Application of longitudinal multilevel zero inflated Poisson regression in modeling of infectious diseases among infants in Ethiopia.

BACKGROUND: In sub-Saharan African countries, preventable and manageable diseases such as diarrhea and acute respiratory infections still claim the lives of children. Hence, this study aims to estimate the rate of change in the log expected number of days a child suffers from Diarrhea (NOD) and flu/common cold (NOF) among children aged 6 to 11 months at the baseline of the study. METHODOLOGY: This study used secondary data which exhibit a longitudinal and multilevel structure. Based on the results of exploratory analysis, a multilevel zero-inflated Poisson regression model with a rate of change in the log expected NOD and NOF described by a quadratic trend was proposed to efficiently analyze both outcomes accounting for correlation between observations and individuals through random effects. Furthermore, residual plots were used to assess the goodness of fit of the model. RESULTS: Considering subject and cluster-specific random effects, the results revealed a quadratic trend in the rate of change of the log expected NOD. Initially, low dose iron Micronutrient Powder (MNP) users exhibited a higher rate of change compared to non-users, but this trend reversed over time. Similarly, the log expected NOF decreased for children who used MNP and exclusively breastfed for six months, in comparison to their counterparts. In addition, the odds of not having flu decreased with each two-week increment for MNP users, as compared to non-MNP users. Furthermore, an increase in NOD resulted in an increase in the log expected NOF. Region and exclusive breastfeeding also have a significant relationships with both NOD and NOF. CONCLUSION: The findings of this study underscore the importance of commencing analysis of data generated from a study with exploratory analysis. The study highlights the critical role of promoting EBF for the first six months and supporting children with additional food after six months to reduce the burden of infectious diseases.

Large-scale data decipher children's scale errors: A meta-analytic approach using the zero-inflated Poisson models.

Scale errors are intriguing phenomena in which a child tries to perform an object-specific action on a tiny object. Several viewpoints explaining the developmental mechanisms underlying scale errors exist; however, there is no unified account of how different factors interact and affect scale errors, and the statistical approaches used in the previous research do not adequately capture the structure of the data. By conducting a secondary analysis of aggregated datasets across nine different studies (n = 528) and using more appropriate statistical methods, this study provides a more accurate description of the development of scale errors. We implemented the zero-inflated Poisson (ZIP) regression that could directly handle the count data with a stack of zero observations and regarded developmental indices as continuous variables. The results suggested that the developmental trend of scale errors was well documented by an inverted U-shaped curve rather than a simple linear function, although nonlinearity captured different aspects of the scale errors between the laboratory and classroom data. We also found that repeated experiences with scale error tasks reduced the number of scale errors, whereas girls made more scale errors than boys. Furthermore, a model comparison approach revealed that predicate vocabulary size (e.g., adjectives or verbs), predicted developmental changes in scale errors better than noun vocabulary size, particularly in terms of the presence or absence of scale errors. The application of the ZIP model enables researchers to discern how different factors affect scale error production, thereby providing new insights into demystifying the mechanisms underlying these phenomena. A video abstract of this article can be viewed at https://youtu.be/1v1U6CjDZ1Q RESEARCH HIGHLIGHTS: We fit a large dataset by aggregating the existing scale error data to the zero-inflated Poisson (ZIP) model. Scale errors peaked along the different developmental indices, but the underlying statistical structure differed between the in-lab and classroom datasets. Repeated experiences with scale error tasks and the children's gender affected the number of scale errors produced per session. Predicate vocabulary size (e.g., adjectives or verbs) better predicts developmental changes in scale errors than noun vocabulary size.

Quantifying the risk of mass shootings at specific locations.

Mass shootings are horrific events that annually take scores of innocent lives in the United States. Federal, state, and local governments as well as educational, religious, and private-sector organizations propose and enact polices and strategies to protect people from and during active shooter situations. A probabilistic risk assessment of a mass shooting for a specific organization, jurisdiction, or location can be the first step toward evaluating the effectiveness of risk mitigation strategies and determining which strategies might be most appropriate for a location. This article proposes a novel hierarchical method to assess the probability of a mass shooting at specific locations based on available historical data. First, the method generates a probability distribution over the annual number of mass shootings in the United States. Second, the article uses this national number of mass shootings to determine the risk for each state. Third, the state risk assessment is decomposed to calculate the probability of a mass shooting in a specific location such as a school. Multiple ways to assess the risk are presented, leading to slightly different probability assessments for a location. Results indicate that annual probability of a mass shooting in the largest high school in California is on the order of 10 - 6 - 10 - 5 $10^{-6}-10^{-5}$ , and the annual probability of a mass shooting in the largest high school in Iowa is about half as likely as in the California school.

