A nonparametric visual test of mixed hazard models

We consider mixed hazard models and introduce a new visual inspection technique capable of detecting the credibility of our model assumptions. Our technique is based on a transformed data approach, where the density of the transformed data should be close to the uniform distribution when our model assumptions are correct. To estimate the density on the transformed axis we take advantage of a recently defined local linear density estimator based on filtered data. We apply the method to national mortality data and show that it is capable of detecting signs of heterogeneity even in small data sets with substantial variability in observed death rates

Risk-adjusted impact of administrative costs on the distribution of terminal wealth for long-term investment

The impact of administrative costs on the distribution of terminal wealth is approximated using a simple formula applicable to many investment situations. We show that the reduction in median returns attributable to administrative fees is usually at least twice the amount of the administrative costs charged for most investment funds, when considering a risk-adjustment correction over a reasonably long-term time horizon. The example we present covers a number of standard cases and can be applied to passive investments, mutual funds, and hedge funds. Our results show investors the potential losses they face in performance due to administrative costs

A review of spatial causal inference methods for environmental and epidemiological applications

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality, and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies, and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided

Convergence rates and moments of Markov chains associated with the mean of Dirichlet processes

We give necessary and sucient conditions for geometric and polynomial ergodicity of a Markov chain on the real line with invariant distribution M equal to the distribution of the mean of a Dirichlet process with parameter . This extends the applicability of a recent MCMC method for sampling from M . We show that the existence of polynomial moments of is necessary and sucient for geometric ergodicity, while logarithmic moments are necessary and sucient for polynomial ergodicity. As corollaries it is shown that and M have polynomial moments of the same order, while the order of the logarithmic moments dier by one. Work supported in part by NSF Grant DMS 9803682 and the EU TMR network ERB-FMRX-CT96-0095 on \Computational and statistical methods for the analysis of spatial data" y Postal Address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England; email: [email protected] z Postal Address: Division of Biostatistics, School of Public Health, A460 Mayo Building, Box 303 420 Delaware Street SE Minneapolis, MN 55455-0378, USA; email: [email protected] 0 Keywords: Dirichlet processes; Markov chains; Markov chain Monte Carlo; geometric and polynomial ergodicity; polynomial and logarithmic moments AMS 2000 Subject Classication: Primary 60J05; 60J10 1

Convergence rates and moments of Markov chains associated with the mean of Dirichlet processes

We give necessary and sufficient conditions for geometric and polynomial ergodicity of a Markov chain on the real line with invariant distribution equal to the distribution of the mean of a Dirichlet process with parameter [alpha]. This extends the applicability of a recent MCMC method for sampling from . We show that the existence of polynomial moments of [alpha] is necessary and sufficient for geometric ergodicity, while logarithmic moments of [alpha] are necessary and sufficient for polynomial ergodicity. As corollaries it is shown that [alpha] and have polynomial moments of the same order, while the order of the logarithmic moments differ by one.Dirichlet processes Markov chains Markov chain Monte Carlo Geometric and polynomial ergodicity Polynomial and logarithmic moments

Locally contracting iterated functions and stability of Markov chains.

We consider Markov chains in the context of iterated random functions and show the existence and uniqueness of an invariant distribution under a local contraction condition combined with a drift condition, extending results of Diaconis and Freedman. From these we deduce various other topological stability properties of the chains. Our conditions are typically satisfied by, for example, queueing and storage models where the global Lipschitz condition used by Diaconis and Freedman normally fails

LBA-2 A randomized trial of long-term tinzaparin, a Low Molecular Weight Heparin (LMWH), versus warfarin for treatment of acute venous thromboembolism (VTE) in cancer patients-the CATCH study

Background Patients with cancer and VTE have a substantial risk of recurrent VTE. LMWH reduces the risk of symptomatic, recurrent VTE compared with warfarin and is recommended as the preferred anticoagulant by consensus guidelines. However, the evidence is based largely on a single, open-label randomized trial (CLOT; Lee et al NEJM 2003). Warfarin is still often used for the treatment of VTE in cancer patients worldwide. Methods The primary objective of this randomized, open-label, multicenter, Phase III trial (CATCH; NCT01130025) was to assess the efficacy of tinzaparin in preventing recurrent VTE in patients with active cancer and acute, symptomatic proximal deep vein thrombosis (DVT) and/or pulmonary embolism (PE). Patients were randomized (stratified by geographic region, tumor characteristic [distant metastasis, no distant metastasis, hematological malignancy] and history of VTE) to receive tinzaparin 175 IU/kg once daily for 6 months or initial tinzaparin 175 IU/kg once daily for 5 10 days overlapped and followed by dose-adjusted warfarin (target INR 2.0 3.0) for 6 months. The primary efficacy outcome was time to recurrent VTE verified by objective, standard imaging and blinded central adjudication; this was a composite primary endpoint that included symptomatic DVT and/or PE, incidental proximal DVT and/or PE and fatal PE. The primary safety endpoint was incidence of major bleeding. All patients were followed up to 6 months or death, whichever came sooner. Blinded central adjudication was also performed for all bleeding events and causes of death. A proportional hazards model for competing risks was applied to all randomized patients, treating all non-VTE-related deaths as competing events. An independent Data Safety Monitoring Board reviewed safety data at regular intervals. Results Nine hundred patients were included from 165 sites in 32 countries across 5 continents. Of these, 449 were randomized to tinzaparin and 451 to warfarin. Mean age was 59 years (range 18 89); 59% female. A total of 77% of patients had a baseline ECOG performance status (PS) of 0 1 and 23% had a PS of 2. The most common primary tumor sites were gynecologic (23%), colorectal (13%), lung (12%), breast (9%); 10% had hematological malignancies. At the time of randomization, metastatic disease was present in 55% of patients and 44% had received prior cancer treatment (chemotherapy, surgery and/or radiation). Time-in-therapeutic range was 47% in the warfarin arm, with 27% above and 26% below the range. Over the 6-month trial period, 31 patients (6.9%) in the tinzaparin arm experienced recurrent VTE compared with 45 (10%) in the warfarin arm (hazard ratio [HR] 0.65 [95% CI 0.41 1.03; P=0.07]) (see figure). There were 2 patients with incidental VTE, both were in the warfarin arm. Symptomatic non-fatal DVT occurred in 12 patients (2.7%) in the tinzaparin arm and 24 (5.3%) in the warfarin arm (HR 0.48 [95% CI 0.24 0.96]; P=0.04). Symptomatic non-fatal PE occurred in 3 patients in the tinzaparin arm and 2 in the warfarin arm; fatal PE occurred in 17 (3.8%) patients in each arm (HR 0.96 [95% CI 0.49 1.88]; P=0.90). There was no difference in the incidence of major bleeding events (n=13 [2.9%] in the tinzaparin arm and 12 [2.7%] in the warfarin arm), but significantly fewer patients experienced clinically relevant non-major bleeding with tinzaparin than warfarin (50 [11%] and 73 [16%] patients, respectively; P=0.03). No difference in mortality was seen with 6-month survival rates of 59% and 60%, respectively. Conclusions In cancer patients with symptomatic VTE, tinzaparin lowered the risk of recurrent VTE compared with warfarin, with a significant reduction in symptomatic DVT and clinically relevant non-major bleeding. No difference in major bleeding or overall mortality was observed. (Figure Presented)