Taeyoung Park

Partially Collapsed Gibbs Samplers: Theory and Methods

Ever-increasing computational power, along with ever–more sophisticated statistical computing techniques, is making it possible to fit ever–more complex statistical models. Among the more computationally intensive methods, the Gibbs sampler is popular because of its simplicity and power to effectively generate samples from a high-dimensional probability distribution. Despite its simple implementation and description, however, the Gibbs sampler is criticized for its sometimes slow convergence, especially when it is used to fit highly structured complex models. Here we present partially collapsed Gibbs sampling strategies that improve the convergence by capitalizing on a set of functionally incompatible conditional distributions. Such incompatibility generally is avoided in the construction of a Gibbs sampler, because the resulting convergence properties are not well understood. We introduce three basic tools (marginalization, permutation, and trimming) that allow us to transform a Gibbs sampler into a partially collapsed Gibbs sampler with known stationary distribution and faster convergence.

BAYESIAN ESTIMATION OF HARDNESS RATIOS: MODELING AND COMPUTATIONS

A commonly used measure to summarize the nature of a photon spectrum is the so-called hardness ratio, which compares the numbers of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize weak sources as a proxy for detailed spectral fitting. However, in this regime classical methods of error propagation fail, and the estimates of spectral hardness become unreliable. Here we develop a rigorous statistical treatment of hardness ratios that properly deals with detected photons as independent Poisson random variables and correctly deals with the non-Gaussian nature of the error propagation. The method is Bayesian in nature and thus can be generalized to carry out a multitude of source-population-based analyses. We verify our method with simulation studies and compare it with the classical method. We apply this method to real-world examples, such as the identification of candidate quiescent low-mass X-ray binaries in globular clusters and tracking the time evolution of a flare on a low-mass star.

Partially Collapsed Gibbs Samplers: Illustrations and Applications

Among the computationally intensive methods for fitting complex multilevel models, the Gibbs sampler is especially popular owing to its simplicity and power to effectively generate samples from a high-dimensional probability distribution. The Gibbs sampler, however, is often justifiably criticized for its sometimes slow convergence, especially when it is used to fit highly structured complex models. The recently proposed Partially Collapsed Gibbs (PCG) sampler offers a new strategy for improving the convergence characteristics of a Gibbs sampler. A PCG sampler achieves faster convergence by reducing the conditioning in some or all of the component draws of its parent Gibbs sampler. Although this strategy can significantly improve convergence, it must be implemented with care to be sure that the desired stationary distribution is preserved. In some cases the set of conditional distributions sampled in a PCG sampler may be functionally incompatible and permuting the order of draws can change the stationary distribution of the chain. In this article, we draw an analogy between the PCG sampler and certain efficient EM-type algorithms that helps to explain the computational advantage of PCG samplers and to suggest when they might be used in practice. We go on to illustrate the PCG samplers in three substantial examples drawn from our applied work: a multilevel spectral model commonly used in high-energy astrophysics, a piecewise-constant multivariate time series model, and a joint imputation model for nonnested data. These are all useful highly structured models that involve computational challenges that can be solved using PCG samplers. The examples illustrate not only the computation advantage of PCG samplers but also how they should be constructed to maintain the desired stationary distribution. Supplemental materials for the examples given in this article are available online.

Endovascular repair of ruptured abdominal aortic aneurysm does not confer survival benefits over open repair

OBJECTIVE Endovascular repair of ruptured abdominal aortic aneurysm (rAAA) is being increasingly performed despite lack of good evidence for its superiority. Other reported studies suffer from patient selection and publication bias with limited follow-up. This study is a single-center propensity score comparing early and midterm outcomes between open surgical repair (OSR) and endovascular repair of rAAA (REVAR). METHODS A retrospective review from January 2001 to November 2010 identified 312 patients who underwent rAAA repairs. Thirty-one patients with antecedent AAA repair and three with incomplete records were excluded, leaving 37 REVARs and 241 OSRs. Propensity score-based matching for sex, age, preoperative hemodynamic status, surgeons annual AAA volume, and preoperative cardiopulmonary resuscitation was performed in a 1:3 ratio to compare outcomes. Thirty-seven REVARs were matched with 111 OSRs. Late survival was estimated by Kaplan-Meier methods. RESULTS Operative time and blood replacement were higher with OSR. Overall complication rates were similar (54% REVAR vs 66% OSR; P = .23), except for higher incidences of tracheostomies (21% vs 3%; P = .015), myocardial infarction (38% vs 18%; P = .036), and acute tubular necrosis (47% vs 21%; P = .009) with OSR. Operative mortality rates were similar (22% REVAR vs 32% OSR), with an odds ratio of 0.63 for REVAR (95% confidence interval = [0.24, 1.48]; P = .40). No differences in the incidences for secondary interventions for aneurysm- or graft-related complications were noted (22% REVAR vs 22% OSR; P = .99). Kaplan-Meier estimates of 1-, 2-, and 3-year survival rates were also similar (50%, 50%, 42% REVAR vs 54%, 52%, 47% OSR; P = .66). CONCLUSIONS REVAR for rAAA does not seem to conclusively confer either acute or late survival advantages. Routine use of REVAR should be deferred until prospective, randomized trial data become available.

