Linear models

In his seminal book, Shewhart (1931) makes no demand on the distribution of the characteristic to be plotted on a control chart. How then can we explain the idea that normality is, if not required, at least highly desirable? I believe that it has come about through the many statistical studies of control-chart behavior. If one is to study how a control chart behaves, it is necessary to relate it to some distribution. The obvious choice is the normal distribution because of its ubiquity as a satisfactory model. This is bolstered by the existence of the Central Limit Theorem.

Sampling: Design and Analysis

Analysis of Contingency Tables

This paper reports trends in educational assortative marriage from 1940 to 2003 in the U.S. Analyses of Census and Current Population Survey data show that educational homogamy increased over most of this period, although there is some evidence of stabilization in the 1990s. From 1940 to the early-1970s, these increases were generated by decreasing intermarriage among groups of relatively well educated persons. Beginning in the early-1970s, the odds of intermarriage among the highly educated stabilized while the odds that high school dropouts marry up dropped substantially. These trends are similar for a broad cross-section of married couples and for newlyweds.

/pdf/trends-in-educational-assortative-marriage-from-1940-to-2003-2x4odsxvpk.pdf

Trends in Educational Assortative Marriage From 1940 to 2003 - eScholarship

Redundancy and reduction: Speakers manage syntactic information density

Bilder and Tebbs review An Introduction to Categorical Data Analysis (2nd ed.) by Alan Agresti.

An Introduction to Categorical Data Analysis

OBJECTIVES: To establish the optimal parameters for group testing of pooled specimens for the detection of SARS-CoV-2. METHODS: The most efficient pool size was determined to be five specimens using a web-based application. From this analysis, 25 experimental pools were created using 50 µL from one SARS-CoV-2 positive nasopharyngeal specimen mixed with 4 negative patient specimens (50 µL each) for a total volume of 250 µL. Viral RNA was subsequently extracted from each pool and tested using the CDC SARS-CoV-2 RT-PCR assay. Positive pools were consequently split into individual specimens and tested by extraction and PCR. This method was also tested on an unselected group of 60 nasopharyngeal specimens grouped into 12 pools. RESULTS: All 25 pools were positive with cycle threshold (Ct) values within 0 and 5.03 Ct of the original individual specimens. The analysis of 60 specimens determined that 2 pools were positive followed by identification of 2 individual specimens among the 60 tested. This testing was accomplished while using 22 extractions/PCR tests, a savings of 38 reactions. CONCLUSIONS: When the incidence rate of SARS-CoV-2 infection is 10% or less, group testing will result in the saving of reagents and personnel time with an overall increase in testing capability of at least 69%.

/pdf/assessment-of-specimen-pooling-to-conserve-sars-cov-2-19dshmeagy.pdf

Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources.

Since the early 1940s, group testing (pooled testing) has been used to reduce costs in a variety of applications, including infectious disease screening, drug discovery, and genetics. In such applications, the goal is often to classify individuals as positive or negative using initial group testing results and the subsequent process of decoding of positive pools. Many decoding algorithms have been proposed, but most fail to acknowledge, and to further exploit, the heterogeneous nature of the individuals being screened. In this article, we use individuals' risk probabilities to formulate new informative decoding algorithms that implement Dorfman retesting in a heterogeneous population. We introduce the concept of "thresholding" to classify individuals as "high" or "low risk," so that separate, risk-specific algorithms may be used, while simultaneously identifying pool sizes that minimize the expected number of tests. When compared to competing algorithms which treat the population as homogeneous, we show that significant gains in testing efficiency can be realized with virtually no loss in screening accuracy. An important additional benefit is that our new procedures are easy to implement. We apply our methods to chlamydia and gonorrhea data collected recently in Nebraska as part of the Infertility Prevention Project.

Informative Dorfman screening.

Analyzing a Binary Response, Part 1: Introduction One binary variable Two binary variables Analyzing a Binary Response, Part 2: Regression Models Linear regression models Logistic regression models Generalized linear models Analyzing a Multicategory Response Multinomial probability distribution I x J contingency tables and inference procedures Nominal response regression models Ordinal response regression models Additional regression models Analyzing a Count Response Poisson model for count data Poisson regression models for count responses Poisson rate regression Zero inflation Model Selection and Evaluation Variable selection Tools to assess model fit Overdispersion Examples Additional Topics Binary responses and testing error Exact inference Categorical data analysis in complex survey designs "Choose all that apply" data Mixed models and estimating equations for correlated data Bayesian methods for categorical data Appendix A: An Introduction to R Appendix B: Likelihood Methods Bibliography Index Exercises appear at the end of each chapter.

Analysis of Categorical Data with R

Objectives To establish the optimal parameters for group testing of pooled specimens for the detection of SARS-CoV-2. Methods The most efficient pool size was determined to be 5 specimens using a web-based application. From this analysis, 25 experimental pools were created using 50 microliter from one SARS-CoV-2 positive nasopharyngeal specimen mixed with 4 negative patient specimens (50 microliter each) for a total volume of 250 microliter l. Viral RNA was subsequently extracted from each pool and tested using the CDC SARS-CoV-2 RT-PCR assay. Positive pools were consequently split into individual specimens and tested by extraction and PCR. This method was also tested on an unselected group of 60 nasopharyngeal specimens grouped into 12-pools. Results All 25 pools were positive with Cycle threshold (Ct) values within 0 and 5.03 Ct of the original individual specimens. The analysis of 60 specimens determined that two pools were positive followed by identification of two individual specimens among the 60 tested. This testing was accomplished while using 22 extractions/PCR tests, a savings of 38 reactions. Conclusions When the incidence rate of SARS-CoV-2 infection is 10% or less, group testing will result in the saving of reagents and personnel time with an overall increase in testing capability of at least 69%.

https://www.medrxiv.org/content/medrxiv/early/2020/04/06/2020.04.03.20050195.full.pdf

Christopher R. Bilder

Papers

An Introduction to Categorical Data Analysis

Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources.

Informative Dorfman screening.

Analysis of Categorical Data with R

Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources.