Valid Statistical Inference Research Articles

Studying Complex Adaptive Systems With Internal States: A Recurrence Network Approach to the Analysis of Multivariate Time-Series Data Representing Self-Reports of Human Experience

We discuss formal, theoretical and practical issues with the statistical analysis of multivariate time series data that represent self-reports of human experience, often referred to as Ecological Momentary Assessment (EMA) data, or, Experience Sampling Method (ESM) data. We argue such time series likely violate the assumptions required for valid statistical inference, such as the memoryless-ness property (due to the presence of long-range temporal correlations) and ergodicity (due to non-stationarity and non-homogeneity of central moments). Moreover, we consider the common practice of interpreting outcomes of self-reports as if they were outcomes of classical physical measurements as extremely problematic and suggest to consider them as records of the temporal evolution of observables of a complex adaptive system with internal state dynamics. We propose to address some of these issues by analyzing the Change Profile instead of the observed time series, using recurrence-bases analyses, specifically, (multiplex) recurrence networks. We analyze a publicly available data set in which 4 participants rated 6 questions about their self-esteem and physical self, twice a day over a period of 512 days and introduce the concept of recurrence networks weighted by recurrence time. The edge weights represent either recurrence times or recurrence time frequencies and results show the scaling relation between vertex degree and vertex strength (the weighted variant of vertex degree), is associated to the scaling relation between frequency and spectral power based on the ‘raw’ time series. In addition, we present a new spiral layout for recurrence networks that might be more appropriate when the detection of critical periods, regime shifts and tipping points requires insight in the temporal order in which those events occur. We conclude a complex systems approach to analyzing multivariate time series of self-reports of human experience is preferred over and above fitting statistical models like the Gaussian Graphical Model, or its derivatives.

Handling Missing Values in Information Systems Research: A Review of Methods and Assumptions

In today’s big data environment, missing values continues to be a problem that harms the data quality. The bias caused by missing values raises the highest concern as it cannot be eliminated simply by increasing the sample size. Although the statistics literature has developed approaches to handling missing values and formulated assumptions regarding when these approaches generate valid statistical inferences, these prescriptions have yet to be broadly accepted by many social science disciplines including the Information Systems (IS) discipline. By reviewing recently published empirical research in information systems, we find that missing values is indeed an important and pervasive problem. We believe that a review of missing value theory is necessary for the IS community to understand the nature of missing values and to promote more rigorous research practice when missing values is often unavoidable. In addition, the not missing at random (NMAR) mechanism brings in challenges in parameter estimation. We contribute to research practice by proposing and demonstrating the superior performance of a Monte Carlo likelihood approach in correcting bias in parameter estimation. We conclude by suggesting that research validity can be enhanced through reasoned adoption of missing value handling method and missing value reporting practice.

A cautionary tale on using imputation methods for inference in matched-pairs design.

Imputation procedures in biomedical fields have turned into statistical practice, since further analyses can be conducted ignoring the former presence of missing values. In particular, non-parametric imputation schemes like the random forest have shown favorable imputation performance compared to the more traditionally used MICE procedure. However, their effect on valid statistical inference has not been analyzed so far. This article closes this gap by investigating their validity for inferring mean differences in incompletely observed pairs while opposing them to a recent approach that only works with the given observations at hand. Our findings indicate that machine-learning schemes for (multiply) imputing missing values may inflate type I error or result in comparably low power in small-to-moderate matched pairs, even after modifying the test statistics using Rubin's multiple imputation rule. In addition to an extensive simulation study, an illustrative data example from a breast cancer gene study has been considered. The corresponding R-code can be accessed through the authors and the gene expression data can be downloaded at www.gdac.broadinstitute.org. Supplementary data are available at Bioinformatics online.

