A re-examination of the algebraic properties of the AHP as a ratio-scaling technique

The Analytic Hierarchy Process (AHP) ratio-scaling approach is re-examined in view of the recent developments in mathematical psychology based on the so-called separable representations. The study highlights the distortions in the estimates based on the maximum eigenvalue method used in the AHP distinguishing the contributions due to random noises from the effects due to the nonlinearity of the subjective weighting function of separable representations. The analysis is based on the second order expansion of the Perron eigenvector and Perron eigenvalue in reciprocally symmetric matrices with perturbations. The asymptotic distributions of the Perron eigenvector and Perron eigenvalue are derived and related to the eigenvalue-based index of cardinal consistency used in the AHP. The results show the limits of using the latter index as a rule to assess the quality of the estimates of a ratio scale. The AHP method to estimate the ratio scales is compared with the classical ratio magnitude approach used in psychophysics.Separable representations, reciprocally symmetric matrices, consistency indexes.

Causal Impact of the Hospital Readmissions Reduction Program on Hospital Readmissions and Mortality

Estimating causal effects of the Hospital Readmissions Reduction Program (HRRP), part of the Affordable Care Act, has been very controversial. Associational studies have demonstrated decreases in hospital readmissions, consistent with the intent of the program, although analyses with different data sources and methods have differed in estimating effects on patient mortality. To address these issues, we define the estimands of interest in the context of potential outcomes, we formalize a Bayesian structural time-series model for causal inference, and discuss the necessary assumptions for estimation of effects using observed data. The method is used to estimate the effect of the passage of HRRP on both the 30-day readmissions and 30-day mortality. We show that for acute myocardial infarction and congestive heart failure, HRRP caused reduction in readmissions while it had no statistically significant effect on mortality. However, for pneumonia, HRRP had no statistically significant effect on readmissions but caused an increase in mortality.Comment: 10 pages, 1 figure, 2 table

Trend estimation and short-term forecasting of COVID-19 cases and deaths worldwide

Since the beginning of the COVID-19 pandemic, many dashboards have emerged as useful tools to monitor the evolution of the pandemic, inform the public, and assist governments in decision making. Our goal is to develop a globally applicable method, integrated in a twice daily updated dashboard that provides an estimate of the trend in the evolution of the number of cases and deaths from reported data of more than 200 countries and territories, as well as a seven-day forecast. One of the significant difficulties to manage a quickly propagating epidemic is that the details of the dynamic needed to forecast its evolution are obscured by the delays in the identification of cases and deaths and by irregular reporting. Our forecasting methodology substantially relies on estimating the underlying trend in the observed time series using robust seasonal trend decomposition techniques. This allows us to obtain forecasts with simple, yet effective extrapolation methods in linear or log scale. We present the results of an assessment of our forecasting methodology and discuss its application to the production of global and regional risk maps.Comment: 15 pages including 5 pages of supplementary materia