Digital Commons Network^™

Space-Time Regression Modeling Of Tree Growth Using The Skew-T Distribution, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for the analysis of repeated measures of spatially correlated growth data. Our motivating application, a ten year study of height growth in a plantation of even-aged white spruce, presents several challenges for statistical analysis. Here, the growth measurements arise from an asymmetric distribution, with heavy tails, and thus standard longitudinal regression models based on a Gaussian error structure are not appropriate. We seek more flexibility for modeling both skewness and fat tails, and achieve this within the class of skew-elliptical distributions. Within this framework, robust space-time regression models are formulated using random …

Detection Of Recurrent Copy Number Alterations In The Genome: A Probabilistic Approach, Oscar M. Rueda, Ramon Diaz-Uriarte

COBRA Preprint Series

Copy number variation (CNV) in genomic DNA is linked to a variety of human diseases (including cancer, HIV acquisition, autoimmune and neurodegenerative diseases), and array-based CGH (aCGH) is currently the main technology to locate CNVs. Several methods can analyze aCGH data at the single sample level, but disease-critical genes are more likely to be found in regions that are common or recurrent among samples. Unfortunately, defining recurrent CNV regions remains a challenge. Moreover, the heterogeneous nature of many diseases requires that we search for CNVs that affect only some subsets of the samples (without prior knowledge of which regions and …

Reversal In Declining Trend Of Adult Mortality In Many States Of India, 1970-2001: Is It Due To Aids?, Abhaya Indrayan, Ajay Kumar Bansal

COBRA Preprint Series

Objectives: To investigate the reversal in adult mortality trend from declining to rising in some segments of population in India, and to use an indirect demographic method to examine if this increase could be due to AIDS mortality. Also, to estimate the total excess deaths.

Design: Cross-sectional data on age-specific death rate in 5-year age-intervals from 25 to 44 years for the years 1970 to 1998 for rural/urban and male/female segments for each of 16 major states of India obtained from the government reports, and their projections till the year 2001.

Methods: In view of reversal of trend in some …

Finding Recurrent Regions Of Copy Number Variation: A Review, Oscar M. Rueda, Ramon Diaz-Uriarte

COBRA Preprint Series

Copy number variation (CNV) in genomic DNA is linked to a variety of human diseases, and array-based CGH (aCGH) is currently the main technology to locate CNVs. Although many methods have been developed to analyze aCGH from a single array/subject, disease-critical genes are more likely to be found in regions that are common or recurrent among subjects. Unfortunately, finding recurrent CNV regions remains a challenge. We review existing methods for the identification of recurrent CNV regions. The working definition of ``common'' or ``recurrent'' region differs between methods, leading to approaches that use different types of input (discretized output from a …

Change-Point Problem And Regression: An Annotated Bibliography, Ahmad Khodadadi, Masoud Asgharian

COBRA Preprint Series

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as "the change-point problem" or, in the Eastern literature, as "disorder".

The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis.

Numerous methodological approaches …

A Simple Index Of Smoking, Abhaya Indrayan Dr., Rajeev Kumar Mr., Shridhar Dwivedi Dr.

COBRA Preprint Series

Background: Cigarette smoking is implicated in a large number of diseases and other adverse health conditions. Among the dimensions of smoking are number of cigarettes smoked per day, duration of smoking, passive smoking, smoking of filter cigarettes, age at start, and duration elapsed since quitting by ex-smokers. The practice so far is to study most of these separately. We develop a simple index that integrates these dimensions of smoking into a single metric, and suggest that this index be developed further. Method: The index is developed under a series of natural assumptions. Broadly, these are (i) the burden of smoking …

The Strength Of Statistical Evidence For Composite Hypotheses With An Application To Multiple Comparisons, David R. Bickel

COBRA Preprint Series

The strength of the statistical evidence in a sample of data that favors one composite hypothesis over another may be quantified by the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function. Unlike the p-value and the Bayes factor, this measure of evidence is coherent in the sense that it cannot support a hypothesis over any hypothesis that it entails. Further, when comparing the hypothesis that the parameter lies outside a non-trivial interval to the hypotheses that it lies within the interval, the proposed measure of evidence almost always asymptotically favors the correct hypothesis …

A New Method For Constructing Exact Tests Without Making Any Assumptions, Karl H. Schlag

COBRA Preprint Series

We present a new method for constructing exact distribution-free tests (and con…fidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with fi…nitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create con…fidence intervals for the …

Properties Of Monotonic Effects On Directed Acyclic Graphs, Tyler J. Vanderweele, James M. Robins

COBRA Preprint Series

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.

Joint Spatial Modeling Of Recurrent Infection And Growth With Processes Under Intermittent Observation, Farouk S. Nathoo

COBRA Preprint Series

In this article we present new statistical methodology for longitudinal studies in forestry where trees are subject to recurrent infection and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed; wherein, a …

The Design And Sample Size Requirement For A Cluster Randomized Non-Inferiority Trial With Two Binary Co-Primary Outcomes., William F. Mccarthy

COBRA Preprint Series

This paper will discuss the design and sample size requirement for a cluster randomized non-inferiority trial with two binary co-primary outcomes. A hypothetical study (the EXAMPLE Trial) will be considered.

Lets assume the EXAMPLE Trial will consist of two separate binomial non-inferiority two-sample trials. Trial 1: the Coronary Artery Disease known population (co-primary 1) and Trial 2: the Coronary Artery Disease unknown population (co-primary 2). A physician-month cluster randomization scheme will be used. That is, for each trial (trial 1 and trial 2) every month for a 12-month period, each physician participating in the EXAMPLE Trial will be allocated a …

The Calculation Of The 97.5% Upper Confidence Bound: Application To Clustered Binary Data In A Binomial Non-Inferiority Two-Sample Trial., William F. Mccarthy

COBRA Preprint Series

This paper will discuss the analysis of a cluster randomized binomial non-inferiority two-sample trial. The determination of the intra-cluster correlation coefficient (ICC) and its use in the calculation of the 97.5% upper confidence bound for delta, the true difference in binomial proportions between the active control and the experimental treatment groups, will be outlined.

Bringing Game Theory To Hypothesis Testing: Establishing Finite Sample Bounds On Inference, Karl H. Schlag

COBRA Preprint Series

Small sample properties are of fundamental interest when only limited data is available. Exact inference is limited by constraints imposed by specific nonrandomized tests and of course also by lack of more data. These effects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a fictitious game against nature. We use this method to investigate sequential …

Properties Of Monotonic Effects On Directed Acyclic Graphs, Tyler J. Vanderweele, James M. Robins

COBRA Preprint Series

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.