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In paired-organ studies such as ophthalmology, otolaryngology, and rheumatology, etc., various approaches take highly correlated bilateral data into account for homogeneity tests but are less likely to focus on combined bilateral and unilateral data structures. Also, it is necessary and important to adjust the effect of confounders on stratified combined bilateral and unilateral data since, in these data structures, ignoring intra-class correlation and confounding effects can cause biased statistical inference. This article derived three homogeneity tests (the likelihood ratio test, the Wald test, and the score test) concerning these cooperative structure data to detect if ratios of proportions retain consistency across strata. Simulation shows that the score test provides a robust Type I error rate and satisfactory power performance. Finally, a real example is applied to demonstrate the application of these three proposed tests. [ABSTRACT FROM AUTHOR]

We propose a flexible functional varying-coefficient single-index quantile regression model where the functional covariates of the linear part have time-varying coefficients and the single-index component offers great model flexibility in data analysis while circumventing the curse of dimensionality. The proposed model includes many existing quantile regression models for functional/longitudinal data as special cases. We use B-splines to estimate the link and coefficient functions. Under some mild conditions, we establish the asymptotic normality of the estimated index parameter vector, and obtain the convergence rates of the estimated link and coefficient functions. Moreover, we propose a score test to examine whether the effects of some covariates on the functional response are time-varying. Finally, we provide some numerical studies including Monte Carlo simulations and an empirical application to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Abstract The test-negative design (TND) is an observational study design to evaluate vaccine effectiveness (VE) that enrolls individuals receiving diagnostic testing for a target disease as part of routine care. VE is estimated as one minus the adjusted odds ratio of testing positive versus negative comparing vaccinated and unvaccinated patients. Although the TND is related to case–control studies, it is distinct in that the ratio of test-positive cases to test-negative controls is not typically pre-specified. For both types of studies, sparse cells are common when vaccines are highly effective. We consider the implications of these features on power for the TND. We use simulation studies to explore three hypothesis-testing procedures and associated sample size calculations for case–control and TND studies. These tests, all based on a simple logistic regression model, are a standard Wald test, a continuity-corrected Wald test, and a score test. The Wald test performs poorly in both case–control and TND when VE is high because the number of vaccinated test-positive cases can be low or zero. Continuity corrections help to stabilize the variance but induce bias. We observe superior performance with the score test as the variance is pooled under the null hypothesis of no group differences. We recommend using a score-based approach to design and analyze both case–control and TND. We propose a modification to the TND score sample size to account for additional variability in the ratio of controls over cases. This work enhances our understanding of the data generating mechanism in a test-negative design (TND) and how it is distinct from that of a case-control study due to its passive recruitment of controls.

The test-negative design (TND) is an observational study design to evaluate vaccine effectiveness (VE) that enrolls individuals receiving diagnostic testing for a target disease as part of routine care. VE is estimated as one minus the adjusted odds ratio of testing positive versus negative comparing vaccinated and unvaccinated patients. Although the TND is related to case–control studies, it is distinct in that the ratio of test-positive cases to test-negative controls is not typically pre-specified. For both types of studies, sparse cells are common when vaccines are highly effective. We consider the implications of these features on power for the TND. We use simulation studies to explore three hypothesis-testing procedures and associated sample size calculations for case–control and TND studies. These tests, all based on a simple logistic regression model, are a standard Wald test, a continuity-corrected Wald test, and a score test. The Wald test performs poorly in both case–control and TND when VE is high because the number of vaccinated test-positive cases can be low or zero. Continuity corrections help to stabilize the variance but induce bias. We observe superior performance with the score test as the variance is pooled under the null hypothesis of no group differences. We recommend using a score-based approach to design and analyze both case–control and TND. We propose a modification to the TND score sample size to account for additional variability in the ratio of controls over cases. This work enhances our understanding of the data generating mechanism in a test-negative design (TND) and how it is distinct from that of a case-control study due to its passive recruitment of controls. [ABSTRACT FROM AUTHOR]

The stochastic actor oriented model (SAOM) is a method for modelling social interactions and social behaviour over time. It can be used to model drivers of dynamic interactions using both exogenous covariates and endogenous network configurations, but also the co-evolution of behaviour and social interactions. In its standard implementations, it assumes that all individual have the same interaction evaluation function. This lack of heterogeneity is one of its limitations. The aim of this paper is to extend the inference framework for the SAOM to include random effects, so that the heterogeneity of individuals can be modelled more accurately. We decompose the linear evaluation function that models the probability of forming or removing a tie from the network, in a homogeneous fixed part and a random, individual-specific part. We extend the algorithm so that the variance of the random parameters can be estimated with method of moments. Our method is applicable for the general random effect formulations. We illustrate the method with a random out-degree model and show the parameter estimation of the random components, significance tests and model evaluation. We apply the method to the Kapferer's Tailor shop study. It is shown that a random out-degree constitutes a serious alternative to including transitivity and higher-order dependency effects. • The paper allows effects to be individual-specific to model heterogeneity accurately. • The method of moments is generalized to estimate random effects in the SAOM. • The model evaluation procedure based on the score-test is also been developed. • We identify interesting random effects in the Kapferer's Tailor-shop dataset. [ABSTRACT FROM AUTHOR]

