Frequentist analysis of basket trials with one-sample Mantel-Haenszel procedures

Recent substantial advances of molecular targeted oncology drug development is requiring new paradigms for early-phase clinical trial methodologies to enable us to evaluate efficacy of several subtypes simultaneously and efficiently. The concept of the basket trial is getting of much attention to realize this requirement borrowing information across subtypes, which are called baskets. Bayesian approach is a natural approach to this end and indeed the majority of the existing proposals relies on it. On the other hand, it required complicated modeling and may not necessarily control the type 1 error probabilities at the nominal level. In this paper, we develop a purely frequentist approach for basket trials based on one-sample Mantel-Haenszel procedure relying on a very simple idea for borrowing information under the common treatment effect assumption over baskets. We show that the proposed estimator is consistent under two limiting models of the large strata and sparse data limiting models (dually consistent) and propose dually consistent variance estimators. The proposed Mantel-Haenszel estimators are interpretable even if the common treatment assumptions are violated. Then, we can design basket trials in a confirmatory matter. We also propose an information criterion approach to identify effective subclass of baskets

Higher-spin Currents and Thermal Flux from Hawking Radiation

Quantum fields near black hole horizons can be described in terms of an infinite set of d=2 conformal fields. In this paper, by investigating transformation properties of general higher-spin currents under a conformal transformation, we reproduce the thermal distribution of Hawking radiation in both cases of bosons and fermions. As a byproduct, we obtain a generalization of the Schwarzian derivative for higher-spin currents.Comment: 4 pages, RevTex, accepted for publication in PR

Detecting signals of weakly first-order phase transitions in two-dimensional Potts models

We investigate the first-order phase transitions of the $q$-state Potts models with $q = 5, 6, 7$, and $8$ on the two-dimensional square lattice, using Monte Carlo simulations. At the very weakly first-order transition of the $q=5$ system, the standard data-collapse procedure for the order parameter, carried out with results for a broad range of system sizes, works deceptively well and produces non-trivial critical exponents different from the trivial values expected for first-order transitions. However, a more systematic study reveals significant drifts in the `pseudo-critical' exponents as a function of the system size. For this purpose, we employ two methods of analysis: the data-collapse procedure with narrow range of the system size, and the Binder-cumulant crossing technique for pairs of system sizes. In both methods, the estimates start to drift toward the trivial values as the system size used in the analysis exceeds a certain `cross-over' length scale. This length scale is remarkably smaller than the correlation length at the transition point for weakly first-order transitions, e.g., less than one tenth for $q=5$, in contrast to the naive expectation that the system size has to be comparable to or larger than the correlation length to observe the correct behavior. The results overall show that proper care is indispensable to diagnose the nature of a phase transition with limited system sizes.Comment: 10 pages, 7 figures. One figure has been replaced to make our claim cleare