Homogeneity Test of Many-to-One Risk Differences for Correlated Binary Data under Optimal Algorithms

In clinical studies, it is important to investigate the effectiveness of different therapeutic designs, especially, multiple treatment groups to one control group. The paper mainly studies homogeneity test of many-to-one risk differences from correlated binary data under optimal algorithms. Under Donner’s model, several algorithms are compared in order to obtain global and constrained MLEs in terms of accuracy and efficiency. Further, likelihood ratio, score, and Wald-type statistics are proposed to test whether many-to-one risk differences are equal based on optimal algorithms. Monte Carlo simulations show the performance of these algorithms through the total averaged estimation error, SD, MSE, and convergence rate. Score statistic is more robust and has satisfactory power. Two real examples are given to illustrate our proposed methods.

Modeling of Football Match Outcomes with Expected Goals Statistic

Aim. Our research examined the predictive capabilities of mathematical models that are solely based on the expected goal statistics obtained from a publicly available database. Method. We collected match and expected goals data for 310 matches from three European Leagues (Bundesliga, La Liga, and Serie A). We created three probabilistic models based on the expected goals statistic and compared them with two well-established probabilistic models using binomial deviance, squared error, and profitability in the betting market as evaluation metrics. Results. Our best model adjusted the expected goal statistics for homefield advantage and outperformed the two probabilistic models used for comparison. Two of our models were profitable under certain betting conditions. Limitations. Our models explored a simplistic integration of expected goals into a Poisson based probabilistic model and did not include other contributing factors such as a team’s defensive prowess. The number of games simulated was also limited due to the premature closure of the European Leagues due to the COVID-19 pandemic. Conclusions. The use of a probabilistic model based solely on expected goals score statistic can provide some meaningful insight into forecasting the outcome of a football match and can develop useful betting strategies.

Home sweet home: Quantifying home court advantages for NCAA basketball statistics

Box score statistics are the baseline measures of performance for National Collegiate Athletic Association (NCAA) basketball. Between the 2011-2012 and 2015-2016 seasons, NCAA teams performed better at home compared to on the road in nearly all box score statistics across both genders and all three divisions. Using box score data from over 100,000 games spanning the three divisions for both women and men, we examine the factors underlying this discrepancy. The prevalence of neutral location games in the NCAA provides an additional angle through which to examine the gaps in box score statistic performance, which we believe has been underutilized in existing literature. We also estimate a regression model to quantify the home court advantages for box score statistics after controlling for other factors such as number of possessions, and team strength. Additionally, we examine the biases of scorekeepers and referees. We present evidence that scorekeepers tend to have greater home team biases when observing men compared to women, higher divisions compared to lower divisions, and stronger teams compared to weaker teams. Finally, we present statistically significant results indicating referee decisions are impacted by attendance, with larger crowds resulting in greater bias in favor of the home team.

Identifying High-risk Areas of Foot-and-mouth Disease Outbreak Using a Spatiotemporal Score Statistic: A Case of South Korea

The objective of this study is to identify high-risk areas of foot-and-mouth disease (FMD) in South Korea using nationwide data collected for the disease cases that occurred during the period from December 2014 to April 2015. High-risk areas of FMD occurrence are defined as local clusters or hot spots, where the frequency of disease occurrence is higher than expected. An issue in the FMD detection study is in identifying a spatial pattern deviated significantly from the expected value under the null hypothesis that no spatial process is investigated. While identifying geographic clusters is challenging to reveal the causes of disease outbreak, it is most useful to detect and monitor potential areas of risk occurrence and suggest a further in-depth investigation. This study extended a traditional score statistic (SC) that has limited to identify the spatial pattern by proposing a spatiotemporal score statistic (STSC) that incorporates a temporal component into the SC approach. STSC, a local spatial statistic, was utilized to detect clusters around the known foci with a latent period. This study demonstrated STSC could better exploit the advantage of the original SC and improve the cluster detection due to the latent time component. The empirical results of STSC are expected to provide more useful policy implications with agencies in charge of preventing and controlling the spread of epidemics when deciding where to concentrate the limited resources available.

Statistical Method Based on Bayes-Type Empirical Score Test for Assessing Genetic Association with Multilocus Genotype Data

Simultaneous testing of multiple genetic variants for association is widely recognized as a valuable complementary approach to single-marker tests. As such, principal component regression (PCR) has been found to have competitive power. We focus on exploring a robust test for an unknown genetic mode of all SNPs, an unknown Hardy-Weinberg equilibrium (HWE) in a population, and a large number of all SNPs. First, we propose a new global test by means of the use of codominant codes for all markers and PCR. The new global test is built on an empirical Bayes-type score statistic for testing marginal associations with each single marker. The new global test gains power by robustly exploiting the Hardy-Weinberg equilibrium in the control population and effectively using linkage disequilibrium among test markers. The new global test reduces to PCR when the genotype for each marker is coded as the number of minor alleles. This connection lends insight into the power of the new global test relative to PCR and some other popular multimarker test methods. Second, we propose a robust test method based on the new global test and the ordinary PCR test built on a prospective score statistic for testing marginal associations with each single marker when the genotype for each marker is coded as the number of minor alleles by taking the minimum p value of these two tests. Finally, through extensive simulation studies and analysis of the association between pancreatic cancer and some genes of interest, we show that the proposed robust test method has desirable power and can often identify association signals that may be missed by existing methods.

Asymptotic Relative Efficiencies of the Score and Robust Tests in Genetic Association Studies

Introduction:The score statisticZ(θ)and the maximin efficient robust test statisticZMERTare commonly used in genetic association study, but according to our knowledge there is no formal comparison of them.Methods:In this report, we compare the asymptotic behavior ofZ(θ)andZMERT, by computing their Asymptotic Relative Efficiencies (AREs) relative to each other. Four commonly used ARE measures, the Pitman ARE, Chernoff ARE, Hodges-Lehmann ARE and the Bahadur ARE are considered. Some modifications of these methods are made to simplify the computations. We found that the Chernoff, Hodges-Lehmann and Bahadur AREs are suitable for our setting.Results and Conclusion:Based on our study, the efficiencies of the two test statistic varies for different criterion used, and for different parameter values under the same criterion, so each test has its advantages and dis-advantages according to the criterion used and the parameters involved, which are described in the context. Numerical examples are given to illustrate the use of the two statistics in genetic association study.

Diagnostic methods for uncovering outcome dependent visit processes

Summary With the advent of electronic health records, information collected in the course of regular health care is increasingly being used for clinical research. The hope is that the wealth of clinical data and the realistic setting (compared with information derived from highly controlled experiments like randomized trials) will aid in the investigation of determinants of disease and understanding of which treatments are effective in regular practice and for which patients. The availability of information in such databases is often driven by how a patient feels and may therefore be associated with the health outcomes being considered. We call this an outcome dependent visit process and recent work has shown that ignoring the outcome dependence can produce significant bias in the regression coefficients when fitting longitudinal data models. It is therefore important to have tools to recognize datasets exhibiting outcome dependence. We develop a score statistic to motivate the form of diagnostic test statistics, suggest a variety of approaches for diagnosing such situations, and evaluate their performance. Simple diagnostic tests achieve high power for diagnosing outcome dependent visit processes. This occurs when generalized estimating equations methods begin to be exhibit bias in estimating regression coefficients and before likelihood based methods are substantially biased.

Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.