Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects.

With the increasing availability of large-scale GWAS summary data on various complex traits and diseases, there have been tremendous interests in applications of Mendelian randomization (MR) to investigate causal relationships between pairs of traits using SNPs as instrumental variables (IVs) based on observational data. In spite of the potential significance of such applications, the validity of their causal conclusions critically depends on some strong modeling assumptions required by MR, which may be violated due to the widespread (horizontal) pleiotropy. Although many MR methods have been proposed recently to relax the assumptions by mainly dealing with uncorrelated pleiotropy, only a few can handle correlated pleiotropy, in which some SNPs/IVs may be associated with hidden confounders, such as some heritable factors shared by both traits. Here we propose a simple and effective approach based on constrained maximum likelihood and model averaging, called cML-MA, applicable to GWAS summary data. To deal with more challenging situations with many invalid IVs with only weak pleiotropic effects, we modify and improve it with data perturbation. Extensive simulations demonstrated that the proposed methods could control the type I error rate better while achieving higher power than other competitors. Applications to 48 risk factor-disease pairs based on large-scale GWAS summary data of 3 cardio-metabolic diseases (coronary artery disease, stroke, and type 2 diabetes), asthma, and 12 risk factors confirmed its superior performance.

Focused goodness of fit tests for gene set analyses.

Gene set-based signal detection analyses are used to detect an association between a trait and a set of genes by accumulating signals across the genes in the gene set. Since signal detection is concerned with identifying whether any of the genes in the gene set are non-null, a goodness-of-fit (GOF) test can be used to compare whether the observed distribution of gene-level tests within the gene set agrees with the theoretical null distribution. Here, we present a flexible gene set-based signal detection framework based on tail-focused GOF statistics. We show that the power of the various statistics in this framework depends critically on two parameters: the proportion of genes within the gene set that are non-null and the degree of separation between the null and alternative distributions of the gene-level tests. We give guidance on which statistic to choose for a given situation and implement the methods in a fast and user-friendly R package, wHC (https://github.com/mqzhanglab/wHC). Finally, we apply these methods to a whole exome sequencing study of amyotrophic lateral sclerosis.

Diagnostics for regression models with semicontinuous outcomes.

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (eg, deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that is applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey.

A generalized Hosmer-Lemeshow goodness-of-fit test for a family of generalized linear models.

Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer-Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535-545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available. Supplementary Information: The online version contains supplementary material available at 10.1007/s11749-023-00912-8.

Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference.

Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.

Assessment of nonlinear dose-response relationships via nonparametric regression.

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose-response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study.

The analysis of randomized response "ever" and "last year" questions: A non-saturated Multinomial model.

Randomized response (RR) is a well-known interview technique designed to eliminate evasive response bias that arises from asking sensitive questions. The most frequently asked questions in RR are either whether respondents were "ever" carriers of the sensitive characteristic, or whether they were carriers in a recent period, for instance, "last year". The present paper proposes a design in which both questions are asked, and derives a multinomial model for the joint analysis of these two questions. Compared to the separate analyses with the binomial model, the model makes a useful distinction between last year and former carriers of the sensitive characteristic, it is more efficient in estimating the prevalence of last year carriers, and it has a degree of freedom that allows for a goodness-of-fit test. Furthermore, it is easily extended to a multinomial logistic regression model to investigate the effects of covariates on the prevalence estimates. These benefits are illustrated in two studies on the use of anabolic androgenic steroids in the Netherlands, one using Kuk and one using both the Kuk and forced response. A salient result of our analyses is that the multinomial model provided ample evidence of response biases in the forced response condition.

A Bayesian Measure of Model Accuracy.

Ensuring that the proposed probabilistic model accurately represents the problem is a critical step in statistical modeling, as choosing a poorly fitting model can have significant repercussions on the decision-making process. The primary objective of statistical modeling often revolves around predicting new observations, highlighting the importance of assessing the model's accuracy. However, current methods for evaluating predictive ability typically involve model comparison, which may not guarantee a good model selection. This work presents an accuracy measure designed for evaluating a model's predictive capability. This measure, which is straightforward and easy to understand, includes a decision criterion for model rejection. The development of this proposal adopts a Bayesian perspective of inference, elucidating the underlying concepts and outlining the necessary procedures for application. To illustrate its utility, the proposed methodology was applied to real-world data, facilitating an assessment of its practicality in real-world scenarios.

An information ratio-based goodness-of-fit test for copula models on censored data.

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness.

An accelerated failure time regression model for illness-death data: A frailty approach.

This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well-known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided expectation-maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty-based illness-death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.

Testing for an ignorable sampling bias under random double truncation.