Zero-inflated Poisson models with measurement error in the response.

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.

Two-sample test with g-modeling and its applications.

Many real data analyses involve two-sample comparisons in location or in distribution. Most existing methods focus on problems where observations are independently and identically distributed in each group. However, in some applications the observed data are not identically distributed but associated with some unobserved parameters which are identically distributed. To address this challenge, we propose a novel two-sample testing procedure as a combination of the g $$ g $$ -modeling density estimation introduced by Efron and the two-sample Kolmogorov-Smirnov test. We also propose efficient bootstrap algorithms to estimate the statistical significance for such tests. We demonstrate the utility of the proposed approach with two biostatistical applications: the analysis of surgical nodes data with binomial model and differential expression analysis of single-cell RNA sequencing data with zero-inflated Poisson model.

Evaluating the performance of different Bayesian count models in modelling childhood vaccine uptake among children aged 12-23 months in Nigeria.

BACKGROUND: Choosing appropriate models for count health outcomes remains a challenge to public health researchers and the validity of the findings thereof. For count data, the mean-variance relationship and proportion of zeros is a major determinant of model choice. This study aims to compare and identify the best Bayesian count modelling technique for the number of childhood vaccine uptake in Nigeria. METHODS: We explored the performances of Poisson, negative binomial and their zero-inflated forms in the Bayesian framework using cross-sectional data pooled from the Nigeria Demographic and Health Survey conducted between 2003 and 2018. In multivariable analysis, these Bayesian models were used to identify factors associated with the number of vaccine uptake among children. Model selection was based on the -2 Log-Likelihood (-2 Log LL), Leave-One-Out Cross-Validation Information Criterion (LOOIC) and Watanabe-Akaike/Widely Applicable Information Criterion (WAIC). RESULTS: Exploratory analysis showed the presence of excess zeros and overdispersion with a mean of 4.36 and a variance of 12.86. Observably, there was a significant increase in vaccine uptake over time. Significant factors included the mother's age, level of education, religion, occupation, desire for last-child, place of delivery, exposure to media, birth order of the child, wealth status, number of antenatal care visits, postnatal attendance, healthcare decision maker, community poverty, community illiteracy, community unemployment, rural proportion and number of health facilities per 100,000. The zero-inflated negative binomial model was best fit with -2Log LL of -27171.47, LOOIC of 54464.2, and WAIC of 54588.0. CONCLUSION: The Bayesian zero-inflated negative binomial model was most appropriate to identify factors associated with the number of childhood vaccines received in Nigeria due to the presence of excess zeros and overdispersion. Improving vaccine uptake by addressing the associated risk factors should be promptly embraced.

Spatio-temporal analysis of childhood vaccine uptake in Nigeria: a hierarchical Bayesian Zero-inflated Poisson approach.

BACKGROUND: Globally, child mortality and morbidity remain a serious health challenge and infectious diseases are the leading causes. The use of count models together with spatial analysis of the number of doses of childhood vaccines taken is limited in the literature. We used a Bayesian zero-inflated Poisson regression model with spatio-temporal components to assess the number of doses of childhood vaccines taken among children aged 12-23 months and their associated factors. METHODS: Data of 19,564 children from 2003, 2008, 2013 and 2018 population-based cross-sectional Nigeria Demographic and Health Survey were used. The childhood vaccines include one dose of Bacillus-Calmette-Guérin; three doses of Diphtheria-Pertussis-Tetanus; three doses of Polio and one dose of Measles. Uptake of all nine vaccines was regarded as full vaccination. We examined the multilevel factors associated with the number of doses of childhood vaccines taken using descriptive, bivariable and multivariable Bayesian models. Analysis was conducted in Stata version 16 and R statistical packages, and visualization in ArcGIS. RESULTS: The prevalence of full vaccination was 6.5% in 2003, 14.8% in 2008, 21.8% in 2013 and 23.3% in 2018. Full vaccination coverage ranged from 1.7% in Sokoto to 51.9% in Anambra. Factors associated with the number of doses of childhood vaccines taken include maternal age (adjusted Incidence "risk" Ratio (aIRR) = 1.05; 95% Credible Interval (CrI) = 1.03-1.07) for 25-34 years and (aIRR = 1.07; 95% CrI = 1.05-1.10) for 35-49 years and education: (aIRR = 1.11, 95% CrI = 1.09-1.14) for primary and (aIRR = 1.16; 95% CrI = 1.13-1.19) for secondary/tertiary education. Other significant factors are wealth status, antenatal care attendance, working status, use of skilled birth attendants, religion, mother's desire for the child, community poverty rate, community illiteracy, and community unemployment. CONCLUSION: Although full vaccination has remained low, there have been improvements over the years with wide disparities across the states. Improving the uptake of vaccines by educating women on the benefits of hospital delivery and vaccines through radio jingles and posters should be embraced, and state-specific efforts should be made to address inequality in access to routine vaccination in Nigeria.

On the use of the likelihood ratio test methodology in pharmacovigilance.

The safety of medical products due to adverse events (AE) from drugs, therapeutic biologics, and medical devices is a major public health concern worldwide. Likelihood ratio test (LRT) approaches to pharmacovigilance constitute a class of rigorous statistical tools that permit objective identification of AEs of a specific drug and/or a class of drugs cataloged in spontaneous reporting system databases. However, the existing LRT approaches encounter certain theoretical and computational challenges when an underlying Poisson model assumption is violated, including in cases of zero-inflated data. We briefly review existing LRT approaches and propose a novel class of (pseudo-) LRT methods to address these challenges. Our approach uses an alternative parametrization to formulate a unified framework with a common test statistic that can handle both Poisson and zero-inflated Poisson (ZIP) models. The proposed framework is computationally efficient, and it reveals deeper insights into the comparative behaviors of the Poisson and the ZIP models for handling AE data. Our extensive simulation studies document notably superior performances of the proposed methods over existing approaches particularly under zero-inflation, both in terms of statistical (eg, much better control of the nominal level and false discovery rate with substantially enhanced power) and computational ( ∼ $$ \sim $$ 100-500-fold gains in average running times) performance metrics. An application of our method on the statin drug class from the FDA FAERS database reveals interesting insights on potential AEs. An R package, pvLRT, implementing our methods has been released in the public domain.

A comparison of statistical methods for modeling count data with an application to hospital length of stay.

BACKGROUND: Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. Hospital LOS is often used as a measure of a post-medical procedure outcome, as a guide to the benefit of a treatment of interest, or as an important risk factor for adverse events. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS data can be treated as count data, with discrete and non-negative values, typically right skewed, and often exhibiting excessive zeros. In this study, we compared the performance of the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) regression models using simulated and empirical data. METHODS: Data were generated under different simulation scenarios with varying sample sizes, proportions of zeros, and levels of overdispersion. Analysis of hospital LOS was conducted using empirical data from the Medical Information Mart for Intensive Care database. RESULTS: Results showed that Poisson and ZIP models performed poorly in overdispersed data. ZIP outperformed the rest of the regression models when the overdispersion is due to zero-inflation only. NB and ZINB regression models faced substantial convergence issues when incorrectly used to model equidispersed data. NB model provided the best fit in overdispersed data and outperformed the ZINB model in many simulation scenarios with combinations of zero-inflation and overdispersion, regardless of the sample size. In the empirical data analysis, we demonstrated that fitting incorrect models to overdispersed data leaded to incorrect regression coefficients estimates and overstated significance of some of the predictors. CONCLUSIONS: Based on this study, we recommend to the researchers that they consider the ZIP models for count data with zero-inflation only and NB models for overdispersed data or data with combinations of zero-inflation and overdispersion. If the researcher believes there are two different data generating mechanisms producing zeros, then the ZINB regression model may provide greater flexibility when modeling the zero-inflation and overdispersion.

Investigating the short and long-term effects of "nutritional-score" pricing on food pantry selections.

Approximately one out of ten households in the U.S. experienced food insecurity in 2019 (U. S. Department of Agriculture, 2020). Food pantries have taken on an important role in helping those with both short term and persistent food insecurity. As pantries are increasingly being arranged to allow clients to choose their own food, the question of how to encourage healthy choices is becoming an important topic for discussion. The Des Moines Area Religious Council (DMARC) implemented a "Nutritional-Score" program on September 1, 2017 as an experiment aimed at answering the above question. This program essentially changes the budgets of food pantry clients to make healthier choices cheaper and less healthy choices more expensive. We perform a Bayesian analysis using a zero-inflated Poisson (ZIP) model to help describe the effects of this program on the frequency with which clients choose less healthy items. We find evidence that the Nutritional-score program had a positive effect on the probability of rejecting less healthy items in the short and long term.

Number of antenatal care utilization and associated factors among pregnant women in Ethiopia: zero-inflated Poisson regression of 2019 intermediate Ethiopian Demography Health Survey.

BACKGROUND: The frequency of antenatal care utilization enhances the effectiveness of the maternal health programs to maternal and child health. The aim of the study was to determine the number of antenatal care and associated factors in Ethiopia by using 2019 intermediate EDHS. METHODS: Secondary data analysis was done on 2019 intermediate EDHS. A total of 3916.6 weighted pregnant women were included in the analysis. Zero-inflated Poisson regression analysis was done by Stata version 14.0. Incident rate ratio and odds ratio with a 95% confidence interval were used to show the strength and direction of the association. RESULT: About one thousand six hundred eighty eight (43.11%) women were attending four and more antenatal care during current pregnancy. Attending primary education (IRR = 1.115, 95% CI: 1.061, 1.172), secondary education (IRR = 1.211, 95% CI: 1.131, 1.297) and higher education (IRR = 1.274, 95% CI: 1.177, 1.378), reside in poorer household wealth index (IRR = 1.074, 95% CI: 1.01, 1.152), middle household wealth index (IRR = 1.095, 95% CI: 1.018, 1.178), rich household wealth index (IRR = 1.129, 95% CI: 1.05, 1.212) and richer household wealth index (IRR = 1.186, 95% CI: 1.089, 1.29) increases the number of antenatal care utilization. The frequency of antenatal care was less likely become zero among women attending primary (AOR = 0.434, 95% CI: 0.346, 0.545), secondary (AOR = 0.113, 95% CI: 0.053, 0.24), higher educational level (AOR = 0.052, 95% CI: 0.007, 0.367) in the inflated part. CONCLUSION: The number of antenatal care utilization is low in Ethiopia. Being rural, poorest household index, uneducated and single were factors associated with low number of antenatal care and not attending antenatal care at all. Improving educational coverage and wealth status of women is important to increase the coverage and frequency of antenatal care.

Antenatal care is among the most effective interventions to mitigate maternal mortality and morbidity. It is an entry point for delivery care, postnatal care and child immunization. This study was conducted to determine the frequency and associated factors of antenatal care utilization in Ethiopia by using 2019 intermediate Ethiopian Demography Health Survey.A cross-sectional study design using secondary data from 2019 intermediate Ethiopian demography and health survey was conducted. 3917 weighted women were included in the study. Recoding, variable generation, labeling and analysis were done by using STATA/SE version 14.0.The objective of this study was to identify the determinants of frequency of antenatal care visit in Ethiopia by using zero inflated Poisson regression.In this study 74.38% of women attend antenatal care at least once during their current pregnancy. Only 41.8% of women use WHO recommended number of antenatal care.Conclusion: maternal age, residence, educational status, household wealth index, religion and region show significant association with the frequency of antenatal care utilization. Advocacy and behavioral change communication should be area of concern for different organizations that are working on antenatal care especially for rural, poor and uneducated women through mass campaign, community dialoging and enhance the effectiveness of health extension programs.

Robust inference in the joint modeling of multilevel zero-inflated Poisson and Cox models.

A popular method for simultaneously modeling of correlated count response with excess zeros and time to event is by means of the joint models. In these models, the likelihood-based methods (such as expectation-maximization algorithm and Newton-Raphson) are used for estimating the parameters, but in the presence of contaminations, these methods are unstable. To overcome this challenge, we extend the M-estimator methods and propose a robust estimator approach to obtain a robust estimation of the regression parameters in the joint model. Our proposed algorithm has two steps (Expectation and Solution). In the expectation step, the likelihood function is expected by conditioning on the observed data and in the solution step, the parameters are computed, with solving robust estimating equations. Therefore, this algorithm achieves robustness by applying robust estimating equations and weighted likelihood in the S-step. Simulation studies under various situations of contaminations show that the robust algorithm gives us consistent estimates with a smaller bias than likelihood-based methods. The application section uses data on factors affecting fertility and birth spacing.

Risk-adjusted zero-inflated Poisson CUSUM charts for monitoring influenza surveillance data.

