Models based on the bivariate Poisson distribution are used for modelling sports data. Independent Poisson distributions are usually adopted to model the number of goals of two competing teams. We replace the independence assumption by considering a bivariate Poisson model and its extensions. The models proposed allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing against each other. The effect of introducing even slight correlation is discussed. Using just a bivariate Poisson distribution can improve model fit and prediction of the number of draws in football games. The model is extended by considering an inflation factor for diagonal terms in the bivariate joint distribution.This inflation improves in precision the estimation of draws and, at the same time, allows for overdispersed, relative to the simple Poisson distribution, marginal distributions. The properties of the models proposed as well as interpretation and estimation procedures are provided. An illustration of the models is presented by using data sets from football and water-polo.

Mixed Poisson distributions have been used in a wide range of scientific fields for modeling nonhomogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures. A selective presentation of some of the most prominent members of the family of Poisson mixtures is made.

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In previous research, significant effects of weather conditions on car crashes have been found. However, most studies use monthly or yearly data and only few studies are available analyzing the impact of weather conditions on daily car crash counts. Furthermore, the studies that are available on a daily level do not explicitly model the data in a time-series context, hereby ignoring the temporal serial correlation that may be present in the data. In this paper, we introduce an Integer Autoregressive model for modelling count data with time interdependencies. The model is applied to daily car crash data, metereological data and traffic exposure data from the Netherlands aiming at examining the risk impact of weather conditions on the observed counts. The results show that several assumptions related to the effect of weather conditions on crash counts are found to be significant in the data and that if serial temporal correlation is not accounted for in the model, this may produce biased results.

PURPOSE To better understand the European Society for Medical Oncology-Magnitude of Clinical Benefit Scale version 1.1 (ESMO-MCBS v1.1) and the ASCO Value Framework Net Health Benefit score version 2 (ASCO-NHB v2), ESMO and ASCO collaborated to evaluate the concordance between the frameworks when used to assess clinical benefit attributable to new therapies. METHODS The 102 randomized controlled trials in the noncurative setting already evaluated in the field testing of ESMO-MCBS v1.1 were scored using ASCO-NHB v2 by its developers. Measures of agreement between the frameworks were calculated and receiver operating characteristic curves used to define thresholds for the ASCO-NHB v2 corresponding to ESMO-MCBS v1.1 categories. Studies with discordant scoring were identified and evaluated to understand the reasons for discordance. RESULTS The correlation of the 102 pairs of scores for studies in the noncurative setting is estimated to be 0.68 (Spearman’s rank correlation coefficient; overall survival, 0.71; progression-free survival, 0.67). Receiver operating characteristic curves identified thresholds for ASCO-NHB v2 for facilitating comparisons with ESMO-MCBS v1.1 categories. After applying pragmatic threshold scores of 40 or less (ASCO-NHB v2) and 2 or less (ESMO-MCBS v1.1) for low benefit and 45 or greater (ASCO-NHB v2) and 4 to 5 (ESMO-MCBS v1.1) for substantial benefit, 37 discordant studies were identified. Major factors that contributed to discordance were different approaches to evaluation of relative and absolute gain for overall survival and progression-free survival, crediting tail of the curve gains, and assessing toxicity. CONCLUSION The agreement between the frameworks was higher than observed in other studies that sought to compare them. The factors that contributed to discordant scores suggest potential approaches to improve convergence between the scales.

Adoptive cell therapy (ACT) using autologous tumor-infiltrating lymphocytes (TIL) has been tested in advanced melanoma patients at various centers. We conducted a systematic review and meta-analysis to assess its efficacy on previously treated advanced metastatic cutaneous melanoma. The PubMed electronic database was searched from inception to 17 December 2018 to identify studies administering TIL-ACT and recombinant interleukin-2 (IL-2) following non-myeloablative chemotherapy in previously treated metastatic melanoma patients. Objective response rate (ORR) was the primary end point. Secondary end points were complete response rate (CRR), overall survival (OS), duration of response (DOR) and toxicity. Pooled estimates were derived from fixed or random effect models, depending on the amount of heterogeneity detected. Analysis was carried out separately for high dose (HD) and low dose (LD) IL-2. Sensitivity analyses were carried out. Among 1211 records screened, 13 studies (published 1988 À 2016) were eligible for meta-analysis. Among 410 heavily pretreated patients (some with brain metastasis), 332 received HD-IL-2 and 78 LD-IL-2. The pooled overall ORR estimate was 41% [95% confidence interval (CI) 35% to 48%], and the overall CRR was 12% (95% CI 7% to 16%). For the HD-IL-2 group, the ORR was 43% (95% CI 36% to 50%), while for the LD-IL-2 it was 35% (95% CI 25% to 45%). Corresponding pooled estimates for CRR were 14% (95% CI 7% to 20%) and 7% (95% CI 1% to 12%). The majority of HD-IL-2 complete responders (27/28) remained in remission during the extent of follow-up after CR (median 40 months). Sensitivity analyses yielded similar results. Higher number of infused cells was associated with a favorable response. The ORR for HD-IL-2 compared favorably with the nivolumab/ipilimumab combination following anti-PD-1 failure. TIL-ACT therapy, especially when combined with HD-IL-2, achieves durable clinical benefit and warrants further investigation. We discuss the current position of TIL-ACT in the therapy of advanced melanoma, particularly in the era of immune checkpoint blockade therapy, and review future opportunities for improvement of this approach.

Multivariate extensions of the Poisson distribution are plausible models for multivariate discrete data. The lack of estimation and inferential procedures reduces the applicability of such models. In this paper, an EM algorithm for Maximum Likelihood estimation of the parameters of the Multivariate Poisson distribution is described. The algorithm is based on the multivariate reduction technique that generates the Multivariate Poisson distribution. Illustrative examples are also provided. Extension to other models, generated via multivariate reduction, is discussed.

Modelling football match outcomes is becoming increasingly popular nowadays for both team managers and betting funs. Most of the existing literature deals with modelling the number of goals scored by each team. In this paper, we work in a different direction. Instead of modelling the number of goals directly, we focus on the difference of the number of goals, i.e. the margin of victory. Modelling the differences instead of the scores themselves has some major advantages. Firstly, we eliminate correlation imposed by the fact that the two opponent teams compete each other, and secondly, we do not assume that the scored goals by each team are marginally Poisson distributed. Application of the Bayesian methodology for the Skellam's distribution using covariates is discussed. Illustrations using real data from the English Premiership for the season 2006-2007 are provided. The advantages of the proposed approach are also discussed.