Long-term sac behavior after endovascular abdominal aortic aneurysm repair with the Excluder low-permeability endoprosthesis

PURPOSE Sac regression is a surrogate marker for clinical success in endovascular aneurysm repair (EVAR) and has been shown to be device-specific. The low porosity Excluder endograft (Excluder low-permeability endoprosthesis [ELPE]; W. L. Gore & Associates Inc, Flagstaff, Ariz) introduced in 2004 was reported in early follow-up to be associated with sac regression rates similar to other endografts, unlike the original Excluder which suffered from sac growth secondary to fluid accumulation in the sac. The purpose of this study was to determine whether this behavior is durable in mid-term to long-term follow-up. METHODS Between July 2004 and December 2007, 301 patients underwent EVAR of an abdominal aortic aneurysm (AAA) with the ELPE at two institutions. Baseline sac size was measured by computed tomography (CT) scan at 1 month after repair. Follow-up beyond 1 year was either with a CT or ultrasound scan. Changes in sac size ≥5 mm from baseline were determined to be significant. Endoleak history was assessed with respect to sac behavior using χ(2) and logistic regression analysis. RESULTS Two hundred sixteen patients (mean age 73.6 years and 76% men) had at least 1-year follow-up imaging available for analysis. Mean follow-up was 2.6 years (range, 1-5 years). The average minor-axis diameter was 52 mm at baseline. The proportion of patients with sac regression was similar during the study period: 58%, 66%, 60%, 59%, and 63% at 1 to 5 years, respectively. The proportion of patients with sac growth increased over time to 14.8% at 4-year follow-up. The probability of freedom from sac growth at 4 years was 82.4%. Eighty patients (37.7%) had an endoleak detected at some time during follow-up with 29.6% (16 of 54) residual endoleak rate at 4 years; 13 of the residual 16 endoleaks were type II. All patients with sac growth had endoleaks at some time during the study compared with only 18% of patients with sac regression (P < .0001). CONCLUSION A sustained sac regression after AAA exclusion with ELPE is noted up to 5-year follow-up. Sac enlargement was observed only in the setting of a current or previous endoleak, with no cases of suspected hygroma formation noted.

Prior endovascular abdominal aortic aneurysm repair provides no survival benefits when the aneurysm ruptures

OBJECTIVE It has been proposed that prior endovascular abdominal aortic aneurysm (AAA) repair (EVAR) confers protective effects in the setting of ruptured AAA (rAAA). This study was conducted to compare outcomes of rAAA repairs in patients with and without prior EVAR. METHODS A retrospective review identified 18 patients with (group 1) and 233 patients without (group 2) antecedent EVAR who presented with rAAA from January 2001 to December 2008. Patient characteristics and perioperative variables were noted and the outcomes were compared. Multiple logistic regression was used to identify factors contributing to morbidity and mortality and Kaplan-Meier analyses to estimate late survival rates. RESULTS Baseline characteristics were similar between groups. Mean age was 78 years in group 1 and 74.8 years in group 2 (P=.17). Men comprised 83.3% of patients in group 1 and 77.3% in group 2 (P=.77). Hemodynamic instability at rAAA was noted with similar frequency between groups, 55.6% vs 52.6%, respectively (P=.99). Mean time from EVAR to rAAA was 4.0 years and from last follow-up computed tomography (CT) 1.2 years. The devices involved were Ancure (Guidant, Menlo Park, Calif) (9), AneuRx (Medtronic, Minneapolis, Minn) (5), Zenith (Cook Medical Inc, Bloomington, Ind) (3), and Excluder (W.L Gore, Flagstaff, Ariz) (1). Mean preoperative AAA size was 6.4 cm in group 1. All but 1 patient had an endoleak at the time of rupture. Of 14 patients with CT follow-up, only 3 patients had a known increase in size (≥5 mm) and only 3 were known to have an endoleak. Fifteen patients were treated by a single intervention, whereas 3 patients underwent multiple procedures. In group 2, open repair was performed in 218 patients and EVAR in 15. Morbidity (66.7% vs 56.7%) and in-hospital mortality (38.9% vs 36.9%) were nearly identical between groups. One-year survival rates (27.8% vs 48.2%; P=.15) were also similar. The mortality rates for EVAR for primary rAAA was 20% as compared to 38.1% for open repair for rAAAs (P=.27). CONCLUSION rAAA remains a lethal problem in patients with and without prior EVAR alike. An existing endograft provides neither acute nor 1-year survival benefits after rAAA repairs. Prediction of patients at risk for rupture post-EVAR is difficult, as only a minority of patients had a known prior endoleak or sac enlargement.

Delayed open conversions after endovascular abdominal aortic aneurysm repair

OBJECTIVE Secondary interventions after endovascular aneurysm repair (EVAR) remain a concern. Most are simple catheter-based procedures, but in some instances, open conversions (OCs) are required and carry a worse outcome. We reviewed our experience to characterize these OCs. METHODS A retrospective review was conducted of all patients who underwent an OC after a previous EVAR for an aneurysm-related indication from 2001 to 2010. Clinical outcomes are reported. RESULTS Data were reviewed for 44 patients (77% men) with a mean age of 74 years (range, 55-90 years). The average time from EVAR to the first OC was 45 months (range, 2-190 months). In six patients (14%), the initial EVAR was at another institution. The endografts used were Ancure in 16, Excluder in 13, AneuRx in eight, Zenith in three, Lifepath in one, Renu in one, and undetermined in two. Twenty-two patients had previously undergone a total of 32 endovascular reinterventions before their index OC. Indications for OC were aneurysm expansion in 28 (64%), rupture in 12 (27%), and infection in four (9%). The endograft was preserved in situ in 10 patients (23%). Explantation was partial in 18 (41%) or complete in 16 (36%). Endograft preservation was used for type II endoleak in all but one patient by selective ligation of the culprit arteries (lumbar in four, inferior mesenteric artery in five, and middle sacral in one). Proximal neck banding was performed in one type Ia endoleak. Overall morbidity was 55%, and mortality was 18%. No deaths occurred in a subgroup of patients who underwent endograft preservation with selective ligation of culprit vessels for type II endoleak. Intraoperative complications included bowel injury in two, bleeding in two, splenectomy in one, and ureteral injury in one. At a mean follow-up of 20 months, two patients underwent additional procedures after the index OC: one after endograft preservation and one after partial explantation. None of the patients who underwent elective OC with endograft preservation required subsequent endograft explantation. CONCLUSIONS Most OCs after EVAR are associated with significant morbidity and mortality, except when electively treating an isolated type II endoleak with ligation of branches and preservation of the endograft.