In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques for parameter estimation in Zero-Inflated Poisson models has not been widely explored. This research aims to introduce a new Bayesian approach for estimating the parameters of the Zero-Inflated Poisson model. The method involves employing Gamma and Beta prior distributions to derive closed formulas for Bayes estimators and predictive density. Additionally, we propose a data-driven approach for selecting hyper-parameter values that produce highly accurate Bayes estimates. Simulation studies confirm that, for small and moderate sample sizes, the Bayesian method outperforms the maximum likelihood (ML) method in terms of accuracy. To illustrate the ML and Bayesian methods proposed in the article, a real dataset is analyzed. [ABSTRACT FROM AUTHOR]

Segmented regression is widely used in many disciplines, especially when dealing with environmental data. This paper deals with the problem of selecting the correct number of changepoints in segmented regression models. A review of the usual selection criteria, namely information criteria and hypothesis testing, is provided. We enhance the latter method by proposing a novel sequential hypothesis testing procedure to address this problem. Our sequential procedure's performance is compared to methods based on information-based criteria through simulation studies. The results show that our proposal performs similarly to its competitors for the Gaussian, Binomial, and Poisson cases. Finally, we present two applications to environmental datasets of crime data in Valencia and global temperature land data. [ABSTRACT FROM AUTHOR]

When monitoring risk in public health, count data commonly exhibit an excessive number of zero, and the zero‐inflated Poisson (ZIP) model is often used to fit this type of data. Most previous methods for monitoring of the ZIP model have focused on the changes in the location parameter and the existence of the scale parameter and usually assumed that the scale parameter is zero in the H0 stage. However, in an objective environment, data often have certain fluctuations, meaning that the scale parameter always exists. Therefore, it is more meaningful to monitor the changes in the scale parameter on top of the predefined baseline than to monitor its existence. In this study, we derive a score test statistic based on the generalized Henderson's joint likelihood function, construct a risk‐adjusted exponentially weighted moving average (EWMA) control chart to monitor the variability of the random effects variance component in the ZIP mixed‐effects model. And the convergence property of the score test statistic is proved through derivation, which shows that the new method has theoretical reliability. The simulation results Indicate that when the scale parameter has different predefined baselines and different variation amplitudes, the proposed method is more effective than the existing RA‐ZIP and PR‐ZIP control charts. In addition, the proposed method is applied to real data from a Hong Kong hospital for online influenza surveillance to demonstrate its practicability. [ABSTRACT FROM AUTHOR]

The research on the quantitative trait locus (QTL) mapping of count data has aroused the wide attention of researchers. There are frequent problems in applied research that limit the application of the conventional Poisson model in the analysis of count phenotypes, which include the overdispersion and excess zeros and ones. In this article, a novel model, that is, the zero‐and‐one‐inflated generalized Poisson (ZOIGP) model, is proposed to deal with these problems. Based on the proposed model, a score test is performed for the inflation parameter, in which the ZOIGP model with a constant proportion of excess zeros and ones is compared with a standard generalized Poisson model. To illustrate the practicability of the ZOIGP model, we extend it to the QTL interval mapping application that underpins count phenotype with excess zeros and excess ones. The genetic effects are estimated utilizing the expectation–maximization algorithm embedded with the Newton–Raphson algorithm, and the genome‐wide scan and likelihood ratio test is performed to map and test the potential QTLs. The statistical properties exhibited by the proposed method are investigated through simulation. Finally, a real data analysis example is used to illustrate the utility of the proposed method for QTL mapping. [ABSTRACT FROM AUTHOR]

Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to satisfy different research proposed in randomized clinical trials. In this article, we propose three test statistics (the likelihood ratio test, score test, and Wald-type test statistics) to evaluate the homogeneity of proportion ratios for stratified bilateral correlated data under an equal correlation assumption. Monte Carlo simulations of Type I error and power are performed, and the score test yields a robust outcome based on empirical Type I error and power. Lastly, two real data examples are conducted to illustrate the proposed three tests. [ABSTRACT FROM AUTHOR]

We introduce a robust likelihood approach to inference for paired multiple binary endpoints data. One can easily implement the methodology without dealing with the model that incorporates a large number of joint probabilities of no direct relevance to the inference of interest. We present the robust score test statistic for testing the equality of two treatment effects to exemplify the utility and simplicity of the method. Our novel technique is applicable when patients have different numbers of endpoints and for unpaired endpoints. The extension of our robust approach to multiple endpoints data with more categories is straightforward. We use simulations and real data analysis to highlight the efficacy of our robust procedure. [ABSTRACT FROM AUTHOR]

In this study, we propose three different test procedures by plugging the Wald (W), score (S) and likelihood ratio (LR) statistics into the computational approach test (CAT) to test the equality of inverse Gaussian means when the scale parameters are unknown and arbitrary. Restricted maximum likelihood (RML) estimators are used in developing the proposed test procedures. Since the RML estimators cannot be derived in closed-form, the bisection method is used to obtain the numerical solutions. The motivation behind using the CAT procedure is that it can easily be implemented to hypothesis testing problems without knowing the sampling distributions of the test statistics. The proposed and existing procedures are compared in terms of type I error rates and powers via an extensive Monte Carlo simulation study. In addition, a real data set is analyzed for illustration.