BACKGROUND: The influenza surveillance has been received much attention in public health area. For the cases with excessive zeroes, the zero-inflated Poisson process is widely used. However, the traditional control charts based on zero-inflated Poisson model, ignore the association between influenza cases and risk factors, and thus may lead to unexpected mistakes when implementing monitoring charts. METHOD: In this paper, we proposed risk-adjusted zero-inflated Poisson cumulative sum control charts, in which the risk factors were put to adjust the risk of influenza and the adjustment was made by zero-inflated Poisson regression. We respectively proposed the control chart monitoring the parameters individually and simultaneously. RESULTS: The performance of our proposed risk-adjusted zero-inflated Poisson cumulative sum control chart was evaluated and compared with the unadjusted standard cumulative sum control charts in simulation studies. The results show that for different distribution of impact factors and different coefficients, the risk-adjusted cumulative sum charts can generate much less false alarm than the standard ones. Finally, the influenza surveillance data from Hong Kong is used to illustrate the application of the proposed chart. CONCLUSIONS: Our results suggest that the adjusted cumulative sum control chart we proposed is more accurate and credible than the unadjusted standard control charts because of the lower false alarm rate of the adjusted ones. Even the unadjusted control charts may signal a little faster than the adjusted ones, the alarm they raise may have low credibility since they also raise alarm frequently even the processes are in control. Thus we suggest using the risk-adjusted cumulative sum control charts to monitor the influenza surveillance data to alert accurately, credibly and relatively quickly.

Farm Households' Adoption of Climate-smart Practices in Subsistence Agriculture: Evidence from Northern Togo.

Climate change (CC) effects on agriculture development and households' vulnerability are widely recognized. Being aware of the induced effects of climatic risks, farmers have adopted adaptation strategies to build resilience. Analyzes the determinants of choice of adaptation strategies using binary models can lead to an estimation bias, since the number of adopted strategies may be correlated. This paper analyzes farm households' perception of CC, the determinants of choice of the number of adopted practices, and correlation between the most used climate-smart strategies in subsistence agriculture. Zero-inflated Poisson regression and multivariate analysis are employed using data collected from 704 farm households in Northern Togo. Households' minimum consumption needs, gender, land, access to credit and extension services are the main determinants of the choice of the number of adopted strategies. The use of resistance and high yielding varieties, crops and livestock integration, soil and water conservation practice, the use of organic fertilizer, and adjustment of sowing time are the most adopted farming practices. A strong complementarity between the adopted practices for agriculture development was found. Factors that influence households' choice of adaptation strategies include gender, household location, education level, family size, and allocated labor. Institutional factors including market access, access to credit, and extension services are also key determinants in promoting the use of climate-smart practices that are environmentally friendly.

Variance components genetic association test for zero-inflated count outcomes.

Commonly in biomedical research, studies collect data in which an outcome measure contains informative excess zeros; for example, when observing the burden of neuritic plaques (NPs) in brain pathology studies, those who show none contribute to our understanding of neurodegenerative disease. The outcome may be characterized by a mixture distribution with one component being the "structural zero" and the other component being a Poisson distribution. We propose a novel variance components score test of genetic association between a set of genetic markers and a zero-inflated count outcome from a mixture distribution. This test shares advantageous properties with single-nucleotide polymorphism (SNP)-set tests which have been previously devised for standard continuous or binary outcomes, such as the sequence kernel association test. In particular, our method has superior statistical power compared to competing methods, especially when there is correlation within the group of markers, and when the SNPs are associated with both the mixing proportion and the rate of the Poisson distribution. We apply the method to Alzheimer's data from the Rush University Religious Orders Study and Memory and Aging Project, where as proof of principle we find highly significant associations with the APOE gene, in both the "structural zero" and "count" parameters, when applied to a zero-inflated NPs count outcome.

Extended multi-item gamma Poisson shrinker methods based on the zero-inflated Poisson model for postmarket drug safety surveillance.

Bayesian signal detection methods, including the multiitem gamma Poisson shrinker (MGPS), assume a Poisson distribution for the number of reports. However, the database of the adverse event reporting system often has a large number of zero-count cells. A zero-inflated Poisson (ZIP) distribution can be more appropriate in this situation than a Poisson distribution. Few studies have considered ZIP-based models for Bayesian signal detection. In addition, most studies on Bayesian signal detection methods include simulation studies conducted assuming a gamma distribution for the prior. Herein, we extend the MGPS method using the ZIP model and apply various prior distributions. We evaluated the extended methods through an extensive simulation using more varied settings for the model and prior than existing methods. We varied the total number of reports, the number of true signals, the relative reporting rate, and the probability of observing a true zero. The results show that as the probability of observing a zero count increased, methods based on the ZIP model outperformed the Poisson model in most cases. We also found that using the mixture log-normal prior resulted in more conservative detection than other priors when the relative reporting rate is high. Conversely, more signals were found when using the mixture truncated normal distributions. We applied the Bayesian signal detection methods to data from the Korea Adverse Event Reporting System from 2012 to 2016.

