EM for regularized zero-inflated regression models with applications to postoperative morbidity after cardiac surgery in children

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.

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.

Investigating factors associated with the number of rehospitalizations among patients with schizophrenia disorder using penalized count regression models

Background

Schizophrenia is a chronic, severe, and debilitating mental disorder always considered one of the recurrent psychiatric diseases. This study aimed to use penalized count regression models to determine factors associated with the number of rehospitalizations of schizophrenia disorder.

Methods

This retrospective cohort study was performed on 413 schizophrenic patients who had been referred to the Sina (Farshchian) Educational and Medical Center in Hamadan, Iran, between March 2011 and March 2019. The penalized count regression models were fitted using R.3.5.2.

Results

About 73% of the patients were male. The mean (SD) of age and the number of rehospitalizations were 36.16 (11.18) years and 1.21 (2.18), respectively. According to the results, longer duration of illness (P < 0.001), having a positive family history of psychiatric illness (P = 0.017), having at least three children (P = 0.013), unemployment, disability, and retirement (P = 0.025), residence in other Hamadan province townships (P = 0.003) and having a history of arrest/prison (P = 0.022) were significantly associated with an increase in the number of rehospitalizations.

Conclusion

To reduce the number of rehospitalizations among schizophrenic patients, it is recommended to provide special medical services for patients who do not have access to specialized medical centers and to create the necessary infrastructure for the employment of patients.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01648-z.

Model-based identification of conditionally-essential genes from transposon-insertion sequencing data

The understanding of bacterial gene function has been greatly enhanced by recent advancements in the deep sequencing of microbial genomes. Transposon insertion sequencing methods combines next-generation sequencing techniques with transposon mutagenesis for the exploration of the essentiality of genes under different environmental conditions. We propose a model-based method that uses regularized negative binomial regression to estimate the change in transposon insertions attributable to gene-environment changes in this genetic interaction study without transformations or uniform normalization. An empirical Bayes model for estimating the local false discovery rate combines unique and total count information to test for genes that show a statistically significant change in transposon counts. When applied to RB-TnSeq (randomized barcode transposon sequencing) and Tn-seq (transposon sequencing) libraries made in strains of Caulobacter crescentus using both total and unique count data the model was able to identify a set of conditionally beneficial or conditionally detrimental genes for each target condition that shed light on their functions and roles during various stress conditions.

Variable selection for longitudinal zero-inflated power series transition model

In modeling many longitudinal count clinical studies, the excess of zeros is a common problem. To take into account the extra zeros, the zero-inflated power series (ZIPS) models have been applied. These models assume a latent mixture model consisting of a count component and a degenerated zero component that has a unit point mass at zero. Usually, the current response measurement in a longitudinal sequence is a function of previous outcomes. For example, in a study about acute renal allograft rejection, the number of acute rejection episodes for a patient in current time is a function of this outcome at previous follow-up times. In this paper, we consider a transition model for accounting the dependence of current outcome on the previous outcomes in the presence of excess zeros. New variable selection methods for the ZIPS transition model using least absolute shrinkage and selection operator (LASSO), minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) penalties are proposed. An expectation-maximization (EM) algorithm using the penalized likelihood is applied for both parameters estimations and conducting variable selection. Some simulation studies are performed to investigate the performance of the proposed approach and the approach is applied to analyze a real dataset.

A unified atlas of CD8 T cell dysfunctional states in cancer and infection

CD8 T cells play an essential role in defense against viral and bacterial infections and in tumor immunity. Deciphering T cell loss of functionality is complicated by the conspicuous heterogeneity of CD8 T cell states described across experimental and clinical settings. By carrying out a unified analysis of over 300 assay for transposase-accessible chromatin sequencing (ATAC-seq) and RNA sequencing (RNA-seq) experiments from 12 studies of CD8 T cells in cancer and infection, we defined a shared differentiation trajectory toward dysfunction and its underlying transcriptional drivers and revealed a universal early bifurcation of functional and dysfunctional T cell states across models. Experimental dissection of acute and chronic viral infection using single-cell ATAC (scATAC)-seq and allele-specific single-cell RNA (scRNA)-seq identified state-specific drivers and captured the emergence of similar TCF1+ progenitor-like populations at an early branch point, at which functional and dysfunctional T cells diverge. Our atlas of CD8 T cell states will facilitate mechanistic studies of T cell immunity and translational efforts.

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.

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.

Network analysis for count data with excess zeros

BACKGROUND

Undirected graphical models or Markov random fields have been a popular class of models for representing conditional dependence relationships between nodes. In particular, Markov networks help us to understand complex interactions between genes in biological processes of a cell. Local Poisson models seem to be promising in modeling positive as well as negative dependencies for count data. Furthermore, when zero counts are more frequent than are expected, excess zeros should be considered in the model.

METHODS

We present a penalized Poisson graphical model for zero inflated count data and derive an expectation-maximization (EM) algorithm built on coordinate descent. Our method is shown to be effective through simulated and real data analysis.