In paired-organ studies such as ophthalmology, otolaryngology, and rheumatology, etc., various approaches take highly correlated bilateral data into account for homogeneity tests but are less likely to focus on combined bilateral and unilateral data structures. Also, it is necessary and important to adjust the effect of confounders on stratified combined bilateral and unilateral data since, in these data structures, ignoring intra-class correlation and confounding effects can cause biased statistical inference. This article derived three homogeneity tests (the likelihood ratio test, the Wald test, and the score test) concerning these cooperative structure data to detect if ratios of proportions retain consistency across strata. Simulation shows that the score test provides a robust Type I error rate and satisfactory power performance. Finally, a real example is applied to demonstrate the application of these three proposed tests.

The intraclass correlation coefficient ρ is used as a measure of the degree of resemblance among family members with respect to some biological or psychological attribute, such as blood pressure level or IQ. Many studies have been done in the area. However, a significant gap in the literature is that few statistics are available to test the significance ( H 0 : ρ = 0 against H A : ρ ≠ 0 ) of this important biological measure and no study is available as to the performance of these statistics with respect to level and power. In this paper we develop three large sample test statistics and compare these, in terms of level and power, using extensive simulation studies of these, the Wald test developed in this paper is found to have a very simple form and highest power while maintaining level well. [ABSTRACT FROM AUTHOR]

In a matched pairs experiment, two binary variables are typically observed on all subjects in the experiment. However, when one of the variables is missing on some subjects, we have so called the partially observed binary data that consist of two parts: a multinomial from the subjects with a pair of observed variables and two independent binomials from the subjects with only one observed variable. The goal of this paper is to construct exact confidence intervals for the difference of two (success) proportions of the two binary variables. We first derive a new test by combining two score tests for the two parts of the data and invert it to an asymptotic confidence interval. Since asymptotic intervals do not achieve the nominal level, this interval and three other existing intervals are improved to be exact by the general h$$ h $$‐function method. We compare the infimum coverage probability and average interval length of these intervals and recommend the exact intervals that are improved from the newly proposed interval. Two real data sets are used to illustrate the intervals. [ABSTRACT FROM AUTHOR]

Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while having distinguished features. In this project, our primary goal is to develop a stable and practical inference method for the conditional expected shortfall. We consider the joint modelling of conditional quantile and expected shortfall to facilitate the statistical inference procedure. While the regression coefficients can be estimated jointly by minimizing a class of strictly consistent joint loss functions, the computation is challenging, especially when the dimension of parameters is large since the loss functions are neither differentiable nor convex. We propose a two‐step estimation procedure to reduce the computational effort by first estimating the quantile regression parameters with standard quantile regression. We show that the two‐step estimator has the same asymptotic properties as the joint estimator, but the former is numerically more efficient. We develop a score‐type inference method for hypothesis testing and confidence interval construction. Compared to the Wald‐type method, the score method is robust against heterogeneity and is superior in finite samples, especially for cases with many confounding factors. The advantages of our proposed method over existing approaches are demonstrated by simulations and empirical studies based on income and college education data. [ABSTRACT FROM AUTHOR]

The Wald, likelihood ratio, score, and the recently proposed gradient statistics can be used to assess a broad range of hypotheses in item response theory models, for instance, to check the overall model fit or to detect differential item functioning. We introduce new methods for power analysis and sample size planning that can be applied when marginal maximum likelihood estimation is used. This allows the application to a variety of IRT models, which are commonly used in practice, e.g., in large-scale educational assessments. An analytical method utilizes the asymptotic distributions of the statistics under alternative hypotheses. We also provide a sampling-based approach for applications where the analytical approach is computationally infeasible. This can be the case with 20 or more items, since the computational load increases exponentially with the number of items. We performed extensive simulation studies in three practically relevant settings, i.e., testing a Rasch model against a 2PL model, testing for differential item functioning, and testing a partial credit model against a generalized partial credit model. The observed distributions of the test statistics and the power of the tests agreed well with the predictions by the proposed methods in sufficiently large samples. We provide an openly accessible R package that implements the methods for user-supplied hypotheses. [ABSTRACT FROM AUTHOR]