Efficacy of screening using annual fecal immunochemical test alone versus combined with one-time colonoscopy in reducing colorectal cancer mortality: the Akita Japan population-based colonoscopy screening trial (Akita pop-colon trial)

PurposeScreening programs using fecal occult blood testing help reduce mortality from colorectal cancer (CRC). Colonoscopy and colonoscopy combined with fecal occult blood testing are considered alternatives with higher sensitivity than fecal tests; however, to our knowledge, randomized controlled trials (RCTs) providing such evidence have not been reported. Therefore, this study aimed to compare screening using the fecal immunochemical test (FIT) combined with colonoscopy and FIT alone to evaluate the efficacy of colonoscopy screening in reducing CRC mortality.MethodsThis multicenter, prospective, randomized, controlled study included average-risk individuals for CRC living in the study areas and aged 40–74 years. The exclusion criteria were history of CRC, hereditary non-polyposis CRC, familial adenomatous polyposis, inflammatory bowel diseases, history of cancer other than CRC within the past 5 years, and not expected to survive from comorbid illness. The intervention group underwent one-time colonoscopy and annual FIT, while the control group underwent annual FIT. The primary endpoint was mortality from CRC, while the secondary endpoints were cumulative incidence of invasive CRC, advanced CRC (invasion into the muscle layer or deeper), invasive cancer and screening sensitivities and specificities of invasive CRC, whole CRC, advanced neoplasia, and prevalence of adverse events. The intervention and control groups comprised 4876 and 4875 participants, respectively.ConclusionThis explanatory RCT evaluated the efficacy of colonoscopy screening by valid statistical inference based on randomization. Data on adverse events from this kind of screening are necessary when considering implementation of future screening programs.Trial registrationUMIN Clinical Trials Registry, number UMIN000001980.

Data Denoising and Post-Denoising Corrections in Single Cell RNA Sequencing

Single cell sequencing technologies are transforming biomedical research. However, due to the inherent nature of the data, single cell RNA sequencing analysis poses new computational and statistical challenges. We begin with a survey of a selection of topics in this field, with a gentle introduction to the biology and a more detailed exploration of the technical noise. We consider in detail the problem of single cell data denoising, sometimes referred to as “imputation” in the relevant literature. We discuss why this is not a typical statistical imputation problem, and review current approaches to this problem. We then explore why the use of denoised values in downstream analyses invites novel statistical insights, and how denoising uncertainty should be accounted for to yield valid statistical inference. The utilization of denoised or imputed matrices in statistical inference is not unique to single cell genomics, and arises in many other fields. We describe the challenges in this type of analysis, discuss some preliminary solutions, and highlight unresolved issues.

Enhancing validity in psychological research.

Methods to increase Campbell's (1957) internal and external validity as well as Cook and Campbell's (1979) construct and conclusion validity are reviewed. For internal validity or valid causal inference, designs and methods to draw causal conclusions from nonrandomized studies are considered. Greater collaboration between the causal inference and structural equation modeling traditions would benefit both. For external validity, generalizing results, treating partners and studies as well as participants as random is strongly encouraged. For construct validity, particularly the psychological meaning of measures, multivariate models that treat measures from both overtime and dyadic data as being a combination of multiple constructs are discussed. For conclusion validity or valid statistical inference, the problem of low power when generalizability is high and the assumption of independence are discussed. Finding the truth in psychological research is a challenge, and seemingly insurmountable difficulties are often encountered. Nonetheless, persistent and diligent efforts using strategies developed by generations of methodologists should lead to scientific advancement. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

The Combined Effects of Omitting Confounders and Measurement Error on Statistical Inference of Mediation and a New Tool for Sensitivity Analysis

To make valid statistical inferences from mediation analysis, a number of assumptions need to be assessed. Two frequently discussed ones are (1) no confounders of the relations among X, M, and Y ar...

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach.

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.

Measurement Invariance of Three Brief Emotion Regulation Questionnaires in People With and Without a History of Non-Suicidal Self-Injury

Abstract. In this study, we investigated the factor structure and measurement invariance of three brief emotion regulation questionnaires in samples of young adults (17–30 years) with and without a history of non-suicidal self-injury (NSSI; n = 705–836). Results revealed configural, full metric, and full scalar invariance for the Difficulties in Emotion Regulation Scale – Short Form (DERS-SF) and the Cognitive Emotion Regulation Questionnaire – Short (CERQ-S). In addition, the CERQ-S also showed full residual error invariance. In contrast, the proposed factor structure of the Emotion Regulation Questionnaire (ERQ) was not confirmed in either sample. Further, we observed that some items function differently for people who self-injure and people who do not, which could result in artificial differences being reported in use of cognitive reappraisal. While the current findings offer confidence that observed differences using the DERS-SF and CERQ-S reflect reliable discrepancies in emotion regulation processes between people who self-injure and do not, the validity of statistical inferences using the ERQ could not be ensured and need further psychometric evaluation.

Chi-square Tests in Medical Research.

KEY POINT: A χ2 test is commonly used to analyze categorical data, but valid statistical inferences rely on its test assumptions being met.In this issue of Anesthesia & Analgesia, Sharkey et al1 report a randomized trial comparing the incidence of bradycardia after phenylephrine versus norepinephrine to prevent and treat spinal-induced hypotension in women undergoing cesarean delivery with spinal anesthesia. The authors used a chi-square (χ2) test to compare the groups and observed a lower incidence of bradycardia in the norepinephrine group. A χ2 test commonly either compares the distribution of a categorical variable to a hypothetical distribution or tests whether 2 categorical variables are independent. We focus here on the Pearson χ2 test of independence used by Sharkey et al.1 The Pearson χ2 test evaluates the null hypothesis that 2 categorical variables (eg, treatment group [norepinephrine versus phenylephrine] and outcome [bradycardia versus no bradycardia]) are not associated with each other.2 In the study by Sharkey et al,1 a total of 27/112 (24.1%) patients developed bradycardia (Figure). Assuming independence between treatment and bradycardia, the same percentage would be expected in each group (ie, 13.5 patients with bradycardia per group). The χ2 test then compares the observed to expected frequencies. The reported P value of .001 suggests that it is very unlikely to observe a difference this large or larger if the null hypothesis was true,3 supporting the conclusion that there is an association between treatment and outcome. While in this example, both categorical variables have 2 levels (2 groups, 2 outcomes), a χ2 test can more generally be used when variables have multiple categories.Figure.: Contingency table with data from Sharkey et al1 showing the observed and expected counts (number of patients) with and without bradycardia per treatment group. Assuming that the probability of developing bradycardia is independent of the group allocation (null hypothesis), 13.5 patients with bradycardia would be expected in each group (given a total of 27 patients who developed bradycardia and equal sample size in both groups). Pearson χ2 test compares observed to expected frequencies.However, valid inferences with a χ2 test rely on a number of assumptions,2 including: The actual frequencies can be crosstabulated in a contingency table. It is not appropriate to use a χ2 test for percentages or other derived statistics. The 2 variables are nominal—there is no natural ordering of the categories. The observations are independent. The expected count or frequency is ≥5 in more than 75%–80% of the cells in the contingency table, and there is no expected cell count of 0. When analyzing ordinal data, the Pearson χ2 test ignores the order (assumption #2), and the Mantel–Haenszel χ2 test provides more power to test for an association.2 Repeated measurements in the same subjects are a common violation of assumption #3. Such data require tests that account for the pairing (eg, McNemar test) or longitudinal models that account for the within-subject correlation.4 When expected counts are lower than specified in assumption #4, Fisher exact test can be used.2 Importantly, the χ2 test assesses for an association but does not provide information on the strength of the association or on whether the relationship is causal. While a properly conducted randomized controlled trial allows causal inferences, observed associations can be confounded in uncontrolled studies. In such cases, techniques that control for confounding, such as multivariable logistic regression,5 are strongly preferred.

Methodology of the National Health and Nutrition Survey for localities with less than 100 000 inhabitants (Ensanut 100k)

To describe the methodological design of the National Health and Nutrition Survey in localities with less than 100 000 inhabitants (Ensanut 100k). The Ensanut 100k is a probabilistic survey that over-represents households with less economic capabilities. This paper describes the scope of the survey, sampling procedures, measurement and inference and logistics organization. 10 461 home interviews and 26 161 individual interviews were obtained. The household response rate was 89 and 92% from individuals. The probabilistic design of the Ensanut 100k allows to make valid statistical inferences about parameters of interest for public health in localities with less than 100 000 inhabitants, localities where 52% of the population lives according to the 2010 census. The comparability of the results with the Ensanut 2012 faci- litates the assessment of the government's support actions to populations with lower economic capacities in the period 2012-2018.

Two-Sample Unpaired t Tests in Medical Research.

KEY POINT: A 2-sample t test is commonly used to analyze continuous data, but valid statistical inferences rely on its test assumptions being met.In this issue of Anesthesia & Analgesia, Wong et al1 report a randomized trial of the effects of high-flow nasal oxygenation on safe apnea time (oxygen saturation measured by pulse oximetry [Spo2], >95%) during anesthetic induction of morbidly obese patients. The authors used a 2-sample, unpaired t test and observed a significantly prolonged safe apnea time in the intervention group (Figure). The 2-sample t test is commonly used to compare 2 independent groups and tests the null hypothesis that the means are equal.2 Its test statistic can be thought of as a “signal-to-noise” ratio3: the ratio of the mean difference between the groups (the “signal”) to a function of the within-group variability (the “noise”). A large mean difference relative to the variability corresponds to a small P value, suggesting that there actually is a difference between the groups.Figure.: Excerpt from Wong et al1 results table: mean values ± standard deviations, MD with CI, and P value for their primary outcome. CI indicates confidence interval; Etco 2, end-tidal carbon dioxide; HFNO, High-flow nasal oxygen; MD, mean difference; Spo 2, oxygen saturation measured by pulse oximetry.Valid inferences with a 2-sample t test rely on several assumptions being met,3 including: The dependent variable is continuous. Observations are independent of each other. The data are approximately normally distributed in each group. The variances are approximately equal in both groups. Assumptions #3 and #4 apply to the population from which the data were sampled, not the sample itself. Hypothesis tests are available to test these assumptions (eg, Shapiro-Wilk test as used by Wong et al1 for #3 and Levene test for #4) but have low power to detect violations at small sample sizes. These tests should be used in combination with graphical methods (eg, Q-Q plots) and a comparison of the group standard deviations to determine whether the assumptions are met.4 The t test is relatively robust against nonnormality with larger sample sizes. Conventionally, the sample size needs to be ≥30; however, a much larger sample may be necessary if the data distribution is severely skewed. Importantly, smaller samples definitely do rely on a normal distribution to avoid erroneous conclusions. Nonparametric methods (eg, Mann-Whitney U tests) can be used if this normality assumption is violated. The t test is also relatively robust against unequal variances if the sample sizes per group are equal and if the sample is large enough (>15 per group). Alternatives like the Welch t test are available if variances are unequal. Beside inappropriately using t tests when assumptions are (grossly) violated, a common mistake is to use multiple pairwise t tests to compare >2 groups. Other techniques are instead needed, like analysis of variance (ANOVA) with appropriate post hoc tests.2 While the 2-sample t test is basically a hypothesis test that gives a P value, statistical software packages routinely report the mean difference between the groups including its confidence interval. As appropriately done by Wong et al,1 we strongly encourage authors to report this estimate because it provides important information about the magnitude of the treatment effect.5

Determinants of stunting among under-five years children in Ethiopia from the 2016 Ethiopia demographic and Health Survey: Application of ordinal logistic regression model using complex sampling designs

BackgroundStunting is a result of chronic under nutrition and a major public health issue in Ethiopia. This study aimed to calculate the prevalence of stunting, and associated factors among children younger than five years. MethodsA total of 9588 children in Ethiopia were included. Proportional Odds Model was used to identify determinants of stunting. The score test and plots were used to see the proportional odds model assumptions. ResultsThe prevalence of stunting was 38% (21% moderately, 17% severely). Children with illiterate mothers were 2 times more likely to be moderately and severely stunted compared with their counterparts with secondary education. The odds of being stunted for children whose age group 24–35 months respectively as compared to children 0–5 months of age were 4.71 times higher. Being female children were 9.66 times more likely to be in normal nutrition status as compared to male. Children of families in the highest wealth quintile were 7.92 times more likely to have normal stature compared with children from poorest ones. ConclusionsChild age, child sex, birth interval, mother's educational status, wealth index, were the important determinants of stunting. Addressing these factors will help to prevent future injury of physical and mental development in children and will assist in alleviating malnutrition and refining their quality of life. Moreover, in a DHS data set, complex sampling design should be incorporated in order to make a valid statistical inference.

Response adaptive randomization procedures in seamless phase II/III clinical trials

ABSTRACTIt is desirable to work efficiently and cost effectively to evaluate new therapies in a time-sensitive and ethical manner without compromising the integrity and validity of the development process. The seamless phase II/III clinical trial has been proposed to meet this need, and its efficient, ethical and economic advantages can be strengthened by its combination with innovative response adaptive randomization (RAR) procedures. In particular, well-designed frequentist RAR procedures can target theoretically optimal allocation proportions, and there are explicit asymptotic results. However, there has been little research into seamless phase II/III clinical trials with frequentist RAR because of the difficulty in performing valid statistical inference and controlling the type I error rate. In this paper, we propose the framework for a family of frequentist RAR designs for seamless phase II/III trials, derive the asymptotic distribution of the parameter estimators using martingale processes and offer solutions to control the type I error rate. The numerical studies demonstrate our theoretical findings and the advantages of the proposed methods.

Black swan models for the entertainment industry with an application to the movie business

Success in popular entertainment is highly unpredictable. Yet it is the high-impact low-probability events—known as ‘black swans’—that drive entertainment industry profitability because success is highly concentrated on a small number of winners. In this research, we apply recently developed statistical tools to model motion-picture success; these tools explicitly account for rare extreme events while permitting valid statistical inferences to be made on how product attributes are associated with product success. The specific empirical application relates the attributes of a film and its theatrical release to the distribution of worldwide cumulative box-office revenue. A regression model with skew-stable random disturbances is applied to a large sample of motion pictures to quantify the correlates of film success while explicitly accounting for skewness and heavy tails. The skew-stable estimates are compared to estimates obtained from symmetric-stable regression, ordinary least-squares regression, and several alternative robust-to-outliers regression models. Failure to control explicitly for heavy tails and skewness generates misleading statistical inferences, particularly regarding the impact of production budget, opening week screens, and star power on a film’s success at the box-office.

Comparison of Outcomes of Patients with Acute Exacerbation of Heart Failure with versus without Sepsis: Nationwide Study from 2007-14

Purpose This study explores the impact of severe sepsis and septic shock on morbidity, mortality and length of stay in patients admitted to the hospital with a primary diagnosis of heart failure in acute exacerbation. Methods We examined National Inpatient Sample (NIS) database from years 2007-14 for all hospital admissions with heart failure admitted with acute exacerbation with vs without sepsis. ICD9 codes were utilized for selecting the study group. We compared baseline characteristics of the two groups using parametric and non-parametric tests for continuous variables and Chi-Squares test for dichotomous variables. Multivariate logistic regression was used to draw comparisons between incidence of cardiogenic shock, in-hospital mortality and length of stay (LOS). Our analysis adjusted for age, sex, race, payer, income quartiles, hospital location, region, size and teaching status. Comorbidities in charlson comorbidity Index were accounted for in our analysis. Missing values for covariates in the regression analysis were adjusted by using multivariate imputation by chained equations technique to ensure valid statistical inference. Results From 2007-2014, a total of 7,000,805 patients were included in the aforementioned study group. 1.08% (75,765) of the study population had concomitant diagnosis of Sepsis. Study population did not significantly differ in age (mean age 72.8 yrs. (HF)vs 71.4 yrs. (HF w Sepsis) p>0.05).HF with sepsis group were more likely to be males (p Conclusion This nation-wide study indicates that concomitant sepsis in patients admitted for heart failure exacerbation significantly increases morbidity and mortality in terms of cardiogenic shock and longer length of stay.

Statistical modeling methods: challenges and strategies

ABSTRACT Statistical modeling methods are widely used in clinical science, epidemiology, and health services research to analyze data that has been collected in clinical trials as well as observational studies of existing data sources, such as claims files and electronic health records. Diagnostic and prognostic inferences from statistical models are critical to researchers advancing science, clinical practitioners making patient care decisions, and administrators and policy makers impacting the health care system to improve quality and reduce costs. The veracity of such inferences relies not only on the quality and completeness of the collected data, but also statistical model validity. A key component of establishing model validity is determining when a model is not correctly specified and therefore incapable of adequately representing the Data Generating Process (DGP). In this article, model validity is first described and methods designed for assessing model fit, specification, and selection are reviewed. Second, data transformations that improve the model’s ability to represent the DGP are addressed. Third, model search and validation methods are discussed. Finally, methods for evaluating predictive and classification performance are presented. Together, these methods provide a practical framework with recommendations to guide the development and evaluation of statistical models that provide valid statistical inferences.

False confidence, non-additive beliefs, and valid statistical inference

Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To bridge this gap, I propose to look beyond the two dominating schools of thought and ask the following three questions: what do scientists need out of statistics, do the existing frameworks meet these needs, and, if not, how to fill the void? To the first question, I contend that scientists seek to convert their data, posited statistical model, etc., into calibrated degrees of belief about quantities of interest. To the second question, I argue that any framework that returns additive beliefs, i.e., probabilities, necessarily suffers from false confidence—certain false hypotheses tend to be assigned high probability—and, therefore, risks systematic bias. This reveals the fundamental importance of non-additive beliefs in the context of statistical inference. But non-additivity alone is not enough so, to the third question, I offer a sufficient condition, called validity, for avoiding false confidence, and present a framework, based on random sets and belief functions, that provably meets this condition. Finally, I discuss characterizations of p-values and confidence intervals in terms of valid non-additive beliefs, which imply that users of these classical procedures are already following the proposed framework without knowing it.

The Practical Significance of Measurement Error in Pulmonary Function Testing Conducted in Research Settings.

Conventional spirometry produces measurement error by using repeatability criteria (RC) to discard acceptable data and terminating tests early when RC are met. These practices also implicitly assume that there is no variation across maneuvers within each test. This has implications for air pollution regulations that rely on pulmonary function tests to determine adverse effects or set standards. We perform a Monte Carlo simulation of 20,902 tests of forced expiratory volume in 1 second (FEV1), each with eight maneuvers, for an individual with empirically obtained, plausibly normal pulmonary function. Default coefficients of variation for inter‐ and intratest variability (3% and 6%, respectively) are employed. Measurement error is defined as the difference between results from the conventional protocol and an unconstrained, eight‐maneuver alternative. In the default model, average measurement error is shown to be ∼5%. The minimum difference necessary for statistical significance at p < 0.05 for a before/after comparison is shown to be 16%. Meanwhile, the U.S. Environmental Protection Agency has deemed single‐digit percentage decrements in FEV1 sufficient to justify more stringent national ambient air quality standards. Sensitivity analysis reveals that results are insensitive to intertest variability but highly sensitive to intratest variability. Halving the latter to 3% reduces measurement error by 55%. Increasing it to 9% or 12% increases measurement error by 65% or 125%, respectively. Within‐day FEV1 differences ≤5% among normal subjects are believed to be clinically insignificant. Therefore, many differences reported as statistically significant are likely to be artifactual. Reliable data are needed to estimate intratest variability for the general population, subpopulations of interest, and research samples. Sensitive subpopulations (e.g., chronic obstructive pulmonary disease or COPD patients, asthmatics, children) are likely to have higher intratest variability, making it more difficult to derive valid statistical inferences about differences observed after treatment or exposure.

A Distance-Based Kernel Association Test Based on the Generalized Linear Mixed Model for Correlated Microbiome Studies.

Researchers have increasingly employed family-based or longitudinal study designs to survey the roles of the human microbiota on diverse host traits of interest (e. g., health/disease status, medical intervention, behavioral/environmental factor). Such study designs are useful to properly control for potential confounders or the sensitive changes in microbial composition and host traits. However, downstream data analysis is challenging because the measurements within clusters (e.g., families, subjects including repeated measures) tend to be correlated so that statistical methods based on the independence assumption cannot be used. For the correlated microbiome studies, a distance-based kernel association test based on the linear mixed model, namely, correlated sequence kernel association test (cSKAT), has recently been introduced. cSKAT models the microbial community using an ecological distance (e.g., Jaccard/Bray-Curtis dissimilarity, unique fraction distance), and then tests its association with a host trait. Similar to prior distance-based kernel association tests (e.g., microbiome regression-based kernel association test), the use of ecological distances gives a high power to cSKAT. However, cSKAT is limited to handling Gaussian traits [e.g., body mass index (BMI)] and a single chosen distance measure at a time. The power of cSKAT differs a lot by which distance measure is used. However, choosing an optimal distance measure is challenging because of the unknown nature of the true association. Here, we introduce a distance-based kernel association test based on the generalized linear mixed model (GLMM), namely, GLMM-MiRKAT, to handle diverse types of traits, such as Gaussian (e.g., BMI), Binomial (e.g., disease status, treatment/placebo) or Poisson (e.g., number of tumors/treatments) traits. We further propose a data-driven adaptive test of GLMM-MiRKAT, namely, aGLMM-MiRKAT, so as to avoid the need to choose the optimal distance measure. Our extensive simulations demonstrate that aGLMM-MiRKAT is robustly powerful while correctly controlling type I error rates. We apply aGLMM-MiRKAT to real familial and longitudinal microbiome data, where we discover significant disparity in microbial community composition by BMI status and the frequency of antibiotic use. In summary, aGLMM-MiRKAT is a useful analytical tool with its broad applicability to diverse types of traits, robust power and valid statistical inference.