An Online Updating Approach for Testing the Proportional Hazards Assumption with Streams of Big Survival Data

The Cox model, which remains as the first choice in analyzing time-to-event data even for large datasets, relies on the proportional hazards assumption. When the data size exceeds the computer memory, the standard statistics for testing the proportional hazards assumption can no longer b e easily calculated. We propose an online up dating approach with minimal storage requirement that up dates the standard test statistic as each new block of data becomes available. Under the null hypothesis of proportional hazards, the proposed statistic is shown to have the same asymptotic distribution as the standard version if it could be computed with a super computer. In simulation studies, the test and its variant based on most recent data blocks maintain their sizes when the proportional hazards assumption holds and have substantial power to detect different violations of the proportional hazards assumption. The approach is illustrated with the survival analysis of patients with lymphoma cancer from the Surveillance, Epidemiology, and End Results Program. The proposed test promptly identified deviation from the proportional hazards assumption that was not captured by the test based on the entire data

The radiative decays of 0++0^{++} and 1+−1^{+-} heavy mesons

The radiative decay is believed to be an ideal lab to study hadronic structure of newly observed resonances because the reactions are governed by only the electromagnetic interaction (tree level). However, to obtain correct theoretical values, one has to properly deal with the non-perturbative QCD effects in the wavefunction and hadronization. In this work we derive the formulas for the radiative decays of $0^{++}$ and $1^{-+}$ heavy mesons in the light front quark model (LFQM). Because $\mathcal{B}(\chi_{c0}\rightarrow J/\psi\gamma)$ is well measured, the theoretical evaluation of the transition rate can be used to test our approach. Within this theoretical framework, the width of $\chi_{b0}\rightarrow \Upsilon(1S)\gamma$ is evaluated. The formulas can be applied to identify the inner structures of new resonances, for example the isospin of $h_{c(b)}$ and the structure of $D_s(2317)$, via processes $h_c\rightarrow \eta_c\gamma$, $h_b\rightarrow \eta_b\gamma$ and $D_s(2317)\rightarrow D_s^*+\gamma$.Comment: 10 pages, 1 figure, Accepted by PR

Constraints on the Asymptotic Baryon Fractions of Galaxy Clusters at Large Radii

While X-ray measurements have so far revealed an increase in the volume-averaged baryon fractions $f_b(r)$ of galaxy clusters with cluster radii $r$, $f_b(r)$ should asymptotically reach a universal value $f_b(\infty)=f_b$, provided that clusters are representative of the Universe. In the framework of hydrostatic equilibrium for intracluster gas, we have derived the necessary conditions for $f_b(\infty)=f_b$: The X-ray surface brightness profile described by the $\beta$ model and the temperature profile approximated by the polytropic model should satisfy $\gamma\approx2(1-1/3\beta)$ and $\gamma\approx1+1/3\beta$ for $\beta1$, respectively, which sets a stringent limit to the polytropic index: $\gamma<4/3$. In particular, a mildly increasing temperature with radius is required if the observationally fitted $\beta$ parameter is in the range $1/3<\beta<2/3$. It is likely that a reliable determination of the universal baryon fraction can be achieved in the small $\beta$ clusters because the disagreement between the exact and asymptotic baryon fractions for clusters with $\beta>2/3$ breaks down at rather large radii (\ga30r_c) where hydrostatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value $f_b(\infty)$ of baryon fraction from the X-ray measurement made primarily over the finite central region of a cluster. We demonstrate our method using a sample of 19 strong lensing clusters, which enables us to place a useful constraint on $f_b(\infty)$: $0.094\pm0.035 \leq f_b(\infty) \leq 0.41\pm0.18$. An optimal estimate of $f_b(\infty)$ based on three cooling flow clusters with $\beta = 0.142\pm0.007$ or $\Omega_M = 0.35\pm0.09$.Comment: 6 pages + 4 figures; accepted for publication in MNRA