Journal of Data Science

In this paper, maximum likelihood and Bayesian methods of estimation are used to estimate the unknown parameters of two Weibull populations with the same shape parameter under joint progressive Type-I (JPT-I) censoring scheme. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. The approximate confidence intervals and the credible intervals for the unknown parameters are also obtained. Finally, we analyze a one real data set for illustration purpose.

Abstract: The self-controlled case series (SCCS) and the matched cohort are two frequently used study designs to adjust for known and unknown confounding effects in epidemiological studies. Count data arising from these two designs may not be independent. While conditional Poisson regression models have been used to take into account the dependence of such data, these models have not been available in some standard statistical software packages (e.g., SAS). This article demonstrates 1) the relationship of the likelihood function and parameter estimation between the conditional Poisson regression models and Cox’s proportional hazard models in SCCS and matched cohort studies; 2) that it is possible to fit conditional Poisson regression models with procedures (e.g., PHREG in SAS) using Cox’s partial likelihood model. We tested both conditional Poisson likelihood and Cox’s partial likelihood models on data from studies using either SCCS or a matched cohort design. For the SCCS study, we fitted both parametric and semi-parametric models to model age effects, and described a simple way to apply the parametric and complex semi-parametric analysis to case series data.

Abstract: Meta-analytic methods for diagnostic test performance, Bayesian methods in particular, have not been well developed. The most commonly used method for meta-analysis of diagnostic test performance is the Summary Receiver Operator Characteristic (SROC) curve approach of Moses, Shapiro and Littenberg. In this paper, we provide a brief summary of the SROC method, then present a case study of a Bayesian adaptation of their SROC curve method that retains the simplicity of the original model while additionally incorporating uncertainty in the parameters, and can also easily be extended to incorporate the effect of covariates. We further derive a simple transformation which facilitates prior elicitation from clinicians. The method is applied to two datasets: an assessment of computed tomography for detecting metastases in non-small-cell lung cancer, and a novel dataset to assess the diagnostic performance of endoscopic ultrasound (EUS) in the detection of biliary obstructions relative to the current gold standard of endoscopic retrograde cholangiopancreatography (ERCP).

Abstract: In this study, first exit time of a compound Poisson process with positive jumps and an upper horizontal boundary is considered. An explicit formula is derived for the mean first exit time associated with the compound Poisson process. Finally, an application on traffic accidents is given to illustrate the usage of the mean first exit time.

We demonstrate how to test for conditional independence of two variables with categorical data using Poisson log-linear models. The size of the conditioning set of variables can vary from 0 (simple independence) up to many variables. We also provide a function in R for performing the test. Instead of calculating all possible tables with for loop we perform the test using the loglinear models and thus speeding up the process. Time comparison simulation studies are presented.

Abstract: In this study, we propose a pattern matching procedure to seize similar price movements of two stocks. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time periods in which the two stocks have the same integrated volatility levels and price rise/drop trends. Next we transform the price data in the found matching time periods to the Bollinger Percent b data. The low frequency power spectra of the transformed data are used to extract trends. Pearson’s chi square test is used to assess similarity of the price movement patterns in the matching periods. Simulation results show the proposed procedure can effectively detect the co-movement periods of two price sequences. Finally, we apply the proposed procedure to empirical high frequency transaction data of NYSE.

Abstract: We consider a fully Bayesian treatment of radial basis function regression, and propose a solution to the instability of basis selection. Indeed, when bases are selected solely according to the magnitude of their posterior inclusion probabilities, it is often the case that many bases in the same neighborhood end up getting selected leading to redundancy and ultimately inaccuracy of the representation. In this paper, we propose a straightforward solution to the problem based on post-processing the sample path yielded by the model space search technique. Specifically, we perform an a posteriori model-based clustering of the sample path via a mixture of Gaussians, and then select the points closer to the means of the Gaussians. Our solution is found to be more stable and yields a better performance on simulated and real tasks.

The paper presents an investigation of estimating treatment effect using differ- ent matching methods through Monte Carlo simulation. The study proposed a new method which is computationally efficient and convenient in implication—largest caliper matching and compared the performance with other five popular matching methods. The bias, empirical standard deviation and the mean square error of the estimates in the simulation are checked under different treatment prevalence and different distributions of covariates. It is shown that largest caliper matching improves estimation of the population treatment effect in a wide range of settings compare to other methods. It reduces the bias if the data contains the selection on observables and treatment imbalances. Also, findings about the relative performance of the different matching methods are provided to help practitioners determine which method should be used under certain situations. An application of these methods is implemented on the Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments (SUPPORT) data and, important demographic and socioeconomic factors that may affect the clinical outcome are also reported in this paper.

Abstract: In this paper, a tree-structured method is proposed to extend Classification and Regression Trees (CART) algorithm to multivariate survival data, assuming a proportional hazard structure in the whole tree. The method works on the marginal survivor distributions and uses a sandwich estimator of variance to account for the association between survival times. The Wald-test statistics is defined as the splitting rule and the survival trees are developed by maximizing between-node separation. The proposed method intends to classify patients into subgroups with distinctively different prognosis. However, unlike the conventional tree-growing algorithms which work on a subset of data at every partition, the proposed method deals with the whole data set and searches the global optimal split at each partition. The method is applied to a prostate cancer data and its performance is also evaluated by several simulation studies.