In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable, so proper corrections of ordinary estimation and inference procedures must be used. Unfortunately, the nonparametric maximum likelihood estimator of a doubly truncated distribution has several drawbacks, like potential nonexistence and nonuniqueness issues, or large estimation variance. Interestingly, no correction for double truncation is needed when the sampling bias is ignorable, which may occur with interval sampling and other sampling designs. In such a case the ordinary empirical distribution function is a consistent and fully efficient estimator that generally brings remarkable variance improvements compared to the nonparametric maximum likelihood estimator. Thus, identification of such situations is critical for the simple and efficient estimation of the target distribution. In this article, we introduce for the first time formal testing procedures for the null hypothesis of ignorable sampling bias with doubly truncated data. The asymptotic properties of the proposed test statistic are investigated. A bootstrap algorithm to approximate the null distribution of the test in practice is introduced. The finite sample performance of the method is studied in simulated scenarios. Finally, applications to data on onset for childhood cancer and Parkinson's disease are given. Variance improvements in estimation are discussed and illustrated.

Goodness-of-fit test for a parametric mixture cure model with partly interval-censored data.

Partly interval-censored event time data arise naturally in medical, biological, sociological and demographic studies. In practice, some patients may be immune from the event of interest, invoking a cure model for survival analysis. Choosing an appropriate parametric distribution for the failure time of susceptible patients is an important step to fully structure the mixture cure model. In the literature, goodness-of-fit tests for survival models are usually restricted to uncensored or right-censored data. We fill in this gap by proposing a new goodness-of-fit test dealing with partly interval-censored data under mixture cure models. Specifically, we investigate whether a parametric distribution can fit the susceptible part by using a Cramér-von Mises type of test, and establish the asymptotic distribution of the test . Empirically, the critical value is determined from the bootstrap resamples. The proposed test, compared to the traditional leveraged bootstrap approach, yields superior practical results under various settings in extensive simulation studies. Two clinical data sets are analyzed to illustrate our method.

Incremental Model Fit Assessment in the Case of Categorical Data: Tucker-Lewis Index for Item Response Theory Modeling.

The Tucker-Lewis index (TLI; Tucker & Lewis, 1973), also known as the non-normed fit index (NNFI; Bentler & Bonett, 1980), is one of the numerous incremental fit indices widely used in linear mean and covariance structure modeling, particularly in exploratory factor analysis, tools popular in prevention research. It augments information provided by other indices such as the root-mean-square error of approximation (RMSEA). In this paper, we develop and examine an analogous index for categorical item level data modeled with item response theory (IRT). The proposed Tucker-Lewis index for IRT (TLIRT) is based on Maydeu-Olivares and Joe's (2005) [Formula: see text] family of limited-information overall model fit statistics. The limited-information fit statistics have significantly better Chi-square approximation and power than traditional full-information Pearson or likelihood ratio statistics under realistic situations. Building on the incremental fit assessment principle, the TLIRT compares the fit of model under consideration along a spectrum of worst to best possible model fit scenarios. We examine the performance of the new index using simulated and empirical data. Results from a simulation study suggest that the new index behaves as theoretically expected, and it can offer additional insights about model fit not available from other sources. In addition, a more stringent cutoff value is perhaps needed than Hu and Bentler's (1999) traditional cutoff criterion with continuous variables. In the empirical data analysis, we use a data set from a measurement development project in support of cigarette smoking cessation research to illustrate the usefulness of the TLIRT. We noticed that had we only utilized the RMSEA index, we could have arrived at qualitatively different conclusions about model fit, depending on the choice of test statistics, an issue to which the TLIRT is relatively more immune.

Optimal Stein-type goodness-of-fit tests for count data.

Common count distributions, such as the Poisson (binomial) distribution for unbounded (bounded) counts considered here, can be characterized by appropriate Stein identities. These identities, in turn, might be utilized to define a corresponding goodness-of-fit (GoF) test, the test statistic of which involves the computation of weighted means for a user-selected weight function f. Here, the choice of f should be done with respect to the relevant alternative scenario, as it will have great impact on the GoF-test's performance. We derive the asymptotics of both the Poisson and binomial Stein-type GoF-statistic for general count distributions (we also briefly consider the negative-binomial case), such that the asymptotic power is easily computed for arbitrary alternatives. This allows for an efficient implementation of optimal Stein tests, that is, which are most powerful within a given class  F $\mathcal {F}$ of weight functions. The performance and application of the optimal Stein-type GoF-tests is investigated by simulations and several medical data examples.

Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton-Oakes model.

The Kaplan-Meier estimator is ubiquitously used to estimate survival probabilities for time-to-event data. It is nonparametric, and thus does not require specification of a survival distribution, but it does assume that the risk set at any time t consists of independent observations. This assumption does not hold for data from paired organ systems such as occur in ophthalmology (eyes) or otolaryngology (ears), or for other types of clustered data. In this article, we estimate marginal survival probabilities in the setting of clustered data, and provide confidence limits for these estimates with intra-cluster correlation accounted for by an interval-censored version of the Clayton-Oakes model. We develop a goodness-of-fit test for general bivariate interval-censored data and apply it to the proposed interval-censored version of the Clayton-Oakes model. We also propose a likelihood ratio test for the comparison of survival distributions between two groups in the setting of clustered data under the assumption of a constant between-group hazard ratio. This methodology can be used both for balanced and unbalanced cluster sizes, and also when the cluster size is informative. We compare our test to the ordinary log rank test and the Lin-Wei (LW) test based on the marginal Cox proportional Hazards model with robust standard errors obtained from the sandwich estimator. Simulation results indicate that the ordinary log rank test over-inflates type I error, while the proposed unconditional likelihood ratio test has appropriate type I error and higher power than the LW test. The method is demonstrated in real examples from the Sorbinil Retinopathy Trial, and the Age-Related Macular Degeneration Study. Raw data from these two trials are provided.