Outcomes of endovascular abdominal aortic aneurysm repair in high-risk patients

OBJECTIVE Although the endovascular aneurysm repair trial 2 (EVAR-2) demonstrated no benefit of EVAR in high-risk (HR) patients, EVAR is still performed widely in this patient cohort. This study compares the midterm outcomes after EVAR in HR patients with those in normal-risk (NR) patients. In turn, these data are compared with the EVAR-2 data. METHODS A retrospective review from January 2006 to December 2013 identified 247 patients (75 HR [30.4%], 172 NR [69.6%]) who underwent elective EVAR for infrarenal aortic aneurysm in an academic tertiary institution and its affiliated Veterans Administration hospital. The same HR criteria used in the EVAR-2 trial were employed. Overall survival, graft-related complications, and reintervention rates were estimated by the Kaplan-Meier method. HR group outcomes were compared with the EVAR-2 data. RESULTS HR patients had a larger abdominal aortic aneurysm size and had a higher prevalence of cardiac disease (P < .01), chronic obstructive pulmonary disease (P = .02), renal insufficiency (P < .01), and cancer (P < .01). Use of aspirin (63% HR vs 66% NR; P = .6), statin (83% HR vs 72% NR; P = .2), and beta-blockers (71% HR vs 60% NR; P = .2) was similar; in the EVAR-2 trial, the corresponding use of these medications was 58%, 42%, and not available, respectively. Perioperative mortality (0% HR vs 1.2% NR; P = 1.0) and early complication rates (4% HR vs 6% NR; P = .8) were similar. In contrast, perioperative mortality in the EVAR-2 trial was 9%. At a mean follow-up of 3 years, the incidence rates of delayed secondary interventions for aneurysm- or graft-related complications were 7% for HR patients and 10% for NR patients (P = .5). The 1-, 2-, and 4-year survival rates in HR patients (85%, 77%, 65%) were lower than those in NR patients (97%, 97%, 93%; P < .001), but this was more favorable compared with a 36% 4-year survival in the EVAR-2 trial. No difference was seen in long-term reintervention-free survival in HR and NR patients (P = .8). Backward stepwise logistic regression analysis identified five prognostic indicators for post-EVAR death: age, chronic kidney disease stages 4 and 5, congestive heart failure, home oxygen use, and current cancer therapy. CONCLUSIONS EVAR can be performed in patients unfit for open surgical repair with excellent early survival and long-term durability. These outcomes in the HR group compare more favorably to the EVAR-2 trial data. However, not all HR patients for open surgical repair derive the benefit from EVAR. The decision to proceed with EVAR in HR patients should be individualized, depending on the number and severity of risk factors.

SEARCHING FOR NARROW EMISSION LINES IN X-RAY SPECTRA: COMPUTATION AND METHODS

The detection and quantification of narrow emission lines in X-ray spectra is a challenging statistical task. The Poisson nature of the photon counts leads to local random fluctuations in the observed spectrum that often result in excess emission in a narrow band of energy resembling a weak narrow line. From a formal statistical perspective, this leads to a (sometimes highly) multimodal likelihood. Many standard statistical procedures are based on (asymptotic) Gaussian approximations to the likelihood and simply cannot be used in such settings. Bayesian methods offer a more direct paradigm for accounting for such complicated likelihood functions, but even here multimodal likelihoods pose significant computational challenges. The new Markov chain Monte Carlo (MCMC) methods developed in 2008 by van Dyk and Park, however, are able to fully explore the complex posterior distribution of the location of a narrow line, and thus provide valid statistical inference. Even with these computational tools, standard statistical quantities such as means and standard deviations cannot adequately summarize inference and standard testing procedures cannot be used to test for emission lines. In this paper, we use new efficient MCMC algorithms to fit the location of narrow emission lines, we develop new statistical strategies for summarizing highly multimodal distributions and quantifying valid statistical inference, and we extend the method of posterior predictive p-values proposed by Protassov and coworkers to test for the presence of narrow emission lines in X-ray spectra. We illustrate and validate our methods using simulation studies and apply them to the Chandra observations of the high-redshift quasar PG 1634+706.

Coffee consumption patterns in Korean adults: The Korean national health and nutrition examination survey (2001-2011)

We examined coffee consumption patterns over the past decade among Korean adults. This study was based on seven different cross-sectional data from the Korean National Health and Nutrition Examination Survey (KNHANES) between 2001 and 2011 (17,367 men and 23,591 women aged 19-103 y, mean 48.1 y). Information on frequency and type of coffee consumption was derived from frequency questionnaires or 24-hour recalls. For the study period, the prevalence of daily coffee consumption increased by 20.3% (from 54.6 to 65.7%; p<0.001). For those who consumed 2 or more cups of coffee daily, it dramatically increased by 48.8% (from 29.1 to 43.3%; p<0.001). The instant coffee mix was consumed the most frequently by Korean adults, and it was on the increasing trend among people who were middle aged or older (>=40 y), while it was on the slowdown in young men or on the declining trend in young women. Brewed coffee consumption had an increasing trend by all age groups in recent years. Especially, there was a rapid increase in brewed coffee consumption among young women (strongly) and young men. The instant coffee mix that contains non-dairy creamer and/or sugar still takes up a significant portion of coffee consumption in Korea, which may result in weight gain and insulin resistance, and potential benefits of coffee may be offset. Given high prevalence of coffee consumption in Korea, nutrition education should be conducted to help people (especially the elderly) to make healthy coffee drinking habits.