RESULTS

Results from the simulated data indicate that our method outperforms the local Poisson graphical model in the presence of excess zeros. In an application to a RNA sequencing data, we also investigate the gender effect by comparing the estimated networks according to different genders. Our method may help us in identifying biological pathways linked to sex hormone regulation and thus understanding underlying mechanisms of the gender differences.

CONCLUSIONS

We have presented a penalized version of zero inflated spatial Poisson regression and derive an efficient EM algorithm built on coordinate descent. We discuss possible improvements of our method as well as potential research directions associated with our findings from the RNA sequencing data.

Stochastic variable selection strategies for zero-inflated models

When count data exhibit excess zero, that is more zero counts than a simpler parametric distribution can model, the zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) models are often used. Variable selection for these models is even more challenging than for other regression situations because the availability of p covariates implies 4 p possible models. We adapt to zero-inflated models an approach for variable selection that avoids the screening of all possible models. This approach is based on a stochastic search through the space of all possible models, which generates a chain of interesting models. As an additional novelty, we propose three ways of extracting information from this rich chain and we compare them in two simulation studies, where we also contrast our approach with regularization (penalized) techniques available in the literature. The analysis of a typical dataset that has motivated our research is also presented, before concluding with some recommendations.

Early detection of acute kidney injury after pediatric cardiac surgery

Acute kidney injury (AKI) is increasingly recognized as a common problem in children undergoing cardiac surgery, with well documented increases in morbidity and mortality in both the short and the long term. Traditional approaches to the identification of AKI such as changes in serum creatinine have revealed a large incidence in this population with significant negative impact on clinical outcomes. However, the traditional diagnostic approaches to AKI diagnosis have inherent limitations that may lead to under-diagnosis of this pathologic process. There is a dearth of randomized controlled trials for the prevention and treatment of AKI associated with cardiac surgery, at least in part due to the paucity of early predictive biomarkers. Novel non-invasive biomarkers have ushered in a new era that allows for earlier detection of AKI. With these new diagnostic tools, a more consistent approach can be employed across centers that may facilitate a more accurate representation of the actual prevalence of AKI and more importantly, clinical investigation that may minimize the occurrence of AKI following pediatric cardiac surgery. A thoughtful management approach is necessary to mitigate the effects of AKI after cardiac surgery, which is best accomplished in close collaboration with pediatric nephrologists. Long-term surveillance for improvement in kidney function and potential development of chronic kidney disease should also be a part of the comprehensive management strategy.

EM Adaptive LASSO-A Multilocus Modeling Strategy for Detecting SNPs Associated with Zero-inflated Count Phenotypes

Count data are increasingly ubiquitous in genetic association studies, where it is possible to observe excess zero counts as compared to what is expected based on standard assumptions. For instance, in rheumatology, data are usually collected in multiple joints within a person or multiple sub-regions of a joint, and it is not uncommon that the phenotypes contain enormous number of zeroes due to the presence of excessive zero counts in majority of patients. Most existing statistical methods assume that the count phenotypes follow one of these four distributions with appropriate dispersion-handling mechanisms: Poisson, Zero-inflated Poisson (ZIP), Negative Binomial, and Zero-inflated Negative Binomial (ZINB). However, little is known about their implications in genetic association studies. Also, there is a relative paucity of literature on their usefulness with respect to model misspecification and variable selection. In this article, we have investigated the performance of several state-of-the-art approaches for handling zero-inflated count data along with a novel penalized regression approach with an adaptive LASSO penalty, by simulating data under a variety of disease models and linkage disequilibrium patterns. By taking into account data-adaptive weights in the estimation procedure, the proposed method provides greater flexibility in multi-SNP modeling of zero-inflated count phenotypes. A fast coordinate descent algorithm nested within an EM (expectation-maximization) algorithm is implemented for estimating the model parameters and conducting variable selection simultaneously. Results show that the proposed method has optimal performance in the presence of multicollinearity, as measured by both prediction accuracy and empirical power, which is especially apparent as the sample size increases. Moreover, the Type I error rates become more or less uncontrollable for the competing methods when a model is misspecified, a phenomenon routinely encountered in practice.

Variable selection for zero-inflated and overdispersed data with application to health care demand in Germany

In health services and outcome research, count outcomes are frequently encountered and often have a large proportion of zeros. The zero-inflated negative binomial (ZINB) regression model has important applications for this type of data. With many possible candidate risk factors, this paper proposes new variable selection methods for the ZINB model. We consider maximum likelihood function plus a penalty including the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and minimax concave penalty (MCP). An EM (expectation-maximization) algorithm is proposed for estimating the model parameters and conducting variable selection simultaneously. This algorithm consists of estimating penalized weighted negative binomial models and penalized logistic models via the coordinated descent algorithm. Furthermore, statistical properties including the standard error formulae are provided. A simulation study shows that the new algorithm not only has more accurate or at least comparable estimation, but also is more robust than the traditional stepwise variable selection. The proposed methods are applied to analyze the health care demand in Germany using the open-source R package mpath.