Advanced Statistics for Health Research

The following sections are included:

• Dedication
• Preface
• About the Authors
• Acknowledgments
• Contents

The following sections are included:

• Saundra’s Checkup Screening
• Flipping the Empirical Rule: New Data Research and a Trip to the Statistical Formulary
• Getting Started in R
• SAS Equivalent
• Stata Equivalent
• Caveats and Final Observations
• Appendix on Data and Matrices
• References

The following sections are included:

• Observations on Individuals (Rows) and Variables (Columns) for Analysis
• Central Tendency (Means) and Spread (Standard Deviations) and The Empirical Rule
• Relationships Between Variables
• Regression Models: The Swiss Army Knife of Multivariate Relationships
• What Happens When There are More than Three Observations?
• The Three Ps: Important Vector Operations for Statistics
• Multiple Determinants of an Outcome Modeled with Multiple Regression
• Appendix on Data and Matrices
• References

The following sections are included:

• Multiple Regression Model
• Correlations Between Treatment and Control Variables
• Variances and Standard Deviations
• Appendix on Data and Matrices
• References

The Data-Generating Process (DGP) is a description of how an outcome, Y, is determined by independent variables, X, for all the population under consideration. In prior chapters, we saw how sample means, variances, covariances of a subset of those Y s and Xs were merged to generate OLS orthogonal projections (which are the predicted values of Y in the X-plane) to estimate key features of the underlying population DGP. But the population DGP itself is not directly observable. We use sample statistics to make inferences about the population…

In Chapter 3, we found that the OLS coefficients were ratios of particular covariances to variances. Variances are always positive. Hence, a coefficient, ${\widehat{\beta }}_j$ generally has the same sign as the simple covariance between the associated regressor x_j and y, and always has the same sign as the covariance between that part of x_j unassociated with other x_ks and y. In Chapter 4, we found that OLS estimators could not reflect causal impacts unless E(μ|X) = 0 (assumption 3 held), which further implied that the error term was uncorrelated with the right-hand side regressors (or anything that should have been included in the model). We stress these two things in this chapter: first, a covariance (or correlation) does not indicate causality, and second, that causal estimates require that the treatment is either randomly assigned or can be treated “as if” it was randomly assigned.

The following sections are included:

• Manning et al. (1987) Analysis of the Rand Health Insurance Experiment
• Weaver et al. (2012) Continuous Positive Airway Pressure Treatment of Sleepy Patients with Milder Obstructive Sleep Apnea with Results of the CPAP Apnea Trial North American Program Randomized Clinical Trial
• Statistical Analysis: Randomization, ANOVA, and Regressions
• Programming interactions in R, STATA, and SAS
• References

The following sections are included:

• Matching
  • Background
  • Caballero-Granado et al. (2001)
  • What are they trying to do?
  • Why is it important?
  • Matching patients
  • R: Code to calculate the marginal effect by averaging across individual observations
  • STATA and SAS marginal effects computations (logits and probits)
• Propensity-Score Matching (Kim et al., 2011)
  • Background
  • What are they trying to do?
  • Why is it important?
  • Sampling
  • Propensity score matching patients
  • Summary of what is learned?
• References

The following sections are included:

• Forward
• Illustrating the Importance of Instrumental Variables Using a Sample of Acute Myocardial Infarction (AMI) (McClellan et al., 1994)
• A Fuller Instrumental Variable Analysis
• Can’t Do IV for Nonlinear Models: Probits, Logits, Count Models, and Multinomial Logits
• References

The following sections are included:

• Background: Medical Insurance Program (MIP) in Georgia
• Regression Discontinuity: At the Discontinuity, the Treatment Effect is Identified
• Labor Unionization in Nursing Homes: Quality and Productivity Effects (Sojourner et al., 2014)
• References

The following sections are included:

• Pay for Performance in Managing Hepatitis B Virus (HBV) and Hepatitis C Virus (HCV): Difference-in-Difference with Propensity Score Matching
• Public Healthcare Entitlements and Health Care Among Ireland’s Elderly: Difference-in-Difference with Propensity Score Matching
• Split-Sample Instrumental Variable Estimation
• Obesity and Phobic Anxiety: The Walter et al. (2015) Study in Psychological Medicine
• References

The following sections are included:

• Background: Longitudinal Data with Initial Randomization — Two Great Ideas Merged
• Toh and Hernan (2008). Causal Estimates of Atypical Antipsychotics on Psychiatric Rating Scale (BPRS)
• Holme et al. (2014). Effect of Flexible Sigmoidoscopy Screening on Colorectal Cancer Incidence and Mortality
• References

Both papers considered in this chapter (Mark et al., 2004; Aakvik and Holmas, 2006) focus on the impact of healthcare providers on patient outcome, measured as hospital mortality rates (and various morbidity rates) in the first paper and as community mortality rates in the second paper. The treatment variables — right-hand side variables of interest — are, respectively, the nurse to patient ratio in hospitals, and the general healthcare provider/practitioner to municipal population ratio in the second paper. Among the possible techniques to get causal estimates given the authors’ data, random assignments of treatments are not feasible (from several politico-economic perspectives), neither are regression discontinuity designs. Matching on the basis of medical professional/exposed population is also rather difficult for these datasets. Hence, these papers rely heavily on fixed effects in panel datasets, and lagged outcomes in panel datasets as control variables, and instrumental variables to handle the problem using the lagged outcome as a predictor variable. The Arellano and Bond (1991) method is the generalized method of moments estimator employed for this purpose in each of the papers reviewed in this chapter…

The following sections are included:

• Background
• Bhargava and Mishra (2014). Electronic Medical Records and Physician Productivity: Evidence from Panel Data Analysis
• Akinci et al. (2014). Examining the Impact of Health Care Expenditures on Health Outcomes in the Middle East and North Africa
• Conclusion
• References

The following sections are included:

• Background
  • Maximum likelihood estimation (MLE)
  • Kelly Gee and Butler (2021). Impact of nurse burnout on organizational and position turnover
  • Shields and Ward (2001). Improving nurse retention in the National Health Service in England: The impact of job satisfaction on intentions to quit
  • Kwak and Clayton-Matthews (2002). Multinomial logistic regression. Nursing Research, 51(6), 404–410
• References

The following sections are included:

• Measuring Fit: R-square for Regression; AUC for Logits, Probits, Linear Probability Models
• Flentje et al. (2020). Screening Gender-Minority People for Harmful Alcohol Use
• Moon and Shin (2006). Healthcare Utilization among Medicare-Medicaid Dual Eligibles: A Count Data Analysis
• References

The following sections are included:

• Background
• Butler et al. (2011). Effects of Non-adherence with Prescription Drugs among Older Adults
• Pollak et al. (1990). Sleep Problems in the Community Elderly as Predictors of Death and Nursing Home Placement
• References

The following sections are included:

• Background: Workers’ Compensation Insurance Pays for Injured Workers’ Sick Leave
• Butler and Worrall (1985). Workers’ Compensation Claim Duration and Benefits
• Johnson et al. (1999). The Costs and Outcomes of Chiropractic and Physician Care for Workers’ Compensation Low Back Claims
• References

The following sections are included:

• Background
• Kniesner et al. (2008). Policy-relevant Heterogeneity in the Value of Statistical Life: New Evidence from Panel Data Quantile Regressions
• Butler et al. (2021). COVID-19 and Gender Wage Inequality in the US: A Quantile Regression Analysis
• References

The following sections are included:

• Background
• LASSO (least absolute shrinkage and selection operator) Restrictions as an Example
• Predicting Nurse Job Satisfaction: Machine Learning Analyses
• Supervised Machine Learning I: Linear Probability and Logistic Regression Methods
• Supervised Machine Learning II: Random Forest Regressions and Out-of-Sample ROCs
• References

In this chapter, we pull together some of the strands of research in the last few chapters of Advanced Statistics by merging CPS employment surveys with CDC data on state-specific, month-by-month COVID-19 cases to estimate wage-offer equations since January 2020 for female nurses until September 2021, which we compare to the wage-offer distributions for males across all occupations. We estimate OLS models, 2SLS models, and Random Forest Residuals Regression (RFRR) analysis in our female–male analyses. We find that the machine learning nature of RFRR provides the most feasible results in terms of linear fit and identification of the wage-offer functions for our sample. Relative to all males working, gender inequality against nurses declined over the period. RFRR indicates that female nurse wage inequality fell by 10%.

The following section is included:

• Index