John T. Chen

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).

The Distribution of Stock Returns When the Market Is Up

Abstract For some investments, the relation between stock returns and the market proxy is conventionally described by a linear regression model with the normality assumption. This paper derives the distribution of stock returns for a security in an upgrade (or downgrade) market with the assumption that the log stock returns of the market proxy follow a mixture of normal distributions. We discuss MLE and the method of moment estimation for parameters involved in the model. An analysis of stock data in Johannesburg Stock Exchange is included to illustrate the model. This note explains the phenomenon in financial analysis regarding the shape of the distribution of long-run stock returns limited on an upgrade or downgrade market index.

Comparison of vein valve function following pharmacomechanical thrombolysis versus simple catheter-directed thrombolysis for iliofemoral deep vein thrombosis.

BACKGROUND Successful catheter-directed thrombolysis (CDT) for iliofemoral deep vein thrombosis (IFDVT) reduces post-thrombotic morbidity and is a suggested treatment option by the American College of Chest Physicians for patients with IFDVT. Pharmacomechanical thrombolysis (PMT) is also suggested to shorten treatment time and reduce the dose of plasminogen activator. However, concern remains that mechanical devices might damage vein valves. The purpose of this study is to examine whether PMT adversely affects venous valve function compared to CDT alone in IFDVT patients treated with catheter-based techniques. METHODS Sixty-nine limbs in 54 patients (39 unilateral, 15 bilateral) who underwent catheter-based treatment for IFDVT form the basis of this study. Lytic success and degree of residual obstruction were analyzed by reviewing postprocedural phlebograms. All patients underwent bilateral postprocedure duplex to evaluate patency and valve function. Phlebograms and venous duplex examinations were interpreted in a blinded fashion. Limbs were analyzed based on the method of treatment: CDT alone (n = 20), PMT using rheolytic thrombolysis (n = 14), and isolated pharmacomechanical thrombolysis (n = 35). The validated outcome measures were compared between the treatment groups. RESULTS Sixty-nine limbs underwent CDT with or without PMT. The average patient age was 47 years (range, 16-78). Venous duplex was performed 44.4 months (mean) post-treatment. Of the limbs treated with CDT with drip technique, 65% demonstrated reflux vs 53% treated with PMT (P = .42). There was no difference in long-term valve function between patients treated with rheolytic and isolated pharmacomechanical thrombolysis. In the bilateral group, 87% (13/15) demonstrated reflux in at least one limb. In the unilateral group, 64% (25/39) had reflux in their treated limb and 36% (14/39) in their contralateral limb. There was no correlation effect of residual venous obstruction on valve function, although few patients had >50% residual obstruction. CONCLUSIONS In patients undergoing catheter-based intervention for IFDVT, PMT does not adversely affect valve function compared with CDT alone. A higher than expected number of patients had reflux in their uninvolved limb.

The density of the skew normal sample mean and its applications

This paper focuses on the distribution of the skew normal sample mean. For a random sample drawn from a skew normal population, we derive the density function and the moment generating function of the sample mean. The density function derived can be used for statistical inference on the disease occurrence time of twins in epidemiology, in which the skew normal model plays a key role.

Inference on the Minimum Effective Dose Using Binary Data

This article proposes a confidence interval procedure for an open question posted by Tamhane and Dunnett regarding the inference on the minimum effective dose of a drug for binary data. We use a partitioning approach in conjunction with a confidence interval procedure to provide a solution to this problem. Binary data frequently arise in medical investigations in connection with dichotomous outcomes such as the development of a disease or the efficacy of a drug. The proposed procedure not only detects the minimum effective dose of the drug, but also provides estimation information on the treatment effect of the closest ineffective dose. Such information benefits follow-up investigations in clinical trials. We prove that, when the confidence interval for the pairwise comparison has (or asymptotically controls) confidence level 1 − α, the stepwise procedure strongly controls (or asymptotically controls) the familywise error rate at level α, which is a key criterion in dose finding. The new method is compared with other procedures in terms of power performance and coverage probability using simulations. The simulated results shed new light on the discernible features of the new procedure. An example on the investigation of acetaminophen is included.

Detecting the association between residual thrombus and post-thrombotic classification of chronic venous disease with range regression.

