Limitations of P-Values and R-squared for Stepwise Regression Building: A Fairness Demonstration in Health Policy Risk Adjustment

ABSTRACT

Stepwise regression building procedures are commonly used applied statistical tools, despite their well-known drawbacks. While many of their limitations have been widely discussed in the literature, other aspects of the use of individual statistical fit measures, especially in high-dimensional stepwise regression settings, have not. Giving primacy to individual fit, as is done with p-values and R², when group fit may be the larger concern, can lead to misguided decision making. One of the most consequential uses of stepwise regression is in health care, where these tools allocate hundreds of billions of dollars to health plans enrolling individuals with different predicted health care costs. The main goal of this “risk adjustment” system is to convey incentives to health plans such that they provide health care services fairly, a component of which is not to discriminate in access or care for persons or groups likely to be expensive. We address some specific limitations of p-values and R² for high-dimensional stepwise regression in this policy problem through an illustrated example by additionally considering a group-level fairness metric.     

How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts?

The procedure suggested by DerSimonian and Laird is the simplest and most commonly used method for fitting the random effects model for meta-analysis. Here it is shown that, unless all studies are of similar size, this is inefficient when estimating the between-study variance, but is remarkably efficient when estimating the treatment effect. If formal inference is restricted to statements about the treatment effect, and the sample size is large, there is little point in implementing more sophisticated methodology. However, it is further demonstrated, for a simple special case, that use of the profile likelihood results in actual coverage probabilities for 95% confidence intervals that are closer to nominal levels for smaller sample sizes. Alternative methods for making inferences for the treatment effect may therefore be preferable if the sample size is small, but the DerSimonian and Laird procedure retains its usefulness for larger samples.     

Probabilistic Applications of the Schlömilch Transformation

The Schlömilch transformation, long used by mathematicians for integral evaluation, allows probability mass to be redistributed, thus transforming old distributions to new ones. The transformation is used to introduce some new families of distributions on ⁺. Their general properties are studied, i.e., distributional shape and skewness, moments and inverse moments, hazard function, and random number generation. In general, these distributions are suitable for modeling data where the hazard function initially rises steeply. Their usefulness is illustrated by fitting some human weight data. Besides data fitting, one possible use of the new distributions could be in sensitivity or robustness studies, for example as Bayesian prior distributions.     

Lessons from life. The biology of business transformation

Biology and business face similar challenges when it comes to change. Living organisms experience constant change. And successful health care organizations must be ready and willing to embrace transition if they are to survive. Take an in-depth look at the biology-to-business metaphor and see how to better manage information technology changes in your organization.     

Data-Based Modeling of the Failure Rate of Repairable Equipment

A databaseof failures of many types of medical equipment was analysed,to study the dependence of failure rate on equipment age andon time since repair. The intention was to use this large datasetto assess the validity of some widely-used models of failurerate, such as the power-law and loglinear Poisson processes,and so to recommend simple and adequate models to those practitionershaving little data to discriminate between rival models. Theaim is also to illustrate a methodology for computing policycosts from failure databases. The power-law process model wasfound to fit slightly better overall than did the loglinear andlinear processes. Some related models were created to fit anobserved peaking of failure rate. The data showed a decreasinghazard of (first) failure after repair for some equipment types.This can be due to imperfect or hazardous repair, and also todiffering failure rates among a population of machines. Two simplemodels of imperfect repair were used to fit the data, and anEmpirical Bayes method was used to fit a model of variable failurerate between machines. Neglect of such variation can lead toan over-estimate of the hazardousness of repair.     

'Second generation' Internet e-health: the gladiator for HIPAA compliance?

The Health Insurance Portability and Accountability Act (HIPAA) is intended to simplify administrative processes and improve health information security. There are a number of traditional ways to address the expense and complexities of simplification, but none of them are bargains or beauties to behold: (1) Do-it-yourself encryption; (2) new back-end system purchases; (3) legacy system re-programming; or (4) onerous paper documentation. The good news is that 'second generation' e-health solutions are emerging that act as internal "wrappers" for health plan or provider data systems. They provide both an interface for end-users and a layer of security for organizational information and allow detailed patient-related data to remain at the system owner's physical location. These second generation solutions don't just 'connect,' data, they actually 'understand' the information, and can use data elements to invoke necessary rules, processing pathways, or personalization for specific stakeholders as required by HIPAA.     

Peer cluster theory and adolescent alcohol use: an explanation of alcohol use and a comparative analysis between two causal models

This study tests the premise of peer cluster theory as it applies to individual alcohol use, and makes a comparative analysis between its ability to explain alcohol use and marijuana use. Using the results of a 1996 drug and alcohol survey of 1312 Western Kentucky University students, path analysis was used to measure the influence of six of peer cluster theory's psychosocial characteristics on the percentage of the respondent's college friends who use alcohol. All of these variables were then regressed on the respondent's alcohol use. The results of the causal models did show some support for peer cluster theory. The direct effect of the student's association with alcohol-using peers on individual alcohol use was shown to have the strongest direct influence on this outcome variable. However, a few limitations of this theoretical perspective were identified. The causal model for alcohol use showed that the indirect influence of two of these psychosocial characteristics (parental attitudes on alcohol use and success in school) was weaker than their direct influence on individual alcohol use. And, the comparative analysis showed that peer cluster theory is better suited to explain the use of marijuana than the use of alcohol.