Hypothesis testing and sample size considerations for the test-negative design.

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.

Simple methods for comparing two predictive values with incomplete data.

Statistical methods have been well developed for comparing the predictive values of two binary diagnostic tests under a paired design. However, existing methods do not make allowance for incomplete data. Although maximum likelihood based method can be used to deal with incomplete data, it requires iterative algorithm for implementation. A simple and easily implemented statistical method is therefore needed. Simple methods exist for comparing two sensitivities or specificities with incomplete data but such simple methods are not available for comparing two predictive values with incomplete data. In this paper, we propose two simple methods for comparing two predictive values with incomplete data. The test statistics derived by these two methods are simple to compute, only involving some minor modification of the existing weighted generalized score statistics with complete data. Simulation results demonstrate that the proposed methods are more efficient than the ad-hoc method that only uses the subjects wit complete data. As an illustration, the proposed methods are applied to an observational study comparing two non-invasive methods in detecting endometriosis.

Mapping QTL controlling count traits with excess zeros and ones using a zero-and-one-inflated generalized Poisson regression model.

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.

A gene based combination test using GWAS summary data.

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.

Multikink quantile regression for longitudinal data with application to progesterone data analysis.

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.

Score test for missing at random or not under logistic missingness models.

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.

Saddlepoint approximations to score test statistics in logistic regression for analyzing genome-wide association studies.

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.

Modification Indices for Diagnostic Classification Models.

Diagnostic classification models (DCMs) are psychometric models for evaluating a student's mastery of the essential skills in a content domain based upon their responses to a set of test items. Currently, diagnostic model and/or Q-matrix misspecification is a known problem with limited avenues for remediation. To address this problem, this paper defines a one-sided score statistic that is a computationally efficient method for detecting under-specification at the item level of both the Q-matrix and the model parameters of the particular DCM chosen in an analysis. This method is analogous to the modification indices widely used in structural equation modeling. The results of a simulation study show the Type I error rate of modification indices for DCMs are acceptably close to the nominal significance level when the appropriate mixture χ2 reference distribution is used. The simulation results indicate that modification indices are very powerful in the detection of an under-specified Q-matrix and have ample power to detect the omission of model parameters in large samples or when the items are highly discriminating. An application of modification indices for DCMs to an analysis of response data from a large-scale administration of a diagnostic test demonstrates how they can be useful in diagnostic model refinement.

A powerful global test for spliceQTL effects.

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.

A conditional autoregressive model for genetic association analysis accounting for genetic heterogeneity.

Converging evidence from genetic studies and population genetics theory suggest that complex diseases are characterized by remarkable genetic heterogeneity, and individual rare mutations with different effects could collectively play an important role in human diseases. Many existing statistical models for association analysis assume homogeneous effects of genetic variants across all individuals, and could be subject to power loss in the presence of genetic heterogeneity. To consider possible heterogeneous genetic effects among individuals, we propose a conditional autoregressive model. In the proposed method, the genetic effect is considered as a random effect and a score test is developed to test the variance component of genetic random effect. Through simulations, we compare the type I error and power performance of the proposed method with those of the generalized genetic random field and the sequence kernel association test methods under different disease scenarios. We find that our method outperforms the other two methods when (i) the rare variants have the major contribution to the disease, or (ii) the genetic effects vary in different individuals or subgroups of individuals. Finally, we illustrate the new method by applying it to the whole genome sequencing data from the Alzheimer's Disease Neuroimaging Initiative.

Sample size determination for the association between longitudinal and time-to-event outcomes using the joint modeling time-dependent slopes parameterization.

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.

On testing for homogeneity with zero-inflated models through the lens of model misspecification.

In many applications of two-component mixture models such as the popular zero-inflated model for discrete-valued data, it is customary for the data analyst to evaluate the inherent heterogeneity in view of observed data. To this end, the score test, acclaimed for its simplicity, is routinely performed. It has long been recognized that this test may behave erratically under model misspecification, but the implications of this behavior remain poorly understood for popular two-component mixture models. For the special case of zero-inflated count models, we use data simulations and theoretical arguments to evaluate this behavior and discuss its implications in settings where the working model is restrictive with regard to the true data generating mechanism. We enrich this discussion with an analysis of count data in HIV research, where a one-component model is shown to fit the data reasonably well despite apparent extra zeros. These results suggest that a rejection of homogeneity does not imply that the underlying mixture model is appropriate. Rather, such a rejection simply implies that the mixture model should be carefully interpreted in the light of potential model misspecifications, and further evaluated against other competing models.

Multiple imputation analysis of Miettinen-Nurminen interval for difference in proportions.