This paper addresses a clinical hypothesis detected by the method of range regression, a new statistical method portraying the clinical response via the range of an explanatory variable. For patients with iliofemoral deep venous thrombosis, it has long been clinically suspected that residual thrombus affects the quality of life after catheter-directed thrombolysis. However, such important medical experience has not been validated or scientifically quantified by experimental or observational data. In clinical practice, this association may directly affect the duration of thrombolytic therapy or other attempts at clot removal. In this study, we develop a new regression model to identify how the quantity of clot lysed affects the clarification of chronic venous disease after catheter-directed thrombolysis (a correlated index on postthrombotic quality of life). Bridging clinical insight with statistics by means of medical records of 62 IFDVT patients, the new method reveals that residual thrombus significantly and substantially affects post-thrombotic clarification of chronic venous disease. The conclusion of the new method is confirmed by a conventional logistic regression method when 50% thrombus removal is treated as a categorization threshold. This new approach is applicable to analyze other clinical or medical variables on the treatment of venous diseases.

A Two-Stage Stepwise Estimation Procedure

This article proposes a two-stage simultaneous confidence procedure for the comparisons of k pairs of population means, without using multiplicity adjustment of more than two populations. The proposed procedure can be broadly applied to parametric or nonparametric models. It is robust and versatile because its derivation only utilizes a partitioning approach in conjunction with a bivariate adjustment, without any assumption on the underlying distribution. To elucidate the application, the proposed procedure is intertwined with the estimation of the therapeutic window of a drug. It provides confidence limits for the efficacy and the toxicity of the effective doses, highest ineffective dose, safe doses, and lowest unsafe dose, simultaneously. Such estimation information facilitates follow-up studies in clinical trials. As an illustrative example, the new procedure is applied to analyze a data set on molecular cancer therapeutics regarding the apoptotic killing effects of different chemical compounds on two leukemia cell lines.

Effects of Thermomechanical Stimulation during Vaccination on Anxiety, Pain, and Satisfaction in Pediatric Patients: A Randomized Controlled Trial

Purpose: Vaccination can be a significant source of pain for pediatric patients, which could result in fear of medical procedures and future reluctance to seek medical care. It is important for nurses to provide pain prevention during these procedures. This study sought to measure the impact of an intervention combining cold and vibration on pain scores during routine pediatric immunization. Design and Methods: A prospective, open‐label, randomized controlled trial to examine the effectiveness of the Buzzy device (thermomechanical stimulation) compared to no intervention (control group) in reducing child‐reported pain during routine immunization. The Wong Baker Faces scale was used to collect child, parent, and observer reported anxiety and pain. Parents reported satisfaction with the procedure and overall office visit. Results: Fifty children between the ages of 3 and 18 were included in the present analysis. Mean child‐reported pain scores were significantly lower in the group receiving thermomechanical stimulation compared to control (3.56 vs 5.92, p = 0.015). Buzzy did not impact child‐reported anxiety or how much pain the child expected. Parent‐reported satisfaction did not vary significantly between groups, but was strongly associated with parent‐reported pain scores. Conclusions: Thermomechanical stimulation with the Buzzy device significantly reduced pain during pediatric immunization over a wide range of ages compared to control, but did not impact pre‐procedure anxiety. Practice Implications: The Buzzy device is an easy to implement intervention to reduce pediatric pain during vaccination. It may have the greatest impact in younger children but could be offered during all immunizations. Highlights:Use of Buzzy during vaccine reduced child‐reported pain.Age, gender, and the use of the device were associated with child pain.The device did not impact childrens anxiety or expectation of pain.Parent satisfaction was strongly associated with their perception of child pain (parent‐reported pain).Pain intervention during vaccination has a significant impact on patient experience.

A multivariate two-factor skew model

It is well known that many data, such as the financial or demographic data, exhibit asymmetric distributions. In recent years, researchers have concentrated their efforts to model this asymmetry. Skew normal model is one of such models that are skew and yet possess many properties of the normal model. In this paper, a new multivariate skew model is proposed, along with its statistical properties. It includes the multivariate normal distribution and multivariate skew normal distribution as special cases. The quadratic form of this random vector follows a χ2 distribution. The roles of the parameters in the model are investigated using contour plots of bivariate densities.

Multilevel attributable risk in cross-sectional studies

Applications such as public interventions on risk factors associated with the disease necessitate the inference of population attributable risk, especially when multiple risk levels with confounders appear in a cross-sectional data set. For case control studies, inference procedures for multiple exposure levels are available in the literature. However, corresponding procedures for survey-type data are not available. In this paper, we propose two estimation procedures. The first one is based on the Wald statistic and the second one is based on a logarithmic transformation. Simulation studies show that the confidence interval estimates of the attributable risk based on the Wald statistic perform equally well with the logarithmic transformation procedure. When the sample size is small, the large sample approximation is not plausible, so we discuss an exact test procedure. A data set regarding the impact of body mass index on diastolic blood pressure and the cardiovascular disease is included for illustration.