Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.Comment: Published in at http://dx.doi.org/10.1214/12-STS396 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Empirical and Simulated Adjustments of Composite Likelihood Ratio Statistics

Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward asymptotic distribution. There are many proposals for adjusting composite likelihood ratio tests in order to recover an asymptotic chi square distribution, but they all depend on the sensitivity and variability matrices. The same is true for Wald-type and score-type counterparts. In realistic applications sensitivity and variability matrices usually need to be estimated, but there are no comparisons of the performance of composite likelihood based statistics in such an instance. A comparison of the accuracy of inference based on the statistics considering two methods typically employed for estimation of sensitivity and variability matrices, namely an empirical method that exploits independent observations, and Monte Carlo simulation, is performed. The results in two examples involving the pairwise likelihood show that a very large number of independent observations should be available in order to obtain accurate coverages using empirical estimation, while limited simulation from the full model provides accurate results regardless of the availability of independent observations.Comment: 15 page

Statistical modelling of citation exchange among statistics journals

Scholarly journal rankings based on citation data are often met with skepticism by the scientific community. Part of the skepticism is due to the discrepancy between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of authors. This paper focuses on analysis of the table of cross-citations among a selection of Statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care in order to avoid potential over-interpretation of insignificant differences between journal ratings

Hybrid pairwise likelihood analysis of animal behavior experiments

The study of the determinants of contests between animals is an important issue in understanding animal behavior. Tournament experiments among a set of animals are used by zoologists for this purpose. From a statistical point of view, the results of these tournament experiments are naturally analyzed by paired comparison models such as the Bradley-Terry and the Thurstone models. A major complication is the presence of dependence between the outcomes of couples of contests with an animal in common. Likelihood analysis of this type of animal behavior experiments in presence of interdependence between contests is computationally demanding. An alternative fitting method that mixes optimal estimation equations and pairwise likelihood inference is then suggested. The performance of the proposed methodology is investigated by simulation studies and then applied to a real data set about adult male Cape Dwarf Chameleons

Missing data patterns in runners' careers: do they matter?

Predicting the future performance of young runners is an important research issue in experimental sports science and performance analysis. We analyse a data set with annual seasonal best performances of male middle distance runners for a period of 14 years and provide a modelling framework that accounts for both the fact that each runner has typically run in three distance events (800, 1500 and 5000 meters) and the presence of periods of no running activities. We propose a latent class matrix-variate state space model and we empirically demonstrate that accounting for missing data patterns in runners' careers improves the out of sample prediction of their performances over time. In particular, we demonstrate that for this analysis, the missing data patterns provide valuable information for the prediction of runner's performance

Risk Factors and Outcomes Related to Pediatric Intensive Care Unit Admission after Hematopoietic Stem Cell Transplantation: A Single-Center Experience

Abstract To describe incidence, causes, and outcomes related to pediatric intensive care unit (PICU) admission for patients undergoing hematopoietic stem cell transplantation (HSCT), we investigated the risk factors predisposing to PICU admission and prognostic factors in terms of patient survival. From October 1998 to April 2015, 496 children and young adults (0 to 23 years) underwent transplantation in the HSCT unit. Among them, 70 (14.1%) were admitted to PICU. The 3-year cumulative incidence of PICU admission was 14.3%. The main causes of PICU admission were respiratory failure (36%), multiple organ failure (16%), and septic shock (13%). The overall 90-day cumulative probability of survival after PICU admission was 34.3% (95% confidence interval, 24.8% to 47.4%). In multivariate analysis, risk factors predisposing to PICU admission were allogeneic HSCT (versus autologous HSCT, P  = .030) and second or third HSCT ( P  = .018). Characteristics significantly associated with mortality were mismatched HSCT ( P  = .011), relapse of underlying disease before PICU admission ( P P  = .012), hepatic failure at admission ( P  = .021), and need for invasive ventilation during PICU course (

Impact of safety-related dose reductions or discontinuations on sustained virologic response in HCV-infected patients: Results from the GUARD-C Cohort

BACKGROUND: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. METHODS: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. RESULTS: SVR24 rates were 46.1% (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1, 2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced 651 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with 651 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not 655. CONCLUSIONS: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginterferon alfa-2a/ribavirin

Models for paired comparison data: a review with emphasis on dependent data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments of those models have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specic covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other methods, such as limited information estimation. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students

Stochastic dynamic Thurstone-Mosteller models for sports tournaments

In the course of national sports tournaments, usually lasting several months, it is expected that the abilities of teams taking part in the tournament change in time. A dynamic extension of the Thurstone-Mosteller model for paired comparison data is introduced to model the outcomes of sporting contests allowing for time-varying abilities. It is assumed that the development of teams' abilities follows a stationary process and a team-specific home effect is considered. The likelihood function of the proposed model requires the approximation of a high dimensional integral. This difficulty is overcome by means of maximum simulated likelihood via the Geweke-Hajivassiliou-Keane algorithm. Ranking of teams and forecasting future match results are performed through a Metropolis-Hastings algorithm. The methodology is applied to sports data with and without tied contests, namely the 2006-2007 Italian volleyball league and the 2008-2009 Italian Serie A football season

Empirical and Simulated Adjustments of Composite Likelihood Ratio Statistics

Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward asymptotic distribution. There are many proposals for adjusting composite likelihood ratio tests in order to recover an asymptotic chi square distribution, but they all depend on the sensitivity and variability matrices. The same is true for Wald-type and score-type counterparts. In realistic applications sensitivity and variability matrices usually need to be estimated, but there are no comparisons of the performance of composite likelihood based statistics in such an instance. We compare the accuracy of inference based on the statistics considering two methods typically employed for estimation of sensitivity and variability matrices, namely an empirical method that exploits independent observations, and Monte Carlo simulation. The results in two examples involving the pairwise likelihood show that a very large number of independent observations should be available in order to obtain accurate coverages using empirical estimation, while simulation from the full model provides accurate results regardless of the availability of independent observations