A marginalized zero-inflated Poisson regression model with overall exposure effects

A simulation study of the performance of statistical models for count outcomes with excessive zeros

BACKGROUND

Outcome measures that are count variables with excessive zeros are common in health behaviors research. Examples include the number of standard drinks consumed or alcohol-related problems experienced over time. There is a lack of empirical data about the relative performance of prevailing statistical models for assessing the efficacy of interventions when outcomes are zero-inflated, particularly compared with recently developed marginalized count regression approaches for such data.

METHODS

The current simulation study examined five commonly used approaches for analyzing count outcomes, including two linear models (with outcomes on raw and log-transformed scales, respectively) and three prevailing count distribution-based models (ie, Poisson, negative binomial, and zero-inflated Poisson (ZIP) models). We also considered the marginalized zero-inflated Poisson (MZIP) model, a novel alternative that estimates the overall effects on the population mean while adjusting for zero-inflation. Motivated by alcohol misuse prevention trials, extensive simulations were conducted to evaluate and compare the statistical power and Type I error rate of the statistical models and approaches across data conditions that varied in sample size (N = 100 $$ N=100 $$ to 500), zero rate (0.2 to 0.8), and intervention effect sizes.

RESULTS

Under zero-inflation, the Poisson model failed to control the Type I error rate, resulting in higher than expected false positive results. When the intervention effects on the zero (vs. non-zero) and count parts were in the same direction, the MZIP model had the highest statistical power, followed by the linear model with outcomes on the raw scale, negative binomial model, and ZIP model. The performance of the linear model with a log-transformed outcome variable was unsatisfactory.

CONCLUSIONS

The MZIP model demonstrated better statistical properties in detecting true intervention effects and controlling false positive results for zero-inflated count outcomes. This MZIP model may serve as an appealing analytical approach to evaluating overall intervention effects in studies with count outcomes marked by excessive zeros.

EXPOSURE EFFECTS ON COUNT OUTCOMES WITH OBSERVATIONAL DATA, WITH APPLICATION TO INCARCERATED WOMEN

Causal inference methods can be applied to estimate the effect of a point exposure or treatment on an outcome of interest using data from observational studies. For example, in the Women's Interagency HIV Study, it is of interest to understand the effects of incarceration on the number of sexual partners and the number of cigarettes smoked after incarceration. In settings like this where the outcome is a count, the estimand is often the causal mean ratio, i.e., the ratio of the counterfactual mean count under exposure to the counterfactual mean count under no exposure. This paper considers estimators of the causal mean ratio based on inverse probability of treatment weights, the parametric g-formula, and doubly robust estimation, each of which can account for overdispersion, zero-inflation, and heaping in the measured outcome. Methods are compared in simulations and are applied to data from the Women's Interagency HIV Study.

A Marginalized Zero-Inflated Negative Binomial Model for Spatial Data: Modeling COVID-19 Deaths in Georgia

Spatial count data with an abundance of zeros arise commonly in disease mapping studies. Typically, these data are analyzed using zero-inflated models, which comprise a mixture of a point mass at zero and an ordinary count distribution, such as the Poisson or negative binomial. However, due to their mixture representation, conventional zero-inflated models are challenging to explain in practice because the parameter estimates have conditional latent-class interpretations. As an alternative, several authors have proposed marginalized zero-inflated models that simultaneously model the excess zeros and the marginal mean, leading to a parameterization that more closely aligns with ordinary count models. Motivated by a study examining predictors of COVID-19 death rates, we develop a spatiotemporal marginalized zero-inflated negative binomial model that directly models the marginal mean, thus extending marginalized zero-inflated models to the spatial setting. To capture the spatiotemporal heterogeneity in the data, we introduce region-level covariates, smooth temporal effects, and spatially correlated random effects to model both the excess zeros and the marginal mean. For estimation, we adopt a Bayesian approach that combines full-conditional Gibbs sampling and Metropolis-Hastings steps. We investigate features of the model and use the model to identify key predictors of COVID-19 deaths in the US state of Georgia during the 2021 calendar year.

Population-average mediation analysis for zero-inflated count outcomes

Mediation analysis is an increasingly popular statistical method for explaining causal pathways to inform intervention. While methods have increased, there is still a dearth of robust mediation methods for count outcomes with excess zeroes. Current mediation methods addressing this issue are computationally intensive, biased, or challenging to interpret. To overcome these limitations, we propose a new mediation methodology for zero-inflated count outcomes using the marginalized zero-inflated Poisson (MZIP) model and the counterfactual approach to mediation. This novel work gives population-average mediation effects whose variance can be estimated rapidly via delta method. This methodology is extended to cases with exposure-mediator interactions. We apply this novel methodology to explore if diabetes diagnosis can explain BMI differences in healthcare utilization and test model performance via simulations comparing the proposed MZIP method to existing zero-inflated and Poisson methods. We find that our proposed method minimizes bias and computation time compared to alternative approaches while allowing for straight-forward interpretations.

Predicting the multivariate zero-inflated counts: A novel model averaging method under Pearson loss

Excessive zeros in multivariate count data are often observed in scenarios of biomedicine and public health. To provide a better analysis on this type of data, we first develop a marginalized multivariate zero-inflated Poisson (MZIP) regression model to directly interpret the overall exposure effects on marginal means. Then, we define a multiple Pearson residual for our newly developed MZIP regression model by simultaneously taking heterogeneity and correlation into consideration. Furthermore, a new model averaging prediction method is introduced based on the multiple Pearson residual, and the asymptotical optimality of this model averaging prediction is proved. Simulations and two empirical applications in medicine are used to illustrate the effectiveness of the proposed method.

Is the 21st birthday a turning point for alcohol and cannabis use? A monthly study of young adults

BACKGROUND

An important life-course event with respect to alcohol and cannabis use is turning 21 years of age, which may be associated with increases in use of these substances due to celebrations during the month and easier access to them on and following this birthday. We examined the trajectories of alcohol and cannabis use behaviors in the months leading up to, during, and following the 21st birthday month. We also examined whether the use trajectories vary by college status and baseline levels of use.

METHODS

We used data from 203 young adults recruited from the Greater Seattle region who turned 21 during the course of the study. Surveys were administered each month for 24 consecutive months. Measures included the typical number of drinks per week for the past month, the frequency of heavy episodic drinking, the number of cannabis use days, and any simultaneous alcohol and cannabis use. Multilevel spline models were run that estimated linear slopes over time at four intervals: (1) up to 1 month before the 21st birthday month; (2) from 1 month before to the month of the 21st birthday; (3) from the 21st birthday month to 1 month following; and (4) from 1 month following the 21st birthday month through all following months.

RESULTS

Alcohol use, generally, and simultaneous alcohol and cannabis use showed sharp increases from the month before the 21st birthday month to the 21st birthday month and decreases following the 21st birthday month. For cannabis use, there were significant increases in the months leading up to the 21st birthday and no other significant changes during other time intervals. Patterns differed by baseline substance use and college status.

CONCLUSIONS

Findings from the current study have implications for the timing and personalization of prevention and intervention efforts. Event-specific 21st birthday interventions may benefit from incorporating content targeting specific hazardous drinking behaviors in the month prior to the 21st birthday.

A Bayesian zero-inflated beta-binomial model for longitudinal data with group-specific changepoints

Timeline followback (TLFB) is often used in addiction research to monitor recent substance use, such as the number of abstinent days in the past week. TLFB data usually take the form of binomial counts that exhibit overdispersion and zero inflation. Motivated by a 12-week randomized trial evaluating the efficacy of varenicline tartrate for smoking cessation among adolescents, we propose a Bayesian zero-inflated beta-binomial model for the analysis of longitudinal, bounded TLFB data. The model comprises a mixture of a point mass that accounts for zero inflation and a beta-binomial distribution for the number of days abstinent in the past week. Because treatment effects appear to level off during the study, we introduce random changepoints for each study group to reflect group-specific changes in treatment efficacy over time. The model also includes fixed and random effects that capture group- and subject-level slopes before and after the changepoints. Using the model, we can accurately estimate the mean trend for each study group, test whether the groups experience changepoints simultaneously, and identify critical windows of treatment efficacy. For posterior computation, we propose an efficient Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs and Metropolis-Hastings steps. Our application shows that the varenicline group has a short-term positive effect on abstinence that tapers off after week 9.

Application of marginalized zero-inflated models when mediators have excess zeroes

Mediation analysis has become increasingly popular over the last decade as researchers are interested in assessing mechanistic pathways for intervention. Although available methods have increased, there are still limited options for mediation analysis with zero-inflated count variables where the distribution of response has a "cluster" of data at the zero value (i.e. distribution of number of cigarettes smoked per day, where nonsmokers cluster at zero cigarettes). The currently available methods do not obtain unbiased population average effects of mediation effects. In this paper, we propose an extension of the counterfactual approach to mediation with direct and indirect effects to scenarios where the mediator is a count variable with excess zeroes by utilizing the Marginalized Zero-Inflated Poisson Model (MZIP) for the mediator model. We derive direct and indirect effects for continuous, binary, and count outcomes, as well as adapt to allow mediator-exposure interactions. Our proposed work allows straightforward calculation of direct and indirect effects for the overall population mean values of the mediator, for scenarios in which researchers are interested in generalizing direct and indirect effects to the population. We apply this novel methodology to an application observing how alcohol consumption may explain sex differences in cholesterol and assess model performance via a simulation study comparing the proposed MZIP mediator framework to existing methods for marginal mediator effects.

The selection of statistical models for reporting count outcomes and intervention effects in brief alcohol intervention trials: A review and recommendations

Understanding the efficacy and relative effectiveness of a brief alcohol intervention (BAI) relies on obtaining a credible intervention effect estimate. Outcomes in BAI trials are often count variables, such as the number of drinks consumed, which may be overdispersed (i.e., greater variability than expected based on a given model) and zero-inflated (i.e., greater probability of zeros than expected based on a given model). Ignoring such distribution characteristics can lead to biased estimates and invalid statistical conclusions. In this critical review, we identified and reviewed 64 articles that reported count outcomes from a systematic review of BAI trials for adolescents and young adults from 2013 to 2018. Given many statistical models to choose from when analyzing count outcomes, we reviewed the models used and reporting practices in the BAI trial literature. A majority (61.3%) of analyses with count outcomes used linear models despite violations of normality assumptions; 75.6% of outcome variables demonstrated clear overdispersion. We provide an overview of available count models (Poisson, negative binomial, zero-inflated or hurdle, and marginalized zero-inflated Poisson regression) and formulate practical guidelines for reporting outcomes of BAIs. We provide a visual step-by-step decision guide for selecting appropriate statistical models and reporting results for count outcomes. We list accessible resources to help researchers select an appropriate model with which to analyze their data. Recent advances in count distribution-based models hold promise for evaluating count outcomes to gauge the efficacy and effectiveness of BAIs and identify critical covariates in alcohol epidemiologic research. We recommend that researchers report the distributional properties of count outcomes, such as the proportion of zero counts, and select an appropriate statistical analysis for count outcomes using the provided decision tree. By following these recommendations, future research may yield more accurate, transparent, and reproducible results.

Brief Alcohol Interventions are Effective through 6 Months: Findings from Marginalized Zero-inflated Poisson and Negative Binomial Models in a Two-step IPD Meta-analysis

To evaluate and optimize brief alcohol interventions (BAIs), it is critical to have a credible overall effect size estimate as a benchmark. Estimating such an effect size has been challenging because alcohol outcomes often represent responses from a mixture of individuals: those at high risk for alcohol misuse, occasional nondrinkers, and abstainers. Moreover, some BAIs exclusively focus on heavy drinkers, whereas others take a universal prevention approach. Depending on sample characteristics, the outcome distribution might have many zeros or very few zeros and overdispersion; consequently, the most appropriate statistical model may differ across studies. We synthesized individual participant data (IPD) from 19 studies in Project INTEGRATE (Mun et al., 2015b) that randomly allocated participants to intervention and control groups (N = 7,704 participants, 38.4% men, 74.7% White, 58.5% first-year students). We sequentially estimated marginalized zero-inflated Poisson (Long et al., 2014) or negative binomial regression models to obtain covariate-adjusted, study-specific intervention effect estimates in the first step, which were subsequently combined in a random-effects meta-analysis model in the second step. BAIs produced a statistically significant 8% advantage in the mean number of drinks at both 1-3 months (RR = 0.92, 95% CI = [0.85, 0.98]) and 6 months (RR = 0.92, 95% CI = [0.85, 0.99]) compared to controls. At 9-12 months, there was no statistically significant difference in the mean number of drinks between BAIs and controls. In conclusion, BAIs are effective at reducing the mean number of drinks through at least 6 months post intervention. IPD can play a critical role in deriving findings that could not be obtained in original individual studies or standard aggregate data meta-analyses.

Association of Short-Term Co-Exposure to Particulate Matter and Ozone with Mortality Risk

A complex regional air pollution problem dominated by particulate matter (PM) and ozone (O3) needs drastic attention since the levels of O3 and PM are not decreasing in many parts of the world. Limited evidence is currently available regarding the association between co-exposure to PM and O3 and mortality. A multicounty time-series study was used to investigate the associations of short-term exposure to PM1, PM2.5, PM10, and O3 with daily mortality from different causes, which was based on data obtained from the Mortality Surveillance System managed by the Jiangsu Province Center for Disease Control and Prevention of China and analyzed via overdispersed generalized additive models with random-effects meta-analysis. We investigated the interactions of PM and O3 on daily mortality and calculated the mortality fractions attributable to PM and O3. Our results showed that PM1 is more strongly associated with daily mortality than PM2.5, PM10, and O3, and percent increases in daily all-cause nonaccidental, cardiovascular, and respiratory mortality were 1.37% (95% confidence interval (CI), 1.22-1.52%), 1.44% (95% CI, 1.25-1.63%), and 1.63% (95% CI, 1.25-2.01%), respectively, for a 10 μg/m3 increase in the 2 day average PM1 concentration. We found multiplicative and additive interactions of short-term co-exposure to PM and O3 on daily mortality. The risk of mortality was greatest among those with higher levels of exposure to both PM (especially PM1) and O3. Moreover, excess total and cardiovascular mortality due to PM1 exposure is highest in populations with higher O3 exposure levels. Our results highlight the importance of the collaborative governance of PM and O3, providing a scientific foundation for pertinent standards and regulatory interventions.

Palliative care for persons with late-stage Alzheimer's and related dementias and their caregivers: protocol for a randomized clinical trial

BACKGROUND

Limited access to specialized palliative care exposes persons with late-stage Alzheimer's disease and related dementias (ADRD) to burdensome treatment and unnecessary hospitalization and their caregivers to avoidable strain and financial burden. Addressing this unmet need, the purpose of this study was to conduct a randomized clinical trial (RCT) of the ADRD-Palliative Care (ADRD-PC) program.

METHODS

The study will use a multisite, RCT design and will be set in five geographically diverse US hospitals. Lead investigators and outcome assessors will be masked. The study will use 1:1 randomization of patient-caregiver dyads, and sites will enroll N = 424 dyads of hospitalized patients with late-stage ADRD with their family caregivers. Intervention dyads will receive the ADRD-PC program of (1) dementia-specific palliative care, (2) standardized caregiver education, and (3) transitional care. Control dyads will receive publicly available educational material on dementia caregiving. Outcomes will be measured at 30 days (interim) and 60 days post-discharge. The primary outcome will be 60-day hospital transfers, defined as visits to an emergency department or hospitalization ascertained from health record reviews and caregiver interviews (aim 1). Secondary patient-centered outcomes, ascertained from 30- and 60-day health record reviews and caregiver telephone interviews, will be symptom treatment, symptom control, use of community palliative care or hospice, and new nursing home transitions (aim 2). Secondary caregiver-centered outcomes will be communication about prognosis and goals of care, shared decision-making about hospitalization and other treatments, and caregiver distress (aim 3). Analyses will use intention-to-treat, and pre-specified exploratory analyses will examine the effects of sex as a biologic variable and the GDS stage.

DISCUSSION

The study results will determine the efficacy of an intervention that addresses the extraordinary public health impact of late-stage ADRD and suffering due to symptom distress, burdensome treatments, and caregiver strain. While many caregivers prioritize comfort in late-stage ADRD, shared decision-making is rare. Hospitalization creates an opportunity for dementia-specific palliative care, and the study findings will inform care redesign to advance comprehensive dementia-specific palliative care plus transitional care.

TRIAL REGISTRATION

ClinicalTrials.gov NCT04948866. Registered on July 2, 2021.

Subjective and objective indicators of neighbourhood safety and physical activity among UK adolescents

BACKGROUND

The health benefits of regular physical activity in adolescence are well-documented and many health-related behaviours are established in adolescence. The neighbourhood environment is a key setting for physical activity for adolescents and feeling unsafe in their neighbourhood may be a potential barrier to physical activity.

AIM

This study aimed to examine associations between neighbourhood safety and physical activity using objective and subjective measures for both.

METHODS

Participants (n = 10,913) came from the Millennium Cohort Study, a nationally representative UK longitudinal birth cohort. Linear regression and Zero Inflated Poisson models were used to examine associations between subjective and objective indicators of safety (self-reported safety, Index of Multiple Deprivation crime, Reported Crime Incidence) and physical activity (self-reported weekly and device-measured physical activity).

RESULTS

Adolescents who feel unsafe in their neighbourhood, or who live in areas with high IMD crime or violent crime rates report 0.29 (95% CI -0.49, -0.09) 0.32 (95% CI -0.47, -0.16) and 0.20 (95% CI -0.39, -0.20) fewer days of physical activity, respectively. No associations were found between Reported Crime Incidence and either objective or subjective measures of physical activity.

CONCLUSIONS

This study demonstrates varying associations between subjective safety and objective crime with physical activity levels in adolescence, highlighting the complexities around subjective and objective measurements and their associations with health outcomes.

Diabetes, gaps in care coordination, and preventable adverse events

OBJECTIVES

To compare the frequency of self-reported gaps in care coordination and self-reported preventable adverse events among adults with vs without diabetes.

STUDY DESIGN

Cross-sectional analysis of REasons for Geographic And Racial Differences in Stroke (REGARDS) study participants 65 years and older who completed a survey on health care experiences in 2017-2018 (N = 5634).

METHODS

We analyzed the association of diabetes with self-reported gaps in care coordination and with preventable adverse events. Gaps in care coordination were assessed using 8 validated questions. Four self-reported adverse events were studied (drug-drug interactions, repeat medical tests, emergency department visits, and hospitalizations). Respondents were asked if they thought these events could have been prevented with better communication among providers.

RESULTS

Overall, 1724 (30.6%) participants had diabetes. Among participants with and without diabetes, 39.3% and 40.7%, respectively, reported any gap in care coordination. The adjusted prevalence ratio (aPR) for any gap in care coordination for participants with vs without diabetes was 0.97 (95% CI, 0.89-1.06). Any preventable adverse event was reported by 12.9% and 8.7% of participants with and without diabetes, respectively. The aPR for any preventable adverse event for participants with vs without diabetes was 1.22 (95% CI, 1.00-1.49). Among participants with and without diabetes, the aPRs for any preventable adverse event associated with any gap in care coordination were 1.53 (95% CI, 1.15-2.04) and 1.50 (95% CI, 1.21-1.88), respectively (P comparing aPRs = .922).

CONCLUSIONS

Interventions to improve quality of care for patients with diabetes could incorporate patient-reported gaps in care coordination to aid in preventing adverse events.

Does abstaining from alcohol in high school moderate intervention effects for college students? Implications for tiered intervention strategies

Brief motivational intervention (BMI) and personalized feedback intervention (PFI) are individual-focused brief alcohol intervention approaches that have been proven efficacious for reducing alcohol use among college students and young adults. Although the efficacy of these two intervention approaches has been well established, little is known about the factors that may modify their effects on alcohol outcomes. In particular, high school drinking may be a risk factor for continued and heightened use of alcohol in college, and thus may influence the outcomes of BMI and PFI. The purpose of this study was to investigate whether high school drinking was associated with different intervention outcomes among students who received PFI compared to those who received BMI. We conducted moderation analyses examining 348 mandated students (60.1% male; 73.3% White; and 61.5% first-year student) who were randomly assigned to either a BMI or a PFI and whose alcohol consumption was assessed at 4-month and 15-month follow-ups. Results from marginalized zero-inflated Poisson models showed that high school drinking moderated the effects of PFI and BMI at the 4-month follow-up but not at the 15-month follow-up. Specifically, students who reported no drinking in their senior year of high school consumed a 49% higher mean number of drinks after receiving BMI than PFI at the 4-month follow-up. The results suggest that alcohol consumption in high school may be informative when screening and allocating students to appropriate alcohol interventions to meet their different needs.

Differential expression of single-cell RNA-seq data using Tweedie models

The performance of computational methods and software to identify differentially expressed features in single-cell RNA-sequencing (scRNA-seq) has been shown to be influenced by several factors, including the choice of the normalization method used and the choice of the experimental platform (or library preparation protocol) to profile gene expression in individual cells. Currently, it is up to the practitioner to choose the most appropriate differential expression (DE) method out of over 100 DE tools available to date, each relying on their own assumptions to model scRNA-seq expression features. To model the technological variability in cross-platform scRNA-seq data, here we propose to use Tweedie generalized linear models that can flexibly capture a large dynamic range of observed scRNA-seq expression profiles across experimental platforms induced by platform- and gene-specific statistical properties such as heavy tails, sparsity, and gene expression distributions. We also propose a zero-inflated Tweedie model that allows zero probability mass to exceed a traditional Tweedie distribution to model zero-inflated scRNA-seq data with excessive zero counts. Using both synthetic and published plate- and droplet-based scRNA-seq datasets, we perform a systematic benchmark evaluation of more than 10 representative DE methods and demonstrate that our method (Tweedieverse) outperforms the state-of-the-art DE approaches across experimental platforms in terms of statistical power and false discovery rate control. Our open-source software (R/Bioconductor package) is available at https://github.com/himelmallick/Tweedieverse.

Does dropout from school matter in taking antenatal care visits among women in Bangladesh? An application of marginalized poisson-poisson mixture model

Background

There exists a lack of research in explaining the link between dropout from school and antenatal care (ANC) visits of women during pregnancy in Bangladesh. The aim of this study is to investigate how the drop out from school influences the ANC visits after controlling the relevant covariates using an appropriate count regression model.

Methods

The association between the explanatory variables and the outcome of interest, ANC visits, have been performed using one-way analysis of variance/independent sample t-test. To examine the adjusted effects of covariates on the marginal mean of count data, Marginalized Poison-Poisson mixture regression model has been fitted.

Results

The estimated incidence rate of antenatal care visits was 10.6% lower for the mothers who were not continued their education after marriage but had at least 10 years of schooling (p-value <0.01) and 20.2% lower for the drop-outed mothers (p-value <0.01) than the mothers who got continued their education after marriage.

Conclusions

To ensure the WHO recommended 8+ ANC visits for the pregnant women of Bangladesh, it is essential to promote maternal education so that at least ten years of schooling should be completed by a woman and dropout from school after marriage should be prevented.

Frailty, gaps in care coordination, and preventable adverse events

Background

Older US adults often receive care from multiple ambulatory providers. Seeing multiple providers may be clinically appropriate but creates challenges for communication. Whether frailty is a risk factor for gaps in communication among older adults and subsequent preventable adverse events is unknown.

Methods

We conducted a cross-sectional analysis of community-dwelling US adults ≥ 65 years of age in the REasons for Geographic And Racial Differences in Stroke (REGARDS) study who attended an in-home study examination in 2013–2016 and completed a survey on experiences with healthcare in 2017–2018 (n = 5,024). Using 5 frailty indicators (low body mass index, exhaustion, slow walk, weakness, and history of falls), we characterized participants into 3 mutually exclusive groups: not frail (0 indicators), intermediate-frail (1–2 indicators), and frail (3–5 indicators). We used survey data on self-reported gaps in care coordination and self-reported adverse events that participants attributed to poor communication among providers (a drug-drug interaction, repeat testing, an emergency department visit, or a hospital admission).

Results

Overall, 2,398 (47.7%) participants were not frail, 2,436 (48.5%) were intermediate-frail, and 190 (3.8%) were frail. The prevalence of any gap in care coordination was 37.0%, 40.8%, and 51.1% among participants who were not frail, intermediate-frail and frail, respectively. The adjusted prevalence ratio (PR) for any gap in care coordination among intermediate-frail and frail versus not frail participants was 1.09 (95% confidence interval [95%CI] 1.02–1.18) and 1.34 (95%CI 1.15–1.56), respectively. The prevalence of any preventable adverse event was 7.0%, 11.3% and 20.0% among participants who were not frail, intermediate-frail and frail, respectively. The adjusted PR for any preventable adverse event among those who were intermediate-frail and frail versus not frail was 1.47 (95%CI 1.22–1.77) and 2.24 (95%CI 1.60–3.14), respectively.

Conclusion

Among older adults, frailty is associated with an increased prevalence for self-reported gaps in care coordination and preventable adverse events. Targeted interventions to address patient-reported concerns regarding care coordination among intermediate-frail and frail older adults may be warranted.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12877-022-03164-7.

Sample size calculation for cluster randomized trials with zero-inflated count outcomes

Cluster randomized trials (CRT) have been widely employed in medical and public health research. Many clinical count outcomes, such as the number of falls in nursing homes, exhibit excessive zero values. In the presence of zero inflation, traditional power analysis methods for count data based on Poisson or negative binomial distribution may be inadequate. In this study, we present a sample size method for CRTs with zero-inflated count outcomes. It is developed based on GEE regression directly modeling the marginal mean of a zero-inflated Poisson outcome, which avoids the challenge of testing two intervention effects under traditional modeling approaches. A closed-form sample size formula is derived which properly accounts for zero inflation, ICCs due to clustering, unbalanced randomization, and variability in cluster size. Robust approaches, including t-distribution-based approximation and Jackknife re-sampling variance estimator, are employed to enhance trial properties under small sample sizes. Extensive simulations are conducted to evaluate the performance of the proposed method. An application example is presented in a real clinical trial setting.

A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables

In this paper, we focus on the comparison of the bivariate zero-inflated Poisson inverse Gaussian regression (BZIPIGR) type II model in two cases: with and without exposure variables. The BZIPIGR type II model is applied to analyze the occurrence of maternal and early neonatal mortality in South Sulawesi Province, Indonesia using 2019 data, which contain many zero values and have the issue of overdispersion in the response variable. Furthermore, to analyze the number of deaths in various areas, the exposure variable is considered. The maximum likelihood estimation (MLE) is used in parameter estimation, which involves numerical iteration and application of the Berndt–Hall–Hall–Hausman (BHHH) algorithm. Sum square error (SSE) serves as the criterion of model selection when exposure variables are included. The existence of exposure variables strongly affects the model’s accuracy, especially using the BZIPIGR type II model. According to the SSE and RMSE values, the BZIPIGR type II model with exposure variables performs better than the model without exposure variables in estimating parameter values. All predictors with exposure variables in this study had a significant influence on the number of maternal and early neonatal mortalities.

A bias correction method in meta-analysis of randomized clinical trials with no adjustments for zero-inflated outcomes

Many clinical endpoint measures, such as the number of standard drinks consumed per week or the number of days that patients stayed in the hospital, are count data with excessive zeros. However, the zero‐inflated nature of such outcomes is sometimes ignored in analyses of clinical trials. This leads to biased estimates of study‐level intervention effect and, consequently, a biased estimate of the overall intervention effect in a meta‐analysis. The current study proposes a novel statistical approach, the Zero‐inflation Bias Correction (ZIBC) method, that can account for the bias introduced when using the Poisson regression model, despite a high rate of inflated zeros in the outcome distribution of a randomized clinical trial. This correction method only requires summary information from individual studies to correct intervention effect estimates as if they were appropriately estimated using the zero‐inflated Poisson regression model, thus it is attractive for meta‐analysis when individual participant‐level data are not available in some studies. Simulation studies and real data analyses showed that the ZIBC method performed well in correcting zero‐inflation bias in most situations.

Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods.

Modeling daily and weekly moderate and vigorous physical activity using zero-inflated mixture Poisson distribution

Recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities. Typically, physical movements are summarized as minutes in light, moderate, and vigorous physical activities in each wearing day. Because of preponderance of zeros, zero-inflated distributions have been used for modeling the daily moderate or higher levels of physical activity. Yet, these models do not fully account for variations in daily physical activity and cannot be extended to model weekly physical activity explicitly, while the weekly physical activity is considered as an indicator for a subject's average level of physical activity. To overcome these limitations, we propose to use a zero-inflated Poisson mixture distribution that can model daily and weekly physical activity in same family of mixture distributions. Under this method, the likelihood of an inactive day and the amount of exercise in an active day are simultaneously modeled by a joint random effects model to incorporate heterogeneity across participants. If needed, the method has the flexibility to include an additional random effect to address extra variations in daily physical activity. Maximum likelihood estimation can be obtained through Gaussian quadrature technique, which is implemented conveniently in an R package GLMMadaptive. Method performances are examined using simulation studies. The method is applied to data from the Hispanic Community Health Study/Study of Latinos to examine the relationship between physical activity and BMI groups and within a participant the difference in physical activity between weekends and weekdays.

Family Caregiver Skills Training to Improve Experiences of Care: a Randomized Clinical Trial

OBJECTIVE

To evaluate the effectiveness of Helping Invested Families Improve Veterans' Experiences Study (HI-FIVES), a skills training program for caregivers of persons with functional or cognitive impairments.

DESIGN

A two-arm RCT.

SETTING

Single Veterans Affairs Medical Center.

PARTICIPANTS

Patients and their primary caregivers referred in the past 6 months to home and community-based services or geriatrics clinic.

INTERVENTION

All caregivers received usual care. Caregivers in HI-FIVES also received five training calls and four group training sessions.

MAIN MEASURES

Cumulative patient days at home 12 months post-randomization, defined as days not in an emergency department, inpatient hospital, or post-acute facility. Secondary outcomes included patients' total VA health care costs, caregiver and patient rating of the patient's experience of VA health care, and caregiver depressive symptoms.

RESULTS

Of 241 dyads, caregivers' (patients') mean age was 61 (73) years, 54% (53%) Black and 89% (4%) female. HI-FIVES was associated with a not statistically significant 9% increase in the rate of days at home (95% CI 0.72, 1.65; mean difference 1 day over 12 months). No significant differences were observed in health care costs or caregiver depressive symptoms. Model-estimated mean baseline patient experience of VA care (scale of 0-10) was 8.43 (95% CI 8.16, 8.70); the modeled mean difference between HI-FIVES and controls at 3 months was 0.29 (p = .27), 0.31 (p = 0.26) at 6 months, and 0.48 (p = 0.03) at 12 months. For caregivers, it was 8.34 (95% CI 8.10, 8.57); the modeled mean difference at 3 months was 0.28 (p = .18), 0.53 (p < .01) at 6 months, and 0.46 (p = 0.054) at 12 months.

CONCLUSIONS

HI-FIVES did not increase patients' days at home; it showed sustained improvements in caregivers' and patients' experience of VA care at clinically significant levels, nearly 0.5 points. The training holds promise in increasing an important metric of care quality-reported experience with care.

Does Medicaid Coverage Modify the Relationship between Glycemic Status and Teeth Present in Older Adults?

Understanding the relationships among diabetes, teeth present, and dental insurance is essential to improving primary and oral health care. Participants were older adults who attended senior centers in northern Manhattan (New York, N.Y.). Sociodemographic, health, and health care information were obtained via intake interviews, number of teeth present via clinical dental examinations, and glycemic status via measurement of glycosylated hemoglobin (HbA1c). Complete data on dental insurance coverage status for 785 participants were available for analysis (1,015 after multiple imputation). For participants with no dental insurance and any private/other dental insurance, number of teeth present is less for participants with diabetes than for participants without diabetes; however, for participants with Medicaid coverage only, the relationship is reversed. Potential explanations include the limited range of dental services covered under the Medicaid program, inadequate diabetes screening and monitoring of Medicaid recipients, and the poor oral and general health of Medicaid recipients.

Overall Effects of Risk Factors Associated with Dental Caries Indices Using the Marginalized Zero-Inflated Negative Binomial Model

The purpose of this paper is to identify risk factors for decayed, missing, and filled permanent teeth (DMFT) in a population of 12-15-year-old schoolchildren and to apply the marginalized zero-inflated negative binomial (MZINB) model for determination and estimation of the overall effects of the risk factors. A cross-sectional survey comprising 764 students aged between 12 and 15 years was used to analyze the association between caries in children and some background characteristics in children and their parents. Information on the samples' social, behavioral, and demographic status was obtained through a series of closed questions. The incidence rate ratios (IRR) were used to associate some risk factors with caries. In the entire sample, the frequency of zero was 194 (25.4%). The result of the shared-parameter marginalized zero-inflated negative binomial (SP-MZINB) model showed that being a girl (IRR = 1.18; p value = 0.021), higher dental visits frequency (IRR = 1.20; p value <0.001), lower tooth brushing frequency (IRR = 0.91; p value = 0.019), higher flossing frequency (IRR = 1.11; p value = 0.001), and lower mothers' education (IRR = 0.89; p value = 0.042) are associated with DMFT. Our results may provide better insights of the factors associated with DMFT, and health programs should focus their efforts on healthcare services, for both preventive and curative purposes. This regression model provides an appropriate fit and meaningful interpretation to handling zero-inflated count outcomes. Also, it provides direct estimates of the effects of risk factors on the overall mean that does not require postmodeling computations.

A Randomized Trial of an Online Risk Reduction Intervention for Young Black MSM

HealthMpowerment.org (HMP), is a mobile optimized, online intervention to reduce sexual risk behaviors among HIV-positive and HIV-negative young Black men who have sex with men (BMSM) by providing information and resources, fostering social support, and including game-based elements. A randomized controlled trial with 474 young BMSM compared HMP to an information-only control website. The rate of self-reported condomless anal intercourse (CAI) at 3-months was 32% lower in the intervention group compared to the control group (IRR 0.68, 95% CI 0.43, 0.93), however this effect was not sustained at 12 months. Among HIV-positive participants, the rate of CAI at 3-month follow-up was 82% lower among participants with detectable viral loads in the intervention group compared to the control group (IRR 0.18, 95% CI 0.04, 0.32). In a secondary analysis, when we limited to those who used HMP for over 60 min during the 3-month intervention period (n = 50, 25.8%), we estimated 4.85 (95% CI 2.15, 7.53) fewer CAI events than we would have expected in control participants, had they used the intervention at the same rate as the intervention group. Findings suggest that exposure to an online intervention can reduce the rate of CAI among young BMSM, at least in the short term. Given the stronger effect seen among those participants who complied with HMP, additional intervention engagement strategies are warranted.

Comparison of carotid plaque burden among healthy middle-aged men living in the US, Japan, and South Korea

BACKGROUND

Carotid plaque has emerged as a marker of coronary heart disease (CHD) risk. Comparison of carotid plaque burden between different race/ethnic groups may provide a relative estimate of their future CHD risk.

METHODS

We conducted a population-based study among apparently healthy middle-aged men aged 40-49 years (ERA JUMP study (n = 924)) and recruited 310 Whites in Pittsburgh, US, 313 Japanese in Otsu, Japan, and 301 Koreans in Ansan, South Korea. The number of carotid plaque and CHD risk factors was assessed using a standardized protocol across all centers. The burden of carotid plaque was compared between race/ethnic groups after adjustment for age and BMI, and after multivariable adjustment for other CHD risk factors using marginalized zero-inflated Poisson regression models. Cross-sectional associations of risk factors with plaque were examined.

RESULTS

Whites (22.8%) had more than four-fold higher prevalence (p < 0.01) of carotid plaque than Japanese men (4.8%) while the prevalence among Koreans was 10.6%. These differences remained significant after adjustment for age, BMI as well as other risk factors - incidence density ratio (95% confidence interval) for plaque was 0.13 (0.07, 0.24) for Japanese and 0.32 (0.18, 0.58) for Koreans as compared to Whites. Age, hypertension and diabetes were the only risk factors significantly associated with presence of carotid plaque in the overall population.

CONCLUSION

Whites have significantly higher carotid plaque burden than men in Japan and Korea. Lower carotid plaque burden among Japanese and Koreans is independent of traditional CVD risk factors.

A semiparametric marginalized zero-inflated model for analyzing healthcare utilization panel data with missingness

Zero-inflated count outcomes arise quite often in research and practice. Parametric models such as the zero-inflated Poisson and zero-inflated negative binomial are widely used to model such responses. However, interpretations of those models focus on the at-risk subpopulation of a two-component population mixture and fail to provide direct inference about marginal effects for the overall population. Recently, new approaches have been proposed to facilitate such marginal inferences for count responses with excess zeros. However, they are likelihood based and impose strong assumptions on data distributions. In this paper, we propose a new distribution-free, or semiparametric, alternative to provide robust inference for marginal effects when population mixtures are defined by zero-inflated count outcomes. The proposed method also applies to longitudinal studies with missing data following the general missing at random mechanism. The proposed approach is illustrated with both simulated and real study data.

A Note on the Adaptive LASSO for Zero-Inflated Poisson Regression

We consider the problem of modelling count data with excess zeros using Zero-Inflated Poisson (ZIP) regression. Recently, various regularization methods have been developed for variable selection in ZIP models. Among these, EM LASSO is a popular method for simultaneous variable selection and parameter estimation. However, EM LASSO suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose a set of EM adaptive LASSO methods using a variety of data-adaptive weights. We show theoretically that the new methods are able to identify the true model consistently, and the resulting estimators can be as efficient as oracle. The methods are further evaluated through extensive synthetic experiments and applied to a German health care demand dataset.

Bayesian models for semicontinuous outcomes in rolling admission therapy groups

Alcohol and other drug abuse are frequently treated in a group therapy setting. If participants are allowed to enroll in therapy on a rolling basis, irregular patterns of participant overlap can induce complex correlations of participant outcomes. Previous work has accounted for common session attendance by modeling random effects for each therapy session, which map to participant outcomes via a multiple membership construction when modeling normally distributed outcome measures. We build on this earlier work by extending the models to semicontinuous outcomes, or outcomes that are a mixture of continuous and discrete distributions. This results in multivariate session effects, for which we allow temporal dependencies of various orders. We illustrate our methods using data from a group-based intervention to treat substance abuse and depression, focusing on the outcome of average number of drinks per day. Alcohol and other drug abuse are frequently treated in a group therapy setting. If 2 clients attend the some of the same sessions, we might expect that-on average-their posttreatment outcomes would be more similar than if they had not attended any sessions together. Hence, if participants are allowed to enroll in therapy on a rolling basis, irregular patterns of session attendance can induce complex relationships between participant outcomes. Statistical methods have been developed previously to account for rolling admission group therapy when the outcomes are normally distributed. In the case of alcohol and other drug use interventions, however, a substantial fraction of participants often report zero use after treatment. We extend previous work to build models that accommodate semicontinuous outcomes, which are a mixture of continuous and discrete distributions, for such situations. We find that modern Bayesian statistical methods and software allow users to efficiently estimate nonstandard models such as these. We illustrate our methods using data from a group-based intervention to treat substance abuse and depression, focusing on the outcome of average number of drinks per day. We find that the intervention is associated with a drop in the probability of any drinking, but find no evidence of a change in the amount of drinking, conditional on some drinking. (PsycINFO Database Record

A marginalized two-part Beta regression model for microbiome compositional data

In microbiome studies, an important goal is to detect differential abundance of microbes across clinical conditions and treatment options. However, the microbiome compositional data (quantified by relative abundance) are highly skewed, bounded in [0, 1), and often have many zeros. A two-part model is commonly used to separate zeros and positive values explicitly by two submodels: a logistic model for the probability of a specie being present in Part I, and a Beta regression model for the relative abundance conditional on the presence of the specie in Part II. However, the regression coefficients in Part II cannot provide a marginal (unconditional) interpretation of covariate effects on the microbial abundance, which is of great interest in many applications. In this paper, we propose a marginalized two-part Beta regression model which captures the zero-inflation and skewness of microbiome data and also allows investigators to examine covariate effects on the marginal (unconditional) mean. We demonstrate its practical performance using simulation studies and apply the model to a real metagenomic dataset on mouse skin microbiota. We find that under the proposed marginalized model, without loss in power, the likelihood ratio test performs better in controlling the type I error than those under conventional methods.

Group regularization for zero-inflated negative binomial regression models with an application to health care demand in Germany

In many biomedical applications, covariates are naturally grouped, with variables in the same group being systematically related or statistically correlated. Under such settings, variable selection must be conducted at both group and individual variable levels. Motivated by the widespread availability of zero-inflated count outcomes and grouped covariates in many practical applications, we consider group regularization for zero-inflated negative binomial regression models. Using a least squares approximation of the mixture likelihood and a variety of group-wise penalties on the coefficients, we propose a unified algorithm (Gooogle: Group Regularization for Zero-inflated Count Regression Models) to efficiently compute the entire regularization path of the estimators. We investigate the finite sample performance of these methods through extensive simulation experiments and the analysis of a German health care demand dataset. Finally, we derive theoretical properties of these methods under reasonable assumptions, which further provides deeper insight into the asymptotic behavior of these approaches. The open source software implementation of this method is publicly available at: https://github.com/himelmallick/Gooogle.

A Bayesian approach for analyzing zero-inflated clustered count data with dispersion

In practice, count data may exhibit varying dispersion patterns and excessive zero values; additionally, they may appear in groups or clusters sharing a common source of variation. We present a novel Bayesian approach for analyzing such data. To model these features, we combine the Conway-Maxwell-Poisson distribution, which allows both overdispersion and underdispersion, with a hurdle component for the zeros and random effects for clustering. We propose an efficient Markov chain Monte Carlo sampling scheme to obtain posterior inference from our model. Through simulation studies, we compare our hurdle Conway-Maxwell-Poisson model with a hurdle Poisson model to demonstrate the effectiveness of our Conway-Maxwell-Poisson approach. Furthermore, we apply our model to analyze an illustrative dataset containing information on the number and types of carious lesions on each tooth in a population of 9-year-olds from the Iowa Fluoride Study, which is an ongoing longitudinal study on a cohort of Iowa children that began in 1991.

Marginalized mixture models for count data from multiple source populations

Mixture distributions provide flexibility in modeling data collected from populations having unexplained heterogeneity. While interpretations of regression parameters from traditional finite mixture models are specific to unobserved subpopulations or latent classes, investigators are often interested in making inferences about the marginal mean of a count variable in the overall population. Recently, marginal mean regression modeling procedures for zero-inflated count outcomes have been introduced within the framework of maximum likelihood estimation of zero-inflated Poisson and negative binomial regression models. In this article, we propose marginalized mixture regression models based on two-component mixtures of non-degenerate count data distributions that provide directly interpretable estimates of exposure effects on the overall population mean of a count outcome. The models are examined using simulations and applied to two datasets, one from a double-blind dental caries incidence trial, and the other from a horticultural experiment. The finite sample performance of the proposed models are compared with each other and with marginalized zero-inflated count models, as well as ordinary Poisson and negative binomial regression.

Impact of Early Head Start in North Carolina on Dental Care Use Among Children Younger Than 3 Years

OBJECTIVES

To examine the effects of North Carolina Early Head Start (EHS), an early education program for low-income children younger than 3 years and their families, on dental care use among children.

METHODS

We performed a quasi-experimental study in which we interviewed 479 EHS and 699 non-EHS parent-child dyads at baseline (2010-2012) and at a 24-month follow-up (2012-2014). We estimated the effects of EHS participation on the probability of having a dental care visit after controlling for baseline dental care need and use and a propensity score covariate; we included random effects to account for EHS program clustering.

RESULTS

The odds of having a dental care visit of any type (adjusted odds ratio [OR] = 2.5; 95% confidence interval [CI] = 1.74, 3.48) and having a preventive dental visit (adjusted OR = 2.6; 95% CI = 1.84, 3.63) were higher among EHS children than among non-EHS children. In addition, the adjusted mean number of dental care visits among EHS children was 1.3 times (95% CI = 1.17, 1.55) the mean number among non-EHS children.

CONCLUSIONS

This study is the first, to our knowledge, to demonstrate that EHS participation increases dental care use among disadvantaged young children.

Matching the Statistical Model to the Research Question for Dental Caries Indices with Many Zero Counts

Marginalized zero-inflated count regression models have recently been introduced for the statistical analysis of dental caries indices and other zero-inflated count data as alternatives to traditional zero-inflated and hurdle models. Unlike the standard approaches, the marginalized models directly estimate overall exposure or treatment effects by relating covariates to the marginal mean count. This article discusses model interpretation and model class choice according to the research question being addressed in caries research. Two data sets, one consisting of fictional dmft counts in 2 groups and the other on DMFS among schoolchildren from a randomized clinical trial comparing 3 toothpaste formulations to prevent incident dental caries, are analyzed with negative binomial hurdle, zero-inflated negative binomial, and marginalized zero-inflated negative binomial models. In the first example, estimates of treatment effects vary according to the type of incidence rate ratio (IRR) estimated by the model. Estimates of IRRs in the analysis of the randomized clinical trial were similar despite their distinctive interpretations. The choice of statistical model class should match the study's purpose, while accounting for the broad decline in children's caries experience, such that dmft and DMFS indices more frequently generate zero counts. Marginalized (marginal mean) models for zero-inflated count data should be considered for direct assessment of exposure effects on the marginal mean dental caries count in the presence of high frequencies of zero counts.

Two-Part and Related Regression Models for Longitudinal Data

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has been particular interest in the use of these models for the analysis of repeated measures of an outcome variable over time. The aim of this review is to consider motivations for the use of such models in this context and to highlight the central issues that arise with their use. We examine two-part models for semicontinuous and zero-heavy count data, and we also consider models for count data with a two-part random effects distribution.