The partly parametric and partly nonparametric additive risk model.

Aalen's linear hazard rate regression model is a useful and increasingly popular alternative to Cox' multiplicative hazard rate model. It postulates that an individual has hazard rate function [Formula: see text] in terms of his covariate values [Formula: see text]. These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions [Formula: see text] are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model's parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study.

Why we need to abandon fixed cutoffs for goodness-of-fit indices: An extensive simulation and possible solutions.

To evaluate model fit in confirmatory factor analysis, researchers compare goodness-of-fit indices (GOFs) against fixed cutoff values (e.g., CFI > .950) derived from simulation studies. Methodologists have cautioned that cutoffs for GOFs are only valid for settings similar to the simulation scenarios from which cutoffs originated. Despite these warnings, fixed cutoffs for popular GOFs (i.e., χ2, χ2/df, CFI, RMSEA, SRMR) continue to be widely used in applied research. We (1) argue that the practice of using fixed cutoffs needs to be abandoned and (2) review time-honored and emerging alternatives to fixed cutoffs. We first present the most in-depth simulation study to date on the sensitivity of GOFs to model misspecification (i.e., misspecified factor dimensionality and unmodeled cross-loadings) and their susceptibility to further data and analysis characteristics (i.e., estimator, number of indicators, number and distribution of response options, loading magnitude, sample size, and factor correlation). We included all characteristics identified as influential in previous studies. Our simulation enabled us to replicate well-known influences on GOFs and establish hitherto unknown or underappreciated ones. In particular, the magnitude of the factor correlation turned out to moderate the effects of several characteristics on GOFs. Second, to address these problems, we discuss several strategies for assessing model fit that take the dependency of GOFs on the modeling context into account. We highlight tailored (or "dynamic") cutoffs as a way forward. We provide convenient tables with scenario-specific cutoffs as well as regression formulae to predict cutoffs tailored to the empirical setting of interest.

Shifted Mixture Model Using Weibull, Lognormal, and Gamma Distributions.

The objective of this investigation is to provide framework to construct a threefold mixture model and its shifted version using Weibull, lognormal, and gamma distributions. The proposed models are examined by establishing the statistical and reliability indices. The parameter estimation using the maximum likelihood estimation method (MLE) and expectation-maximization has been proposed. The usefulness of the shifted mixture models by fitting them into the actual data set has revealed. The goodness-of-fit tests are used to compare the mixture models for the real-life data. Based on statistical testing, it is established that for small data set, shifted mixture model is the best fitted model in comparison with other single and mixed mixture distributions.

Noninvasive detection of fetal genetic variations through polymorphic site sequencing of maternal plasma DNA.

BACKGROUND: Noninvasive prenatal testing (NIPT) for common fetal aneuploidies has been widely adopted in clinical practice for its sensitivity and accuracy. However, detection of pathogenic copy number variations (pCNVs) or monogenic disorders (MDs) is inaccurate and not cost effective. Here we developed an assay, the noninvasive prenatal testing based on goodness-of-fit and graphical analysis of polymorphic sites (GGAP-NIPT), to simultaneously detect fetal aneuploidies, pCNVs, and MDs. METHODS: Polymorphic sites were amplicon sequenced, followed by fetal fraction estimation using allelic reads counts and a robust linear regression model. The genotype of each polymorphic site or MD variant was then determined by allelic goodness-of-fit test or graphical analysis of its different alleles. Finally, aneuploidies and pCNVs were detected using collective goodness-of-fit test to select each best fit from all possible chromosomal models. RESULTS: Of the simulated 1,692 chromosomes and 1,895 pCNVs, all normals and variants were correctly identified (accuracy 100%, sensitivity 100%, specificity 100%). Of the 713,320 simulated MD variants, more than 90% of the genotypes were determined correctly (accuracy: 98.3 ± 1.0%; sensitivity: 98.7 ± 1.96%; specificity: 99.7 ± 0.6%). The detection accuracies of three public MD datasets were 95.70%, 93.43%, and 96.83%. For an MD validation dataset, 75% detection accuracy was observed when a site with sample replicates was analyzed individually, and 100% accuracy was achieved when analyzed collectively. CONCLUSIONS: Fetal aneuploidies, pCNVs, and MDs could be detected simultaneously and with high accuracy through amplicon sequencing of polymorphic and target sites, which showed the potential of extending NIPT to an expanded panel of genetic disorders.

Advances in nonparametric item response theory for scale construction in quality-of-life research.

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering.