Hybrid-based confidence intervals for the ratio of two treatment means in the over-dispersed Poisson data

In many clinical trials and epidemiological studies, comparing the mean count response of an exposed group to a control group is often of interest. This type of data is often over-dispersed with respect to Poisson variation, and previous studies usually compared groups using confidence intervals (CIs) of the difference between the two means. However, in some situations, especially when the means are small, interval estimation of the mean ratio (MR) is preferable. Moreover, Cox and Lewis [4 D.R. Cox and P.A.W. Lewis, The Statistical Analysis of Series of Events, Methuen, London, 1966.[Crossref] , [Google Scholar]] pointed out many other situations where the MR is more relevant than the difference of means. In this paper, we consider CI construction for the ratio of means between two treatments for over-dispersed Poisson data. We develop several CIs for the situation by hybridizing two separate CIs for two individual means. Extensive simulations show that all hybrid-based CIs perform reasonably well in terms of coverage. However, the CIs based on the delta method using the logarithmic transformation perform better than other intervals in the sense that they have slightly shorter interval lengths and show better balance of tail errors. These proposed CIs are illustrated with three real data examples.     

Bayesian Estimation and Prediction for the Beta-Binomial Model

The beta-binomial distribution, which is generated by a simple mixture model, has been widely applied in the social, physical, and health sciences. Problems of estimation, inference, and prediction have been addressed in the past, but not in a Bayesian framework. This article develops Bayesian procedures for the beta-binomial model and, using a suitable reparameterization, establishes a conjugate-type property for a beta family of priors. The transformed parameters have interesting interpretations, especially in marketing applications, and are likely to be more stable. More specifically, one of these parameters is the market share and the other is a measure of the heterogeneity of the customer population. Analytical results are developed for the posterior and prediction quantities, although the numerical evaluation is not trivial. Since the posterior moments are more easily calculated, we also propose the use of posterior approximation using the Pearson system. A particular case (when there are two trials), which occurs in taste testing, brand choice, media exposure, and some epidemiological applications, is analyzed in detail. Simulated and real data are used to demonstrate the feasibility of the calculations. The simulation results effectively demonstrate the superiority of Bayesian estimators, particularly in small samples, even with uniform (“non-informed”) priors. Naturally, “informed” priors can give even better results. The real data on television viewing behavior are used to illustrate the prediction results. In our analysis, several problems with the maximum likelihood estimators are encountered. The superior properties and performance of the Bayesian estimators and the excellent approximation results are strong indications that our results will be potentially of high value in small sample applications of the beta-binomial and in cases in which significant prior information exists.     

A Test of the Cross-Sectional Robustness of the Arbitrage Pricing Model Using Foreign Exchange Rates*

This paper tests the cross-sectional robustness of the arbitrage pricing theory (APT) model using foreign exchange rate data to determine if the model is robust with respect to the various random samples and various factor analytic techniques. Factor scores are developed using various samples and factor analytic techniques to explain the returns for other samples and groupings. The APT model is found to be robust across samples and techniques.     

Home Visitor Relationship Security: Association With Perceptions of Work,Satisfaction, and Turnover

Home visiting is widely used to improve outcomes in families at risk for poor parenting. Impact is modest and variable, owing in part to poor fidelity. Attachment theory suggests that home visitors' relationship security influences fidelity because establishing a trusting relationship with parents is central to service delivery. This study describes paraprofessional home visitors' relationship security and relates it to demographics, psychological attributes, and work perceptions and intentions. Home visitors (n = 62) varied widely on the two major domains of relationship security: anxiety and avoidance. Relationship security was stable over time. Relationship anxiety and avoidance were associated with psychological and work constructs in theoretically predicted ways. Relationship anxiety was negatively associated with self-efficacy and positively associated with negative affect and indicators of burnout. Relationship avoidance was negatively associated with self-efficacy, job satisfaction, and tenure as a home visitor. Implications for research and practice are discussed.     

Lability of prenatal stress during the COVID-19 pandemic links to negative affect in infancy

The association between prenatal stress and children's socioemotional development is well established. The COVID-19 pandemic has been a particularly stressful period, which may impact the gestational environment. However, most studies to-date have examined prenatal stress at a single time point, potentially masking the natural variation in stress that occurs over time, especially during a time as uncertain as the pandemic. This study leveraged dense ecological momentary assessments from a prenatal randomized control trial to examine patterns of prenatal stress over a 14-week period (up to four assessments/day) in a U.S. sample of 72 mothers and infants. We first examined whether varied features of stress exposure (lability, mean, and baseline stress) differed depending on whether mothers reported on their stress before or during the pandemic. We next examined which features of stress were associated with 3-month-old infants' negative affect. We did not find differences in stress patterns before and during the pandemic. However, greater stress lability, accounting for baseline and mean stress, was associated with higher infant negative affect. These findings suggest that pathways from prenatal stress exposure to infant socioemotional development are complex, and close attention to stress patterns over time will be important for explicating these pathways.     

Optimal Dynamic Upgrading in Revenue Management

We consider a revenue management problem involving a two compartment aircraft flying a single leg, with no cancellations or over‐booking. We apply the practice of transforming a choice revenue management model into an independent demand model. Within this assumed independent model, there are two sets of demands, business and economy, each with multiple fare class products. A business passenger can only be accepted into business. An economy passenger can be accepted into economy or upgraded into business. We define a two‐dimensional dynamic program (DP) and show that the value function is sub‐modular and concave in seat availability in the two compartments. Thus the bid prices are non‐decreasing with respect to these state variables. We use this result to propose an exact algorithm to solve the DP. Our numerical investigation suggests that in contrast to standard backward induction, our method could be included in production revenue management systems. Further, when the economy compartment is capacity constrained, we observe a substantial monetary benefit from optimal dynamic upgrading compared to the static upgrading procedures currently used in practice.     

Estimating DEA confidence intervals with statistical panel data analysis

This paper describes a statistical method for estimating data envelopment analysis (DEA) score confidence intervals for individual organizations or other entities. This method applies statistical panel data analysis, which provides proven and powerful methodologies for diagnostic testing and for estimation of confidence intervals. DEA scores are tested for violations of the standard statistical assumptions including contemporaneous correlation, serial correlation, heteroskedasticity and the absence of a normal distribution. Generalized least squares statistical models are used to adjust for violations that are present and to estimate valid confidence intervals within which the true efficiency of each individual decision-making unit occurs. This method is illustrated with two sets of panel data, one from large US urban transit systems and the other from a group of US hospital pharmacies.