Review of Zero-Inflated Models with Missing Data

Abstract

Abstract:The literature of count regression models covers a large scope of studies and applications that implemented simple and standard models for count response variables by using Poisson regression models, binomial regression models, negative binomial regression models, geometric regression models, or generalized Poisson regression models. These regression models have received considerable attention in various situations. Nevertheless in many fields, the distribution of the count response variable may display a feature of excess zeros for which the aforementioned regression models may fail to provide an adequate fit. To remedy this handicap, a class of distributions known as zero-inflated models is considered as the most appropriate approach for dealing properly with this issue of excess zeros. In addition to the zero-inflated problem, it happens quite often that the sample data sets under investigation are not completely observed. This refers to the missing data problem. In this study, our primary interest is in reviewing studies that considered simultaneously the missing data problem and the zero-inflated feature in modeling zero-inflated data. Moreover, we discuss their methodologies and results and some potential directions of the future research.

Assessing general versus specific liability for externalizing problems in adolescence: Concurrent and prospective prediction of symptoms of conduct disorder, ADHD, and substance use.

“…This listwise exclusion approach was used in part because there is no consensus regarding the optimal handling of missing data in negative binomial regression (see description below; Lukusa et al, 2017). Importantly, the vast majority of excluded participants (>90%) were missing data for age.…”

Modeling the disruption of respiratory disease clinical trials by non-pharmaceutical COVID-19 interventions

“… Impact on trial feasibility Recommendation for the trialist Specific risk mitigation measures Weak (leading to disease burden change similar as year-to-year fluctuations) Assessment of clinical benefit is difficult with low number of events Reinforce and underline clinical significance of the demonstrated effect • Select population/endpoints where a smaller (absolute) effect on RTI prophylaxis is still clinically meaningful (characterized by small minimally important difference). One example is to focus on prophylaxis of viral infection induced wheezing or asthma exacerbations, see 70 , 71 , rather than upper RTI (mostly common cold) in the general population • Comprehensive reporting of rates, relative, and absolute benefit • Include secondary endpoints that add a diversified and multifaceted view to the clinical significance for assessors of the trial results (e.g., symptom-free days as RTI duration related endpoint) • Seek regulator’s feedback on the study protocol and statistical analysis plan with respect to clinical benefit assessment Medium (leading to substantially lower disease burden; magnitude of change with respect to average exceeds year-to-year fluctuations) Reduced post-hoc power with fixed sample size and less available patients that suffer from fixed minimum number of episodes Mitigate loss of power through sample size adjustment, adaptive trial design, and statistical analysis tailored to rare events • Multi-center trials with access to a larger patient pool can facilitate recruitment of larger sample sizes under difficult conditions • Use Model Informed Drug Development (MIDD) to leverage the totality of evidence for an optimal trial design and extrapolation 72 , 73 • Primary endpoint analysis based on event rate ratio (ERR) and accounting for excess zeros, e.g., zero-inflated negative binomial regression (ZINB) in frame of generalized linear models (GLM) 74 , 75 • Use trial monitoring and (Bayesian) adaptive trial design 76 especially sample size reestimation (increasing the sample size based on interim data analysis) 77 , group sequential designs 78 (trials can be stopped early once significant results are obtained, or the trial can be stopped for futility) • Seek regulator’s feedback on any modeling and simulation methods applied (e.g., FDA’s MIDD pilot program) 79 , for complex innovative trial design and the statistical analysis (e.g., FDA’s complex innovative trial design pilot program 80 ) Strong = lockdown (leading to attenuation of seasonal epidemic) High risk of insufficient sample size and severe recruitment issues Change the development plan • Change development timeline • Conduct observational study to assess the effect of NPI, see e.g., ref. …”

“…• Primary endpoint analysis based on event rate ratio (ERR) and accounting for excess zeros, e.g., zero-inflated negative binomial regression (ZINB) in frame of generalized linear models (GLM) 74 , 75…”

What’s the Harm in Getting High? Evaluating Associations Between Marijuana and Harm as Predictors of Concurrent and Prospective Marijuana Use and Misuse

“…By giving more weight to observations that were less likely to be nonmissing (i.e., more likely to be missing) and less weight to observations that were more likely to be nonmissing (i.e., less likely to be missing), model results in the weighted sample should be unbiased assuming data were missing at random. Currently, little is understood about the best approaches for dealing with missing zero-inflated data (Lukusa et al, 2017). We selected this IPCW approach over other common forms of missing data procedures such as multiple imputation because of challenges with imputing zero-inflated outcomes using available statistical software and multilevel modeling because interpretation is not straightforward for the count portion of the model over time among the time-varying nonstructural zeros.…”