With the cost-effectiveness technology in whole-genome sequencing, more sophisticated statistical methods for testing genetic association with both rare and common variants are being investigated to identify the genetic variation between individuals. Several methods which group variants, also called gene-based approaches, are developed. For instance, advanced extensions of the sequence kernel association test, which is a widely used variant-set test, have been proposed for unrelated samples and extended for family data. Family data have been shown to be powerful when analyzing rare variants. However, most of such methods capture familial relatedness using a random effect component within the generalized linear mixed model framework. Therefore, there is a need to develop unified and flexible methods to study the association between a set of genetic variants and a trait, especially for a binary outcome. Copulas are multivariate distribution functions with uniform margins on the [ 0 , 1 ] interval and they provide suitable models to capture familial dependence structure. In this work, we propose a flexible family-based association test for both rare and common variants in the presence of binary traits. The method, termed novel rare variant association test (NRVAT), uses a marginal logistic model and a Gaussian Copula. The latter is employed to model the dependence between relatives. An analytic score-type test is derived. Through simulations, we show that our method can achieve greater power than existing approaches. The proposed model is applied to investigate the association between schizophrenia and bipolar disorder in a family-based cohort consisting of 17 extended families from Eastern Quebec. [ABSTRACT FROM AUTHOR]

In the insurance sector, Zero-Inflated models are commonly used due to the unique nature of insurance data, which often contain both genuine zeros (meaning no claims made) and potential claims. Although active developments in modeling excess zero data have occurred, the use of Bayesian techniques for parameter estimation in Zero-Inflated Poisson models has not been widely explored. This research aims to introduce a new Bayesian approach for estimating the parameters of the Zero-Inflated Poisson model. The method involves employing Gamma and Beta prior distributions to derive closed formulas for Bayes estimators and predictive density. Additionally, we propose a data-driven approach for selecting hyper-parameter values that produce highly accurate Bayes estimates. Simulation studies confirm that, for small and moderate sample sizes, the Bayesian method outperforms the maximum likelihood (ML) method in terms of accuracy. To illustrate the ML and Bayesian methods proposed in the article, a real dataset is analyzed.

The problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a t test or an F test. However, the properties of these model selection procedures are not well-known. The purpose of this paper is to study the properties of these procedures within generalized linear regression models, considering the normal linear regression model as a special case. The main tool that is being used is the score test. However, the F test and other large sample tests, such as the likelihood ratio and the Wald test, the AIC, and the BIC, are included for the comparison. A systematic study, through simulations, of the properties of this procedure was conducted, in terms of level and power, for symmetric and asymmetric distributions, such as normal, Poisson, and binomial regression models. Extensions for skewed distributions, over-dispersed Poisson (the negative binomial), and over-dispersed binomial (the beta-binomial) regression models, are also given and evaluated. The methods are applied to analyze two health datasets. [ABSTRACT FROM AUTHOR]

In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Cratoxylum formosum (Jack) Benth. & Hook.f. ex Dyer is one of the plant species that have the potential to be developed into an antibacterial and antioxidant essential oil product. This study was conducted to determine the value of organoleptic tests and the consumers' willingness to pay (WTP) for the three variants of Cratoxylum formosum essential oil products. For the parameters of colour, hedonic test values and score tests showed good results; panellists did not mind the pure and mixed Cratoxylum formosum essential oil colours. However, for fragrance parameters, the hedonic test showed a dislike score. Most panellists disliked the strong "scent of leaves" of pure C. formosum oil. The score test showed satisfactory values, the panellists accept the fragrance of Cratoxylum formosum essential oil, but it is necessary to add a more preferred scent mixture to reduce the strong original fragrance of the oil. The cost of production of Cratoxylum essential oil is Rp.7,259.23 (USD 0.48)/mL or Rp.72,592.30 (USD 4.84) for every 10 mL. Based on the cost ofproduction, the appropriate selling value for every 10 mL of Cratoxylum essential oil is a minimum of USD 4.84.

Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to satisfy different research proposed in randomized clinical trials. In this article, we propose three test statistics (the likelihood ratio test, score test, and Wald-type test statistics) to evaluate the homogeneity of proportion ratios for stratified bilateral correlated data under an equal correlation assumption. Monte Carlo simulations of Type I error and power are performed, and the score test yields a robust outcome based on empirical Type I error and power. Lastly, two real data examples are conducted to illustrate the proposed three tests.

We investigate saddlepoint approximations of tail probabilities of the score test statistic in logistic regression for genome‐wide association studies. The inaccuracy in the normal approximation of the score test statistic increases with increasing imbalance in the response and with decreasing minor allele counts. Applying saddlepoint approximation methods greatly improve the accuracy, even far out in the tails of the distribution. By using exact results for a simple logistic regression model, as well as simulations for models with nuisance parameters, we compare double saddlepoint methods for computing two‐sided P$$ P $$‐values and mid‐P$$ P $$‐values. These methods are also compared to a recent single saddlepoint procedure. We investigate the methods further on data from UK Biobank with skin and soft tissue infections as phenotype, using both common and rare variants. [ABSTRACT FROM AUTHOR]

