Sheng Mao Chang

Extreme Value Distributions for the Skew-Symmetric Family of Distributions

We derive the extreme value distribution of the skew-symmetric family, the probability density function of the latter being defined as twice the product of a symmetric density and a skewing function. We show that, under certain conditions on the skewing function, this extreme value distribution is the same as that for the symmetric density. We illustrate our results using various examples of skew-symmetric distributions as well as two data sets.

Bayesian Variable Selections for Probit Models with Componentwise Gibbs Samplers

This article considers Bayesian variable selection problems for binary responses via stochastic search variable selection and Bayesian Lasso. To avoid matrix inversion in the corresponding Markov chain Monte Carlo implementations, the componentwise Gibbs sampler (CGS) idea is adopted. Moreover, we also propose automatic hyperparameter tuning rules for the proposed approaches. Simulation studies and a real example are used to demonstrate the performances of the proposed approaches. These results show that CGS approaches do not only have good performances in variable selection but also have the lower batch mean standard error values than those of original methods, especially for large number of covariates.

Double shrinkage estimators for large sparse covariance matrices

Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.

Dynamic changes in quality of life after three first-line therapies for EGFR mutation-positive advanced non-small-cell lung cancer:

Background: Three different tyrosine kinase inhibitors have been approved as first-line therapies for epidermal growth factor receptor (EGFR) mutation-positive advanced non-small-cell lung cancer with similar overall survival. This study determined dynamic changes in quality of life (QoL) for patients using these therapies after controlling for potential confounders. Methods: From 2011 to 2016, we prospectively assessed the utility values and QoL scores of patients using the EuroQol five-dimension and World Health Organization Quality-of-Life – Brief questionnaires. QoL functions after initiation of treatment were estimated using a kernel-smoothing method. Dynamic changes in major determinants were repeatedly assessed for constructing mixed models. Results: A total of 344 patients were enrolled, with 934 repeated assessments. After controlling for performance status, disease progression, EGFR mutation subtype and other confounders, the mixed models showed significantly lower QoL scores for afatinib versus gefitinib in the physical, psychological and social domains, and 10 facets. The differences seemed to appear 10 months after initiation of treatment. In contrast, there was no significant difference between erlotinib and gefitinib in the scores of all domains and facets. Conclusion: QoL in patients receiving afatinib seemed to be lower than in those receiving gefitinib. Since the sample sizes in this study were relatively small, more studies are warranted to corroborate these results.

Power and sample size calculation for paired Right-Censored data based on survival copula models

Abstract Sample size determination is essential during the planning phases of clinical trials. To calculate the required sample size for paired right-censored data, the structure of the within-paired correlations needs to be pre-specified. In this article, we consider using popular parametric copula models, including the Clayton, Gumbel, or Frank families, to model the distribution of joint survival times. Under each copula model, we derive a sample size formula based on the testing framework for rank-based tests and non-rank-based tests (i.e., logrank test and Kaplan–Meier statistic, respectively). We also investigate how the power or the sample size was affected by the choice of testing methods and copula model under different alternative hypotheses. In addition to this, we examine the impacts of paired-correlations, accrual times, follow-up times, and the loss to follow-up rates on sample size estimation. Finally, two real-world studies are used to illustrate our method and R code is available to the user.

Geographic Variations and Time Trends in Cancer Treatments in Taiwan

BackgroundTargeted therapies have become important treatment options for cancer care in many countries. This study aimed to examine recent trends in utilization of antineoplastic drugs, particularly the use of targeted therapies for treatment of cancer, by geographic region in Taiwan (northern, midwestern, southern, and eastern regions and the outer islands).MethodsThis was a retrospective observational study of antineoplastic agents using 2009-2012 quarterly claims data from Taiwan’s National Health Insurance Research Database. Yearly market shares by prescription volume and costs for targeted therapies among total antineoplastic agents by region were estimated. We used multivariate regression model and ANOVA to examine variations in utilization of targeted therapies between geographic regions and used ARIMA models to estimate longitudinal trends.ResultsPopulation-adjusted use and costs of antineoplastic drugs (including targeted therapies) were highest in the southern region of Taiwan and lowest in the outer islands. We found a 4-fold difference in use of antineoplastic drugs and a 49-fold difference in use of targeted therapies between regions if the outer islands were included. There were minimal differences in use of antineoplastic drugs between other regions with about a 2-fold difference in use of targeted therapies. Without considering the outer islands, the market share by prescription volume and costs of targeted therapies increased almost 2-fold (1.84-1.90) and 1.5-fold (1.26-1.61) respectively between 2009 and 2012. Furthermore, region was not significantly associated with use of antineoplastic agents or use of targeted therapies after adjusting for confounders. Region was associated with costs of antineoplastic agents but it was not associated with costs of targeted therapies after confounding adjustments.ConclusionsUse of antineoplastic drugs overall and use of targeted therapies for treatment of cancer varied somewhat between regions in Taiwan; use was notably low in the outer islands. Strategies might be needed to ensure access to cancer care in each region as economic burden of cancer care increase due to growing use of targeted therapies.

Fast Bayesian variable screenings for binary response regressions with small sample size

ABSTRACT Screening procedures play an important role in data analysis, especially in high-throughput biological studies where the datasets consist of more covariates than independent subjects. In this article, a Bayesian screening procedure is introduced for the binary response models with logit and probit links. In contrast to many screening rules based on marginal information involving one or a few covariates, the proposed Bayesian procedure simultaneously models all covariates and uses closed-form screening statistics. Specifically, we use the posterior means of the regression coefficients as screening statistics; by imposing a generalized g-prior on the regression coefficients, we derive the analytical form of their posterior means and compute the screening statistics without Markov chain Monte Carlo implementation. We evaluate the utility of the proposed Bayesian screening method using simulations and real data analysis. When the sample size is small, the simulation results suggest improved performance with comparable computational cost.

Confidence intervals for the ratio of two median residual lifetimes with left‐truncated and right‐censored data

The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.

Maximizing Complex Likelihoods via Directed Stochastic Searching Algorithm

In this article, a directed stochastic searching algorithm is defined. It is a root or optimal parameter searching algorithm with stochastic searching directions. This algorithm is especially relevant when the objective function is complex or is observed with errors. We prove that the resulting roots or estimators have well-controlled biases under certain conditions. We examine the proposed method by finding the maximum likelihood estimates for which the corresponding likelihood function has or does not have a closed-form representation in both the simulations and the real cases. Finally, the limitations and the consequences when multiple solutions exist are addressed.