Comparison of random-effects meta-analysis models for the relative risk in the case of rare events: A simulation study.

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided.

Semiparametric frailty models for zero-inflated event count data in the presence of informative dropout.

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow-up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow-up time and the subject-specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood-based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite-dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.

A new Bayesian joint model for longitudinal count data with many zeros, intermittent missingness, and dropout with applications to HIV prevention trials.

In longitudinal clinical trials, it is common that subjects may permanently withdraw from the study (dropout), or return to the study after missing one or more visits (intermittent missingness). It is also routinely encountered in HIV prevention clinical trials that there is a large proportion of zeros in count response data. In this paper, a sequential multinomial model is adopted for dropout and subsequently a conditional model is constructed for intermittent missingness. The new model captures the complex structure of missingness and incorporates dropout and intermittent missingness simultaneously. The model also allows us to easily compute the predictive probabilities of different missing data patterns. A zero-inflated Poisson mixed-effects regression model is assumed for the longitudinal count response data. We also propose an approach to assess the overall treatment effects under the zero-inflated Poisson model. We further show that the joint posterior distribution is improper if uniform priors are specified for the regression coefficients under the proposed model. Variations of the g-prior, Jeffreys prior, and maximally dispersed normal prior are thus established as remedies for the improper posterior distribution. An efficient Gibbs sampling algorithm is developed using a hierarchical centering technique. A modified logarithm of the pseudomarginal likelihood and a concordance based area under the curve criterion are used to compare the models under different missing data mechanisms. We then conduct an extensive simulation study to investigate the empirical performance of the proposed methods and further illustrate the methods using real data from an HIV prevention clinical trial.

Is antibacterial treatment intensity lower in elderly patients? A retrospective cohort study in a German surgical intensive care unit.

BACKGROUND: Demographic change concurrent with medical progress leads to an increasing number of elderly patients in intensive care units (ICUs). Antibacterial treatment is an important, often life-saving, aspect of intensive care but burdened by the associated antimicrobial resistance risk. Elderly patients are simultaneously at greater risk of infections and may be more restrictively treated because, generally, treatment intensity declines with age. We therefore described utilization of antibacterials in ICU patients older and younger than 80 years and examined differences in the intensity of antibacterial therapy between both groups. METHODS: We analysed 17,464 valid admissions from the electronic patient data management system of our surgical ICU from April 2006 - October 2013. Antibacterial treatment rates were defined as days of treatment (exposed patient days) relative to patient days of ICU stay and calculated for old and young patients. Rates were compared in zero-inflated Poisson regression models adjusted for patients' sex, mean SAPS II- and TISS-scores, and calendar years yielding adjusted rate ratios (aRRs). Rate ratios exceeding 1 represent higher rates in old patients reflecting greater treatment intensity in old compared to younger patients. RESULTS: Observed antibacterial treatment rates were lower in patients 80 years and older compared to younger patients (30.97 and 39.73 exposed patient days per 100 patient days in the ICU, respectively). No difference in treatment intensity, however, was found from zero-inflated Poisson regression models permitting more adequate consideration of patient days with low treatment probability: for all antibacterials the adjusted rate ratio (aRR) was 1.02 (95%CI: 0.98-1.07). Treatment intensities were higher in elderly patients for penicillins (aRR 1.37 (95%CI: 1.26-1.48)), cephalosporins (aRR 1.20 (95%CI: 1.09-1.31)), carbapenems (aRR 1.35 (95%CI: 1.20-1.50)), fluoroquinolones (aRR 1.17 (95%CI: 1.05-1.30), and imidazoles (aRR 1.34 (95%CI: 1.23-1.46)). CONCLUSIONS: Elderly patients were generally less likely to be treated with antibacterials. This observation, however, did not persist in patients with comparable treatment probability. In these, antibacterial treatment intensity did not differ between younger and older ICU patients, for some antibacterial classes treatment intensity was even higher in the latter. Patient-level covariates are instrumental for a nuanced evaluation of age-effects in antibacterial treatment in the ICU.