Estimation of the sum of differences distribution

Consider the distribution of Z_i d_iwhere the d.d_i?s are 1=1 lldifferences independently, identically and symmetrically distributed with mean zero. The problem is to determine properties of the sdd given the distribution of the d._i?fs and the sample size n. The standardized moments as a function of the moments of the d._i!s are developed. A variance reduction technique for estimating the quantiles of the sdd using Monte Carlo methods is developed based on using the randomization sample consisting of the 2ⁿ values of Z _i+d. rather than the single observation i=l lZ d. corresponding to each sample d_id_n. The randomization sample is shown to produce unbiased and consistent estimators.     

Detecting bliss synergy in in vivo combination studies with a tumor kinetic model

Linear models are generally reliable methods for analyzing tumor growth in vivo, with drug effectiveness being represented by the steepness of the regression slope. With immunotherapy, however, not all tumor growth follows a linear pattern, even after log transformation. Tumor kinetics models are mechanistic models that describe tumor proliferation and tumor killing macroscopically, through a set of differential equations. In drug combination studies, although an additional drug‐drug interaction term can be added to such models, however, the drug interactions suggested by tumor kinetics models cannot be translated directly into synergistic effects. We have developed a novel statistical approach that simultaneously models tumor growth in control, monotherapy, and combination therapy groups. This approach makes it possible to test for synergistic effects directly and to compare such effects among different studies.     

R&D production in the United States: Rethinking the Snowbelt–Sunbelt shift

The Frostbelt–Sunbelt shift in the US, which is thought to have accelerated during the 1970s, corresponds with recent findings that invention and innovation in the Southern and Western parts of the country have come to rival the traditional manufacturing belt. Whether research and development (R&D), a key input to new technology, shows a similar pattern is the focus of this study. It is found, that there was a shift in R&D activity to the Sunbelt during some decades, but not all, and that the manufacturing belt has maintained a slight R&D lead in the country. Still, parts of the Sunbelt rivalled the Northeast for R&D already in 1963. Thus, any national shift in the location of R&D must have occurred prior to the 1960s and before it might be thought to have happened. In the US, R&D production associates well with places that have an educated, professional, and technically specialized labor force. Those states that continue to build on these and similar techno-societal conditions will arguably be in a better position to grow.     

Improved variance estimation for balanced samples drawn via the cube method

The cube method proposed by Deville and Tillé (2004) enables the selection of balanced samples: that is, samples such that the Horvitz-Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is maintained, and a “landing phase” in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tillé (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulation-based method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.