In clinical studies, data can be collected either unilaterally or bilaterally in each subject. Especially in bilateral cases, the correlation between responses of a paired organs is non-negligible if we would like to formulate a homogeneity test among groups. In this article, we investigated and derived three test methods based on an equal intraclass correlation model aiming to exploit such combined data samples. The performance of each test method is examined by simulation under various parameter configurations, which suggests the Score test usually has the properties of satisfactory Type I error control and great power performance, and therefore, is recommended among these three proposed and existing methods. A real work example in the otolaryngologic study is analyzed to illustrate the practical application of our proposed test. [ABSTRACT FROM AUTHOR]

Besides the Wald and likelihood-ratio tests, the Lagrange multiplier test (Rao, 1948, Mathematical Proceedings of the Cambridge Philosophical Society 44: 50–57; Aitchison and Silvey, 1958, Annals of Mathematical Statistics 29: 813–828; Silvey, 1959, Annals of Mathematical Statistics 30: 389–407) is the third canonical approach to testing hypotheses after maximum likelihood estimation. While the Stata commands test and lrtest implement the first two, Stata does not have an official command for implementing the third. The community-contributed boottest package (Roodman et al., 2019, Stata Journal 19: 4–60) focuses on methods of bootstrap inference and also implements the Lagrange multiplier test functionality. In this article, I introduce the new community-contributed postestimation command lgrgtest, which allows for straightforwardly using the Lagrange multiplier test after constrained maximum-likelihood estimation. lgrgtest is intended to be compatible with all Stata estimation commands that use maximum likelihood and allow for the options constraints(), iterate(), and from(). lgrgtest can also be used after cnsreg. [ABSTRACT FROM AUTHOR]

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within‐subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly. [ABSTRACT FROM AUTHOR]

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The implementation of the score tests circumvents the identification issue as it requires only parameter estimation under the null MAR assumption. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well‐controlled type I errors and desirable powers. [ABSTRACT FROM AUTHOR]

To study the relationship between genetic variants and phenotypes, association testing is adopted; however, most association studies are conducted by genotype-based testing. Testing methods based on next-generation sequencing (NGS) data without genotype calling demonstrate an advantage over testing methods based on genotypes in the scenarios when genotype estimation is not accurate. Our objective was to develop NGS data-based methods for association studies to fill the gap in the literature. Single-variant testing methods based on NGS data have been proposed, including our previously proposed single-variant NGS data-based testing method, i.e., UNC combo method. The NGS data-based group testing method has been proposed by us using a linear model framework which can handle continuous responses. In this paper, we extend our linear model-based framework to a generalized linear model-based framework so that the methods can handle other types of responses especially binary responses which is a common problem in association studies. To evaluate the performance of various estimators and compare them we performed simulation studies. We found that all methods have Type I errors controlled, and our NGS data-based methods have better performance than genotype-based methods for other types of responses, including binary responses (logistics regression) and count responses (Poisson regression), especially when sequencing depth is low. We have extended our previous linear model (LM) framework to a generalized linear model (GLM) framework and derived NGS data-based methods for a group of genetic variables. Compared with our previously proposed LM-based methods, the new GLM-based methods can handle more complex responses (for example, binary responses and count responses) in addition to continuous responses. Our methods have filled the literature gap and shown advantage over their corresponding genotype-based methods in the literature. [ABSTRACT FROM AUTHOR]

Overdispersion is a common feature in categorical data analysis and several methods have been developed for detecting and handling it in generalized linear models. The first aim of this study is to clarify the relationships among various score statistics for testing overdispersion and to compare their performances. In addition, we investigate a principled way to correct finite sample bias in the score statistic caused by estimating regression parameters with restricted likelihood. The second aim is to reconsider the current practice for handling overdispersed categorical data. Although the conventional models are based on substantially different mechanisms for generating overdispersion, model selection in practice has not been well studied. We perform an intensive numerical study for determining which method is more robust to various overdispersion mechanisms. In addition, we provide some graphical tools for identifying the better model. The last aim is to reconsider the key assumption for deriving the score statistics. We study the meaning of testing overdispersion when this assumption is violated, and we analytically show the conditions for which it is not appropriate to employ the current statistical practices for analyzing overdispersed data. [ABSTRACT FROM AUTHOR]

Abstract Background Gene-based association tests provide a useful alternative and complement to the usual single marker association tests, especially in genome-wide association studies (GWAS). The way of weighting for variants in a gene plays an important role in boosting the power of a gene-based association test. Appropriate weights can boost statistical power, especially when detecting genetic variants with weak effects on a trait. One major limitation of existing gene-based association tests lies in using weights that are predetermined biologically or empirically. This limitation often attenuates the power of a test. On another hand, effect sizes or directions of causal genetic variants in real data are usually unknown, driving a need for a flexible yet robust methodology of gene based association tests. Furthermore, access to individual-level data is often limited, while thousands of GWAS summary data are publicly and freely available. Results To resolve these limitations, we propose a combination test named as OWC which is based on summary statistics from GWAS data. Several traditional methods including burden test, weighted sum of squared score test [SSU], weighted sum statistic [WSS], SNP-set Kernel Association Test [SKAT], and the score test are special cases of OWC. To evaluate the performance of OWC, we perform extensive simulation studies. Results of simulation studies demonstrate that OWC outperforms several existing popular methods. We further show that OWC outperforms comparison methods in real-world data analyses using schizophrenia GWAS summary data and a fasting glucose GWAS meta-analysis data. The proposed method is implemented in an R package available at https://github.com/Xuexia-Wang/OWC-R-package Conclusions We propose a novel gene-based association test that incorporates four different weighting schemes (two constant weights and two weights proportional to normal statistic Z) and includes several popular methods as its special cases. Results of the simulation studies and real data analyses illustrate that the proposed test, OWC, outperforms comparable methods in most scenarios. These results demonstrate that OWC is a useful tool that adapts to the underlying biological model for a disease by weighting appropriately genetic variants and combination of well-known gene-based tests.

