Characterizing Coxian Distributions of Algebraic Degree q and Triangular Order p

In this research note we present a procedure to characterize the set of all Coxian distributions of algebraic degree q that have Coxian representations of order p where p > q

Abiraterone acetate plus prednisolone with or without enzalutamide for patients with metastatic prostate cancer starting androgen deprivation therapy: final results from two randomised phase 3 trials of the STAMPEDE platform protocol

Background: Abiraterone acetate plus prednisolone (herein referred to as abiraterone) or enzalutamide added at the start of androgen deprivation therapy improves outcomes for patients with metastatic prostate cancer. Here, we aimed to evaluate long-term outcomes and test whether combining enzalutamide with abiraterone and androgen deprivation therapy improves survival. Methods: We analysed two open-label, randomised, controlled, phase 3 trials of the STAMPEDE platform protocol, with no overlapping controls, conducted at 117 sites in the UK and Switzerland. Eligible patients (no age restriction) had metastatic, histologically-confirmed prostate adenocarcinoma; a WHO performance status of 0–2; and adequate haematological, renal, and liver function. Patients were randomly assigned (1:1) using a computerised algorithm and a minimisation technique to either standard of care (androgen deprivation therapy; docetaxel 75 mg/m2 intravenously for six cycles with prednisolone 10 mg orally once per day allowed from Dec 17, 2015) or standard of care plus abiraterone acetate 1000 mg and prednisolone 5 mg (in the abiraterone trial) orally or abiraterone acetate and prednisolone plus enzalutamide 160 mg orally once a day (in the abiraterone and enzalutamide trial). Patients were stratified by centre, age, WHO performance status, type of androgen deprivation therapy, use of aspirin or non-steroidal anti-inflammatory drugs, pelvic nodal status, planned radiotherapy, and planned docetaxel use. The primary outcome was overall survival assessed in the intention-to-treat population. Safety was assessed in all patients who started treatment. A fixed-effects meta-analysis of individual patient data was used to compare differences in survival between the two trials. STAMPEDE is registered with ClinicalTrials.gov (NCT00268476) and ISRCTN (ISRCTN78818544). Findings: Between Nov 15, 2011, and Jan 17, 2014, 1003 patients were randomly assigned to standard of care (n=502) or standard of care plus abiraterone (n=501) in the abiraterone trial. Between July 29, 2014, and March 31, 2016, 916 patients were randomly assigned to standard of care (n=454) or standard of care plus abiraterone and enzalutamide (n=462) in the abiraterone and enzalutamide trial. Median follow-up was 96 months (IQR 86–107) in the abiraterone trial and 72 months (61–74) in the abiraterone and enzalutamide trial. In the abiraterone trial, median overall survival was 76·6 months (95% CI 67·8–86·9) in the abiraterone group versus 45·7 months (41·6–52·0) in the standard of care group (hazard ratio [HR] 0·62 [95% CI 0·53–0·73]; p<0·0001). In the abiraterone and enzalutamide trial, median overall survival was 73·1 months (61·9–81·3) in the abiraterone and enzalutamide group versus 51·8 months (45·3–59·0) in the standard of care group (HR 0·65 [0·55–0·77]; p<0·0001). We found no difference in the treatment effect between these two trials (interaction HR 1·05 [0·83–1·32]; pinteraction=0·71) or between-trial heterogeneity (I2 p=0·70). In the first 5 years of treatment, grade 3–5 toxic effects were higher when abiraterone was added to standard of care (271 [54%] of 498 vs 192 [38%] of 502 with standard of care) and the highest toxic effects were seen when abiraterone and enzalutamide were added to standard of care (302 [68%] of 445 vs 204 [45%] of 454 with standard of care). Cardiac causes were the most common cause of death due to adverse events (five [1%] with standard of care plus abiraterone and enzalutamide [two attributed to treatment] and one (<1%) with standard of care in the abiraterone trial). Interpretation: Enzalutamide and abiraterone should not be combined for patients with prostate cancer starting long-term androgen deprivation therapy. Clinically important improvements in survival from addition of abiraterone to androgen deprivation therapy are maintained for longer than 7 years. Funding: Cancer Research UK, UK Medical Research Council, Swiss Group for Clinical Cancer Research, Janssen, and Astellas

Characterization of matrix-exponential distributions.

A random variable that is defined as the absorption time of an evanescent finite-state continuous-time Markov chain is said to have a phase-type distribution. A phase-type distribution is said to have a representation (α,T ) where α is the initial state probability distribution and T is the infinitesimal generator of the Markov chain. The distribution function of a phase-type distribution can be expressed in terms of this representation. The wider class of matrix-exponential distributions have distribution functions of the same form as phase-type distributions, but their representations do not need to have a simple probabilistic interpretation. This class can be equivalently defined as the class of all distributions that have rational Laplace-Stieltjes transform. There exists a one-to-one correspondence between the Laplace-Stieltjes transform of a matrix- exponential distribution and a representation (β,S) for it where S is a companion matrix. In order to use matrix-exponential distributions to fit data or approximate probability distributions the following question needs to be answered: “Given a rational Laplace-Stieltjes transform, or a pair (β,S) where S is a companion matrix, when do they correspond to a matrix-exponential distribution?” In this thesis we address this problem and demonstrate how its solution can be applied to the abovementioned fitting or approximation problem.Thesis (Ph.D.)--School of Applied Mathematics, 2003

The value of communication and cooperation when servers are strategic

In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability; one of the two servers is always inactive; each server knows the other’s successful transmission probability and they are willing to cooperate. Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III. doi:10.1017/S144618112000004