Physical Sciences and Mathematics Commons^™

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 …

Bootstrap Confidence Regions For Optimal Operating Conditions In Response Surface Methodology, Roger D. Gibb, I-Li Lu, Walter H. Carter Jr

COBRA Preprint Series

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical methods based on the stationary point, proper interpretation of this confidence region does not depend on unknown model parameters. In addition, the methodology does not require the assumption of normally distributed errors. The approach is demonstrated for concave-down and saddle system cases in two dimensions. Simulation studies were performed to assess the coverage probability of these regions.

AMS 2000 subj Classification: 62F25, 62F40, 62F30, 62J05.

Key words: Stationary …

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.

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.

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.

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 …

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 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).

Coronary Evaluation Using Multi-Detector Spiral Computed Tomography Angiography: Statistical Design And Analysis, William F. Mccarthy, Douglas R. Thompson, Bruce A. Barton

COBRA Preprint Series

Contrast-enhanced multi-detector row spiral computed tomography (MDCT) has been introduced as a method for non-invasive visualization of coronary artery stenosis. To determine the diagnostic accuracy of MDCT coronary angiography, as compared to the “gold standard” invasive coronary angiography, sensitivity and specificity are estimated (95% Confidence Intervals). Three separate levels of estimation are computed: at the patient level, at the coronary artery level, and at the coronary artery segment level. We review the methodology for the estimation of sensitivity and specificity of non-clustered binary data (patient level analysis) and present a methodology for the estimation of sensitivity and specificity that considers …

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 …

Review Of The Maximum Likelihood Functions For Right Censored Data. A New Elementary Derivation., Stefano Patti, Elia Biganzoli, Patrizia Boracchi

COBRA Preprint Series

Censoring is a well known feature recurrent in the analysis of lifetime data, occurring in the model when exact lifetimes can be collected for only a representative portion of the surveyed individuals. If lifetimes are known only to exceed some given values, it is referred to as right censoring. In this paper we propose a systematization and a new derivation of the likelihood function for right censored sampling schemes; calculations are reported and assumptions are carefully stated. The sampling schemes considered (Type I, II and Random Censoring) give rise to the same ML function. Only the knowledge of elementary probability …

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 …

A Bayesian Hierarchical Model For Spot Fluorescence In Microarrays, Federico Mattia Stefanini

COBRA Preprint Series

Microarray experiments are characterized by the presence of many sources of experimental bias and a remarkably large technical variability. The assessment of differential expression for genes transcribed into a small number of mRNA copies heavily depends on the proper quantification of background fluorescence within spot. The rough model `observed = hybridization plus background' fluorescence is at first reformulated at spot level, then it is embedded into a Bayesian hierarchical model suited for fitting control spots. The novelties of the approach include the background correction performed on the latent mean of replicated spots, and an explicit model for outlying observations at …

False Discovery Rate Analysis Of Brain Diffusion Direction Maps, Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor

COBRA Preprint Series

Diffusion tensor imaging (DTI) is a novel modality of magnetic resonance imaging that allows non-invasive mapping of the brain’s white matter. A particular map derived from DTI measurements is a map of water principal diffusion directions, which are proxies for neural fiber directions. We consider an experiment in which diffusion direction maps were acquired for two groups of subjects. The objective of the analysis is to find regions of the brain in which the corresponding diffusion directions differ between the groups. This is attained by first computing a test statistic for the difference in direction at every brain location using …