Locally Complete Path Independent Choice Functions and Their Lattices

The concept of path independence (PI) was first introduced by Arrow (1963) as a defense of his requirement that collective choices be rationalized by a weak ordering. Plott (1973) highlighted the dynamic aspects of PI implicit in Arrow's initial discussion. Throughout these investigations two questions, both initially raised by Plott, remained unanswered. What are the precise mathematical foundations for path independence? How can PI choice functions be constructed? We give complete answers to both these questions for finite domains and provide necessary conditions for infinite domains. We introduce a lattice associated with each PI function. For finite domains these lattices coincide with locally lower distributive or meet-distributive lattices and uniquely characterize PI functions. We also present an algorithm, effective and exhaustive for finite domains, for the construction of PI choice functions and hence for all finite locally lower distributive lattices. For finite domains, a PI function is rationalizable if and only if the lattice is distributive. The lattices associated with PI functions that satisfy the stronger condition of the weak axiom of revealed preference are chains of Boolean algebras and conversely. Those that satisfy the strong axiom of revealed preference are chains and conversely.

Missing data in randomized controlled trials testing palliative interventions pose a significant risk of bias and loss of power: a systematic review and meta-analyses

Objectives To assess the risk posed by missing data (MD) to the power and validity of trials evaluating palliative interventions. Study Design and Setting A systematic review of MD in published randomized controlled trials (RCTs) of palliative interventions in participants with life-limiting illnesses was conducted, and random-effects meta-analyses and metaregression were performed. CENTRAL, MEDLINE, and EMBASE (2009-2014) were searched with no language restrictions. Results One hundred and eight RCTs representing 15,560 patients were included. The weighted estimate for MD at the primary endpoint was 23.1% (95% confidence interval [CI] 19.3, 27.4). Larger MD proportions were associated with increasing numbers of questions/tests requested (odds ratio [OR] , 1.19; 95% CI 1.05, 1.35) and with longer study duration (OR, 1.09; 95% CI 1.02, 1.17). Meta-analysis found evidence of differential rates of MD between trial arms, which varied in direction (OR, 1.04; 95% CI 0.90, 1.20; I 2 35.9, P = 0.001). Despite randomization, MD in the intervention arms (vs. control) were more likely to be attributed to disease progression unrelated to the intervention (OR, 1.31; 95% CI 1.02, 1.69). This was not the case for MD due to death (OR, 0.92; 95% CI 0.78, 1.08). Conclusion The overall proportion and differential rates and reasons for MD reduce the power and potentially introduce bias to palliative care trials

Impartial Predictive Modeling: Ensuring Fairness in Arbitrary Models

Fairness aware data mining aims to prevent algorithms from discriminating against protected groups. The literature has come to an impasse as to what constitutes explainable variability as opposed to discrimination. This stems from incomplete discussions of fairness in statistics. We demonstrate that fairness is achieved by ensuring impartiality with respect to sensitive characteristics. As these characteristics are determined outside of the model, the correct description of the statistical task is to ensure impartiality. We provide a framework for impartiality by accounting for different perspectives on the data generating process. This framework yields a set of impartial estimates that are applicable in a wide variety of situations and post-processing tools to correct estimates from arbitrary models. This effectively separates prediction and fairness goals, allowing modelers to focus on generating highly predictive models without incorporating the constraint of fairness

ECONOMIC IMPACTS OF FUSARIUM HEAD BLIGHT IN WHEAT AND BARLEY: 1998-2000

Fusarium Head Blight (FHB), commonly known as scab, has been a severe problem for wheat and barley producers since 1993. This study provides an update of economic losses suffered by wheat and barley producers in scab-affected regions in the United States. Emphasis is placed on estimating direct and secondary economic impacts of yield and price losses suffered by wheat and barley producers from 1998 to 2000. Nine states are included in the analysis for three wheat classes. Three of the nine states were also used for the analysis of malting and feed barley. The cumulative direct economic losses from FHB in hard red spring (HRS) wheat, soft red winter (SRW) wheat, durum wheat, and barley is estimated at $870 million from 1998 through 2000. The combined direct and secondary economic losses for all the crops were estimated at$2.7 billion. Two states, North Dakota and Minnesota, account for about 55 percent of the total dollar losses.Fusarium Head Blight, scab, vomitoxin, crop losses, wheat, barley, Crop Production/Industries,