Logistic Regression Model for a Bivariate Binomial Distribution with Applications in Baseball Data Analysis.

There has been a considerable amount of literature on binomial regression models that utilize well-known link functions, such as logistic, probit, and complementary log-log functions. The conventional binomial model is focused only on a single parameter representing one probability of success. However, we often encounter data for which two different success probabilities are of interest simultaneously. For instance, there are several offensive measures in baseball to predict the future performance of batters. Under these circumstances, it would be meaningful to consider more than one success probability. In this article, we employ a bivariate binomial distribution that possesses two success probabilities to conduct a regression analysis with random effects being incorporated under a Bayesian framework. Major League Baseball data are analyzed to demonstrate our methodologies. Extensive simulation studies are conducted to investigate model performances.

Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing intermediate events.

BACKGROUND: In clinical trials and survival analysis, participants may be excluded from the study due to withdrawal, which is often referred to as lost-to-follow-up (LTF). It is natural to argue that a disease would be censored due to death; however, when an LTF is present it is not guaranteed that the disease has been censored. This makes it important to consider both cases; the disease is censored or not censored. We also note that the illness process can be censored by LTF. We will consider a multi-state model in which LTF is not regarded as censoring but as a non-fatal event. METHODS: We propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. More precisely, we employ the additive and multiplicative hazards model with log-normal frailty and construct the conditional likelihood to estimate the transition intensities among states in the multi-state model. Marginalization of the full likelihood is accomplished using adaptive importance sampling, and the optimal solution of the regression parameters is achieved through the iterative quasi-Newton algorithm. RESULTS: Simulation is performed to investigate the finite-sample performance of the proposed estimation method in terms of the relative bias and coverage probability of the regression parameters. The proposed estimators turned out to be robust to misspecifications of the frailty distribution. PAQUID data have been analyzed and yielded somewhat prominent results. CONCLUSIONS: We propose a multi-state model for semi-competing risks data for which there exists information on fatal events, but information on non-fatal events may not be available due to lost to follow-up. Simulation results show that the coverage probabilities of the regression parameters are close to a nominal level of 0.95 in most cases. Regarding the analysis of real data, the risk of transition from a healthy state to dementia is higher for women; however, the risk of death after being diagnosed with dementia is higher for men.

Different cut-off values of the insulin tolerance test, the high-dose short Synacthen test (250 µg) and the low-dose short Synacthen test (1 µg) in assessing central adrenal insufficiency.

OBJECTIVE: The short Synacthen test (SST) is widely used as alternative test to the insulin tolerance test (ITT) to investigate central adrenal insufficiency (CAI), but the methodology and cut-off values of the SST are controversial. Our aim was to evaluate the cut-off value of the ITT in normal subjects and to assess the different cut-off values of the high-dose SST (250 µg, HDT) and the low-dose SST (1 µg, LDT) in subjects with suspected CAI. SUBJECTS AND METHODS: We conducted ITTs in 208 normal subjects to establish the cut-off value for the ITT, and 28 of those subjects underwent the HDT and LDT. From 1999 to 2007, 182 patients with suspected CAI were recruited and underwent ITTs, LDTs and HDTs to establish cut-off values and compare the diagnostic accuracy between the LDT and HDT. RESULTS: The 95th percentile of the peak cortisol level during the ITT in the normal control subjects was 14·8 µg/dl. Receiver operator characteristics (ROC) analysis revealed that the optimal cut-off values of peak cortisol in the LDT and HDT in patients with suspected CAI were 15·8 and 17·4 µg/dl, respectively. However, the cut-off values from normative data (mean - 2 SD) were 18·3 µg/dl for the LDT and 20·5 µg/dl for the HDT in normal control. CONCLUSIONS: The optimal cut-off values of SSTs needed to be individualized according to the type of SST and tested patient population.

Assessing the Optimal Cutpoint for Tumor Size in Patients with Lung Cancer Based on Linear Rank Statistics in a Competing Risks Framework.

PURPOSE: In clinical studies, patients may experience several types of events during follow up under the competing risks (CR) framework. Patients are often classified into low- and high-risk groups based on prognostic factors. We propose a method to determine an optimal cutpoint value for prognostic factors on censored outcomes in the presence of CR. MATERIALS AND METHODS: We applied our method to data collected in a study of lung cancer patients. From September 1, 1991 to December 31, 2005, 758 lung cancer patients received tumor removal surgery at Samsung Medical Center in Korea. The proposed statistic converges in distribution to that of the supremum of a standardized Brownian bridge. To overcome the conservativeness of the test based on an approximation of the asymptotic distribution, we also propose a permutation test based on permuted samples. RESULTS: Most cases considered in our simulation studies showed that the permutation-based test satisfied a significance level of 0.05, while the approximation-based test was very conservative: the powers of the former were larger than those of the latter. The optimal cutpoint value for tumor size (unit: cm) prior to surgery for classifying patients into two groups (low and high risks for relapse) was found to be 1.8, with decent significance reflected as p values less than 0.001. CONCLUSION: The cutpoint estimator based on the maximally selected linear rank statistic was reasonable in terms of bias and standard deviation in the CR framework. The permutation-based test well satisfied type I error probability and provided higher power than the approximation-based test.

Extramedullary plasmacytoma arising from the nasal septum.

We report a rare case of extramedullary plasmacytoma of the nasal septum in a 65-year-old woman. She presented with a 2-month history of left-sided nasal obstruction and intermittent blood-tinged nasal crusting. Nasal endoscopy revealed that a dark-red mass had arisen from the nasal septum; no evidence of invasion to adjacent tissues was seen. A biopsy specimen was diagnosed as a plasmacytoma (kappa light chain-type). Serum and urine electrophoresis failed to detect any myeloma component or Bence Jones protein. All other screening tests to rule out multiple myeloma were negative. These findings confirmed the diagnosis of extramedullary plasmacytoma. The mass was completely removed via an endoscopic approach. No recurrence was noted at the 2-year follow-up.

Bayesian analysis for zero-inflated regression models with the power prior: applications to road safety countermeasures.

We consider zero-inflated Poisson and zero-inflated negative binomial regression models to analyze discrete count data containing a considerable amount of zero observations. Analysis of current data could be empirically feasible if we utilize similar data based on previous studies. Ibrahim and Chen (2000) proposed the power prior to incorporate certain information from the historical data available from previous studies. The power prior is constructed by raising the likelihood function of the historical data to the power a(0), where 0< or =a(0)< or =1. The power prior is a useful informative prior in Bayesian inference. We estimate regression coefficients associated with several safety countermeasures. We use Markov chain and Monte Carlo techniques to execute some computations. The empirical results show that the zero-inflated models with the power prior perform better than the frequentist approach.