methods of inference are readily implementable, but the …

Causal Comparisons In Randomized Trials Of Two Active Treatments: The Effect Of Supervised Exercise To Promote Smoking Cessation, Jason Roy, Joseph W. Hogan

COBRA Preprint Series

In behavioral medicine trials, such as smoking cessation trials, two or more active treatments are often compared. Noncompliance by some subjects with their assigned treatment poses a challenge to the data analyst. Causal parameters of interest might include those defined by subpopulations based on their potential compliance status under each assignment, using the principal stratification framework (e.g., causal effect of new therapy compared to standard therapy among subjects that would comply with either intervention). Even if subjects in one arm do not have access to the other treatment(s), the causal effect of each treatment typically can only be identified from …

New Statistical Paradigms Leading To Web-Based Tools For Clinical/Translational Science, Knut M. Wittkowski

COBRA Preprint Series

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics.

Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal …