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The paper focuses on two estimation methods that have been widely used to address endogeneity in empirical research in health economics and health services research B two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI). 2SPS is the rote extension (to nonlinear models) of the popular linear two-stage least squares estimator. The 2SRI estimator is similar except that in the second stage regression, the endogenous variables are not replaced by first-stage predictors. Instead, first-stage residuals are included as additional regressors. In a generic parametric framework, we show that 2SRI is consistent and 2SPS is not. Results from a simulation study and an illustrative example also recommend against 2SPS and favor 2SRI. Our findings are important given that there are many prominent examples of the application of inconsistent 2SPS in the recent literature. This study can be used as a guide by future researchers in health economics who are confronted with endogeneity in their empirical work.

The third section of our Special Task Force report identifies and defines a series of elements that warrant consideration in value assessments of medical technologies. We aim to broaden the view of what constitutes value in health care and to spur new research on incorporating additional elements of value into cost-effectiveness analysis (CEA). Twelve potential elements of value are considered. Four of them-quality-adjusted life-years, net costs, productivity, and adherence-improving factors-are conventionally included or considered in value assessments. Eight others, which would be more novel in economic assessments, are defined and discussed: reduction in uncertainty, fear of contagion, insurance value, severity of disease, value of hope, real option value, equity, and scientific spillovers. Most of these are theoretically well understood and available for inclusion in value assessments. The two exceptions are equity and scientific spillover effects, which require more theoretical development and consensus. A number of regulatory authorities around the globe have shown interest in some of these novel elements. Augmenting CEA to consider these additional elements would result in a more comprehensive CEA in line with the "impact inventory" of the Second Panel on Cost-Effectiveness in Health and Medicine. Possible approaches for valuation and inclusion of these elements include integrating them as part of a net monetary benefit calculation, including elements as attributes in health state descriptions, or using them as criteria in a multicriteria decision analysis. Further research is needed on how best to measure and include them in decision making.

We propose an equation that describes M2-branes ending on M5-branes, and which generalizes the description of the D1-D3 system via Nahm's equation. The simplest solution to this equation constructs the transverse geometry in terms of a fuzzy three sphere. We show that the solution passes a number of consistency checks including a calculation of the energy of the system, matching to the self-dual string solution in the M5-brane world volume, and a study of simple fluctuations about the ground state configuration. We write down certain terms in the effective action of multiple membranes, which includes a sextic scalar coupling.