In medical clinical studies, we often encounter paired organs' unilateral or bilateral data. For bilateral data, there exists an intraclass correlation between paired organs. Under an intraclass correlation model, this paper proposes asymptotic statistics for testing the equality of many-to-one relative risk ratios in combined unilateral and bilateral data. Furthermore, we calculate the explicit expressions of these statistics. Moreover, these procedures are adequate to solve the hypothesis problems of unilateral or bilateral data. Through comparison, the simulation results show that the score test has a robust empirical type-I error rate and sufficient power. We provide a clinical trial of acute otitis media to illustrate our proposed methods. [ABSTRACT FROM AUTHOR]

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Association testing has been widely used to study the relationship between phenotypes and genetic variants. Most testing methods are based on genotypes. To avoid genotype calling and directly test on next-generation sequencing (NGS) data, sequencing data-based methods have been proposed and shown advantages over genotype-based testing methods in scenarios where genotype calling is inaccurate. Most sequencing data-based testing methods are based on a single genetic marker. The objective of this paper is to extend the methods to allow testing for the association of a continuous response variable with a group of common variants or a group of rare variants without genotype calling. Our proposed methods are derived based on a standard linear model framework. We derive the joint significant test (JS) for a group of common genetic variables and the variable collapse test (VC) for a group of rare genetic variables. We have conducted extensive simulation studies to evaluate the performance of different estimators. According to our results, we found (1) all methods, including our proposed NGS data-based methods and genotype-based methods, can control the Type I error rate probability well; (2) our proposed NGS data-based methods can achieve better performance in terms of statistical power compared with their corresponding genotype-based methods in the literature; (3) when sequencing depth increases, the performance of all methods increases, and the difference between the performance of NGS data-based methods and corresponding genotype-based methods decreases. In conclusion, we have proposed NGS data-based methods that allow testing for the significance of a group of variants using a linear model framework and have shown the advantage of our NGS data-based methods over genotype-based methods in the literature. [ABSTRACT FROM AUTHOR]

In addition to applications in meta-analysis, funnel plots have emerged as an effective graphical tool for visualizing the detection of health care providers with unusual performance. Although there already exist a variety of approaches to producing funnel plots in the literature of provider profiling, limited attention has been paid to elucidating the critical relationship between funnel plots and hypothesis testing. Within the framework of generalized linear models, here we establish methodological guidelines for creating funnel plots specific to the statistical tests of interest. Moreover, we show that the test-specific funnel plots can be created merely leveraging summary statistics instead of individual-level information. This appealing feature inhibits the leak of protected health information and reduces the cost of inter-institutional data transmission. Two data examples, one for surgical patients from Michigan hospitals and the other for Medicare-certified dialysis facilities, demonstrate the applicability to different types of providers and outcomes with either individual- or summary-level information. [ABSTRACT FROM AUTHOR]

Background: Gene-based association tests provide a useful alternative and complement to the usual single marker association tests, especially in genome-wide association studies (GWAS). The way of weighting for variants in a gene plays an important role in boosting the power of a gene-based association test. Appropriate weights can boost statistical power, especially when detecting genetic variants with weak effects on a trait. One major limitation of existing gene-based association tests lies in using weights that are predetermined biologically or empirically. This limitation often attenuates the power of a test. On another hand, effect sizes or directions of causal genetic variants in real data are usually unknown, driving a need for a flexible yet robust methodology of gene based association tests. Furthermore, access to individual-level data is often limited, while thousands of GWAS summary data are publicly and freely available. Results: To resolve these limitations, we propose a combination test named as OWC which is based on summary statistics from GWAS data. Several traditional methods including burden test, weighted sum of squared score test [SSU], weighted sum statistic [WSS], SNP-set Kernel Association Test [SKAT], and the score test are special cases of OWC. To evaluate the performance of OWC, we perform extensive simulation studies. Results of simulation studies demonstrate that OWC outperforms several existing popular methods. We further show that OWC outperforms comparison methods in real-world data analyses using schizophrenia GWAS summary data and a fasting glucose GWAS meta-analysis data. The proposed method is implemented in an R package available at https://github.com/Xuexia-Wang/OWC-R-package Conclusions: We propose a novel gene-based association test that incorporates four different weighting schemes (two constant weights and two weights proportional to normal statistic Z) and includes several popular methods as its special cases. Results of the simulation studies and real data analyses illustrate that the proposed test, OWC, outperforms comparable methods in most scenarios. These results demonstrate that OWC is a useful tool that adapts to the underlying biological model for a disease by weighting appropriately genetic variants and combination of well-known gene-based tests. [ABSTRACT FROM AUTHOR]