The standard multiple imputation technique focuses on parameter estimation and assumes that the parameter estimator is asymptotically normally distributed with a Wald-type confidence interval for the parameter of interest. On the other hand, the Miettinen-Nurminen (MN) method for difference in proportions (Miettinen O, Nurminen M. Stat Med. 1985;4:213-226) constructs the confidence interval using an asymptotic score method and hence is not directly amenable to the standard multiple imputation technique. We propose a multiple imputation analysis that is applicable to the MN method for difference in proportions. We use simulation studies to compare the proposed method with that of Li, Mehrotra and Barnard (LMB), which is based on effective sample sizes (Li X, Mehrotra DV, Barnard J. Stat Med. 2006;25:2107-2124). We show that both methods produce confidence intervals with adequate coverage, while the proposed method produces slightly shorter confidence intervals than the LMB method. In addition, the proposed method is evaluable for all datasets, while the LMB method cannot be used when the imputed cell counts are zero across imputations for a treatment group.

Semiparametric empirical likelihood inference for abundance from one-inflated capture-recapture data.

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.

Genetic association tests in family samples for multi-category phenotypes.

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.

A Mixed-Effects Model for Powerful Association Tests in Integrative Functional Genomics.

Genome-wide association studies (GWASs) have successfully identified thousands of genetic variants for many complex diseases; however, these variants explain only a small fraction of the heritability. Recently, genetic association studies that leverage external transcriptome data have received much attention and shown promise for discovering novel variants. One such approach, PrediXcan, is to use predicted gene expression through genetic regulation. However, there are limitations in this approach. The predicted gene expression may be biased, resulting from regularized regression applied to moderately sample-sized reference studies. Further, some variants can individually influence disease risk through alternative functional mechanisms besides expression. Thus, testing only the association of predicted gene expression as proposed in PrediXcan will potentially lose power. To tackle these challenges, we consider a unified mixed effects model that formulates the association of intermediate phenotypes such as imputed gene expression through fixed effects, while allowing residual effects of individual variants to be random. We consider a set-based score testing framework, MiST (mixed effects score test), and propose two data-driven combination approaches to jointly test for the fixed and random effects. We establish the asymptotic distributions, which enable rapid calculation of p values for genome-wide analyses, and provide p values for fixed and random effects separately to enhance interpretability over GWASs. Extensive simulations demonstrate that our approaches are more powerful than existing ones. We apply our approach to a large-scale GWAS of colorectal cancer and identify two genes, POU5F1B and ATF1, which would have otherwise been missed by PrediXcan, after adjusting for all known loci.

Retrospective versus prospective score tests for genetic association with case-control data.

Since the seminal work of Prentice and Pyke, the prospective logistic likelihood has become the standard method of analysis for retrospectively collected case-control data, in particular for testing the association between a single genetic marker and a disease outcome in genetic case-control studies. In the study of multiple genetic markers with relatively small effects, especially those with rare variants, various aggregated approaches based on the same prospective likelihood have been developed to integrate subtle association evidence among all the markers considered. Many of the commonly used tests are derived from the prospective likelihood under a common-random-effect assumption, which assumes a common random effect for all subjects. We develop the locally most powerful aggregation test based on the retrospective likelihood under an independent-random-effect assumption, which allows the genetic effect to vary among subjects. In contrast to the fact that disease prevalence information cannot be used to improve efficiency for the estimation of odds ratio parameters in logistic regression models, we show that it can be utilized to enhance the testing power in genetic association studies. Extensive simulations demonstrate the advantages of the proposed method over the existing ones. A real genome-wide association study is analyzed for illustration.

A new statistical test for latent class in censored data due to detection limit.

Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.

Testing the homogeneity of proportions for combined unilateral and bilateral data.

Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmologic studies, statistical tests are often based on one or two eyes of an individual. For the bilateral data, recent literatures have shown some test procedures that take into account the intraclass correlation between paired organs of the same person. Ma et al. investigated three test procedures under Rosner's model. In this paper, we extend Ma's work for bilateral data to combined bilateral and unilateral data. The proposed procedures are based on the likelihood estimate algorithm derived from the root of 4th order polynomial equations and the Fisher scoring iterations. Simulation studies are performed to compare the testing procedures under different parameter configurations. The result shows that score test has satisfactory type I error rates and powers. Therefore, we recommend score test for testing the homogeneity of proportions. We illustrate the application of the proposed methods with two real world examples.

Joint modeling of interval counts of recurrent events and death.

When a recurrent event process is ended by death, this may imply dependent censoring if the two processes are associated. Such dependent censoring would have to be modeled to obtain a valid inference. Moreover, the dependence between the recurrence process and the terminal event may be the primary topic of interest. Joint frailty models for recurrent events and death, which include a separate dependence parameter, have been proposed for exactly observed recurrence times. However, in many situations, only the number of events experienced during consecutive time intervals are available. We propose a method for estimating a joint frailty model based on such interval counts and observed or independently censored terminal events. The baseline rates of the two processes are modeled by piecewise constant functions, and Gaussian quadrature is used to approximate the marginal likelihood. Covariates can be included in a proportional rates setting. The observation intervals for the recurrent event counts can differ between individuals. Furthermore, we adapt a score test for the association between recurrent events and death to the setting in which only individual interval counts are observed. We study the performance of both approaches via simulation studies, and exemplify the methodology in a biodemographic study of the dependence between budding rates and mortality in the species Eleutheria dichotoma.