Paul R. Yarnold
Optimal Data Analysis, LLC
This note demonstrates the use of ODA to test the hypothesis of an underlying second-order Markovian process.
Author Archives: paulyarnold
Using ODA to Confirm a First Order Markov Steady State Process
Paul R. Yarnold
Optimal Data Analysis, LLC
Sufficiently iterated over time periods a first order Markovian change process defined by a constant transition matrix yields a steady state. Consecutive transition matrices are compared by Goodman’s chi-square test to assess if a steady state has been achieved. This note demonstrates the analogous use of ODA to assess if such transition matrices differ.
Comparative Accuracy of a Diagnostic Index Modeled Using (Optimized) Regression vs. Novometrics
Ariel Linden & Paul R. Yarnold
Linden Consulting Group, LLC & Optimal Data Analysis, LLC
Diagnostic screening tests are used to predict an individual’s graduated disease status which is measured on an ordered scale assessing disease progression (severity of illness). Maximizing the predictive accuracy of the diagnostic or screening test is paramount to correctly identifying an individual’s actual score along the ordered continuum. The present study compares two approaches for mapping a statistical model to a diagnostic index in order to make accurate outcome predictions for individuals. The application involves a dataset composed of multiple biomedical voice measurements for 42 individuals with early-stage Parkinson’s disease, who completed a six-month trial of a device for remote symptom progression telemonitoring. For 16 voice measures, each treated as a main effect, ordinary least-squares regression is used to predict baseline motor impairment component score. ODA is used to maximize accuracy of the regression model when it is mapped to the diagnostic index, and results are compared with accuracy achieved by the novometric solution.
Identifying Maximum-Accuracy Cut-Points for Diagnostic Indexes via ODA
Ariel Linden & Paul R. Yarnold
Linden Consulting Group, LLC & Optimal Data Analysis, LLC
Maximizing the discriminatory accuracy of a diagnostic or screening test is paramount to correctly identifying individuals with vs. without the disease or disease marker. In this paper we demonstrate the use of ODA to identify the optimal cut-point which best discriminates between those with vs. without the disease (or marker) under study, for any diagnostic test. We illustrate this methodology using a dataset composed of a range of repeated biomedical voice measurements from 31 people, 23 with Parkinson’s disease (PD). A logistic regression model was used to estimate the probability that each observation was from a person with vs. without PD as a function of 22 voice measurement variables, entered in the model as main effects only. Five different methods for computing a diagnostic cut-point on estimated probability are compared.
Reanalysis of the National Supported Work Experiment Using ODA
Ariel Linden & Paul R. Yarnold
Linden Consulting Group, LLC & Optimal Data Analysis, LLC
Data from the National Supported Work (NSW) randomized experiment have been used frequently over the past 30 years to demonstrate the implementation of various non-experimental methods for drawing causal inferences about treatment effects. In the present study we reanalyze the NSW data using ODA and compare results with those estimated using t-tests. Statistical results were largely consistent between methods, however ODA found 22.2% (2 of 9) preintervention characteristics to be imbalanced. Given that ODA avoids assumptions required of parametric methods, and is insensitive to skewed data and outliers, ODA should be considered the preferred approach when evaluating data from randomized experiments.
Using ODA in the Evaluation of Randomized Controlled Trials: Application to Survival Outcomes
Ariel Linden & Paul R. Yarnold
Linden Consulting Group, LLC & Optimal Data Analysis, LLC
In a recent series of papers, ODA has been applied to observational data to draw causal inferences about treatment effects. Presently, ODA is applied to survival outcomes from a randomized controlled trial, with a reanalysis of a study by Linden and Butterworth [2014] that investigated (as a secondary outcome) the effect of a comprehensive hospital-based intervention in reducing mortality at 90 days for chronically ill patients. In the original analysis, differences in mortality rates between treatment and control groups were estimated using logistic regression and calculated as both risk differences and risk ratios, and a treatment effect was found in the subgroup of patients with chronic obstructive pulmonary disease (COPD), but not in the other subgroup of patients with congestive heart failure (CHF). In the present study, we reanalyze these results using both Cox regression, and weighted ODA, wherein the weight of every subject is their follow-up time (i.e., number of days of follow-up).
Using ODA in the Evaluation of Randomized Controlled Trials
Ariel Linden & Paul R. Yarnold
Linden Consulting Group, LLC & Optimal Data Analysis, LLC
In a recent series of papers, ODA has been applied to observational data to draw causal inferences about treatment effects. In this article ODA is applied to data from a randomized controlled trial, with a reanalysis of a study by Linden and Butterworth [2014] that investigated the effect of a comprehensive hospital-based intervention in reducing readmissions for chronically ill patients. In the original analysis, negative binomial regression was used to evaluate readmission rates and emergency department visit rates at 30 and 90 days, and no treatment effects were found. However, ODA is a superior analytic approach because of its insensitivity to skewed data, model-free permutation tests to derive P values, identification of the threshold value which best discriminates intervention and control groups, use of a chance- and complexity-corrected indexes of classification accuracy, and cross-validation to assess generalizability of the findings.