Statistical methods to test for effects of single nucleotide polymorphisms (SNPs) on exon inclusion exist but often rely on testing of associations between multiple exon–SNP pairs, with sometimes subsequent summarization of results at the gene level. Such approaches require heavy multiple testing corrections and detect mostly events with large effect sizes. We propose here a test to find spliceQTL (splicing quantitative trait loci) effects that takes all exons and all SNPs into account simultaneously. For any chosen gene, this score‐based test looks for an association between the set of exon expressions and the set of SNPs, via a random‐effects model framework. It is efficient to compute and can be used if the number of SNPs is larger than the number of samples. In addition, the test is powerful in detecting effects that are relatively small for individual exon–SNP pairs but are observed for many pairs. Furthermore, test results are more often replicated across datasets than pairwise testing results. This makes our test more robust to exon–SNP pair‐specific effects, which do not extend to multiple pairs within the same gene. We conclude that the test we propose here offers more power and better replicability in the search for spliceQTL effects. [ABSTRACT FROM AUTHOR]

Given their improvements in bias reduction and efficiency, joint models (JMs) for longitudinal and time‐to‐event data offer great potential to clinical trials. However, for JM to become more widely used, there is a need for additional development of design considerations. To this end, Chen et al previously developed two closed‐form sample size formulas in the JM setting. In this current work, we expand upon this framework by utilizing the time‐dependent slopes parameterization, where the change in the longitudinal outcome influences the hazard, in addition to the current value of the longitudinal process. Our extended formula for the required number of events can be used when testing significance of the association between the longitudinal and time‐to‐event outcomes. We find that if the data indeed are generated such that not only the current value, but also the slope of the longitudinal outcome influence the hazard of the time‐to‐event process, it is advisable to use the current formula developed utilizing the time‐dependent slopes parameterization. In this setting, our proposed formula will provide a more accurate estimate of power compared to the method by Chen et al. To illustrate our proposed method, we present power calculations of a biomarker qualification study for Hutchinson‐Gilford progeria syndrome, an ultra‐rare premature aging disease. [ABSTRACT FROM AUTHOR]

Abstract This study examines population and small sample properties of the standardized fifth and sixth moments – the “higher moments” – for assessing univariate normality against bimodal and selected unimodal alternatives. Population parameters and distributions for selected bimodal mixtures are calculated and contrasted with those for the normal distribution. Using Gram-Charlier series expansion methods, an omnibus goodness of fit test incorporating the higher moments is specified and Monte Carlo simulation used to compare test power with parametric tests based on the standardized third and fourth sample moments: the asymptotic and size corrected versions of the Jarque-Bera score test and the omnibus D’Agostino K2 test. The studentized range and directional tests using the third through sixth moments are also considered. The results demonstrate that incorporating the fifth and sixth moments can provide enhanced parametric normality test power for bimodal normal mixture alternatives but not for various unimodal alternatives. [ABSTRACT FROM AUTHOR]

By assuming independence between the paired continuous and ordinal responses, we develop a score statistic for testing the difference between two treatment effects for the paired mixed data. The test is easy to implement and is legitimate for general marginal distributions and in the presence of within-pair correlation. Simulations show that our new method outperforms the generalized estimating equations (GEE) and the generalized linear mixed model (GLMM) in terms of performance measures most concerned. [ABSTRACT FROM AUTHOR]

Human microbiome research has become a hot-spot in health and medical research in the past decade due to the rapid development of modern high-throughput. Typical data in a microbiome study consisting of the operational taxonomic unit counts may have over-dispersion and/or structural zero issues. In such cases, negative binomial models can be applied to address the over-dispersion issue, while zero-inflated negative binomial models can be applied to address both issues. In practice, it is essential to know if there is zero-inflation in the data before applying negative binomial or zero-inflated negative binomial models because zero-inflated negative binomial models may be unnecessarily complex and difficult to interpret, or may even suffer from convergence issues if there is no zero-inflation in the data. On the other hand, negative binomial models may yield invalid inferences if the data does exhibit excessive zeros. In this paper, we develop a new test for detecting zero-inflation resulting from a latent class of subjects with structural zeros in a negative binomial regression model by directly comparing the amount of observed zeros with what would be expected under the negative binomial regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Intensive simulation studies are conducted to investigate the performance of the new test and compare it with the classical Wald, likelihood ratio, and score tests. The tests are also applied to human gut microbiome data to test latent class in microbial genera. [ABSTRACT FROM AUTHOR]

The problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a t test or an F test. However, the properties of these model selection procedures are not well-known. The purpose of this paper is to study the properties of these procedures within generalized linear regression models, considering the normal linear regression model as a special case. The main tool that is being used is the score test. However, the F test and other large sample tests, such as the likelihood ratio and the Wald test, the AIC, and the BIC, are included for the comparison. A systematic study, through simulations, of the properties of this procedure was conducted, in terms of level and power, for symmetric and asymmetric distributions, such as normal, Poisson, and binomial regression models. Extensions for skewed distributions, over-dispersed Poisson (the negative binomial), and over-dispersed binomial (the beta-binomial) regression models, are also given and evaluated. The methods are applied to analyze two health datasets.

The purpose of this article was to introduce the score test and the SAS implementation. Concretely， there were five common forms of the score test statistics， namely the general score test statistic，the robust score test statistic，the residual score test statistic，the generalized score test statistic，and the Lagrange multiplier test statistic. The score test was mainly used in the following three situations， namely， testing whether part or all of the regression coefficients were 0， testing whether a single effect was not in the regression model，and testing whether the parallel line hypothesis was established. The paper used two examples and the SAS software to realize the various score tests mentioned above， and focused on explaining the output results related to the score tests.

Abstract Background Advancements in statistical methods and sequencing technology have led to numerous novel discoveries in human genetics in the past two decades. Among phenotypes of interest, most attention has been given to studying genetic associations with continuous or binary traits. Efficient statistical methods have been proposed and are available for both types of traits under different study designs. However, for multinomial categorical traits in related samples, there is a lack of efficient statistical methods and software. Results We propose an efficient score test to analyze a multinomial trait in family samples, in the context of genome-wide association/sequencing studies. An alternative Wald statistic is also proposed. We also extend the methodology to be applicable to ordinal traits. We performed extensive simulation studies to evaluate the type-I error of the score test, Wald test compared to the multinomial logistic regression for unrelated samples, under different allele frequency and study designs. We also evaluate the power of these methods. Results show that both the score and Wald tests have a well-controlled type-I error rate, but the multinomial logistic regression has an inflated type-I error rate when applied to family samples. We illustrated the application of the score test with an application to the Framingham Heart Study to uncover genetic variants associated with diabesity, a multi-category phenotype. Conclusion Both proposed tests have correct type-I error rate and similar power. However, because the Wald statistics rely on computer-intensive estimation, it is less efficient than the score test in terms of applications to large-scale genetic association studies. We provide computer implementation for both multinomial and ordinal traits.

Bilateral correlated data frequently arise in medical clinical studies such as otolaryngology and ophthalmology. Based on an equal correlation coefficient model, this paper mainly aimed to investigate the statistical inference for the odds ratio of two proportions in bilateral correlated data, including not only three test procedures but also four confidence interval (CI) constructions. Through iterative algorithms, all unknown parameters are estimated in order to construct the likelihood ratio, score and Wald-type tests. Furthermore, the profile likelihood CI, score CI, and Wald-type CI are obtained by the bisection root-finding algorithm. We provided another Wald-type CI based on an asymptotic normality property. The performance of the proposed tests were investigated with regard to empirical type I error rate and power, and CI methods were compared in terms of mean coverage probability and mean interval width. Numerical simulations show that the score test is more robust, and has higher power than other tests. The score CI also has a shorter interval width, and its coverage probability is closer to 0.95. A real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

Maximum likelihood estimation of generalized linear mixed models (GLMMs) is difficult due to marginalization of the random effects. Derivative computations of a fitted GLMM's likelihood are also difficult, especially because the derivatives are not by-products of popular estimation algorithms. In this paper, we first describe theoretical results related to GLMM derivatives along with a quadrature method to efficiently compute the derivatives, focusing on fitted lme4 models with a single clustering variable. We describe how psychometric results related to item response models are helpful for obtaining the derivatives, as well as for verifying the derivatives' accuracies. We then provide a tutorial on the many possible uses of these derivatives, including robust standard errors, score tests of fixed effect parameters, and likelihood ratio tests of non-nested models. The derivative computation methods and applications described in the paper are all available in easily obtained R packages. [ABSTRACT FROM AUTHOR]

Abundance estimation from capture–recapture data is of great importance in many disciplines. Analysis of capture–recapture data is often complicated by the existence of one‐inflation and heterogeneity problems. Simultaneously taking these issues into account, existing abundance estimation methods are usually constructed on the basis of conditional likelihood under one‐inflated zero‐truncated count models. However, the resulting Horvitz–Thompson‐type estimators may be unstable, and the resulting Wald‐type confidence intervals may exhibit severe undercoverage. In this paper, we propose a semiparametric empirical likelihood (EL) approach to abundance estimation under one‐inflated binomial and Poisson regression models. To facilitate the computation of the EL method, we develop an expectation‐maximization algorithm. We also propose a new score test for the existence of one‐inflation and prove its asymptotic normality. Our simulation studies indicate that compared with existing estimators, the proposed score test is more powerful and the maximum EL estimator has a smaller mean square error. The advantages of our approaches are further demonstrated by analyses of prinia data from Hong Kong and drug user data from Bangkok. [ABSTRACT FROM AUTHOR]