Large-sample Normal Approximation Research Articles

Randomized comparison of the combined Sirolimus eluting and endothelial progenitor cell ComboTM stent vs. Biolimus eluting absorbable polymer coated BioMatrix AlphaTM stent in patients undergoing percutaneous coronary intervention. Rationale and study design of the Scandinavian Organization for Randomized Trials with Clinical Outcome (SORT OUT) XI trial: SORT-OUT XI Trial Design.

The biodegradable polymer BioMatrix Alpha™ stent contains biolimus A9 drug which is sirolimus derivative increase in lipophicity. The biodegradable polymer sirolimus eluting Combo™ stent is a dual-therapy sirolimus-eluting and CD34+ antobody coated stent capturing endothelial progenitor cells (EPCs). The main hypothesis of the SORT OUT XI trial was that the biodegradable polymer biolimus A9 BioMatrix Alpha ™ stent is noninferior to the biodegradable polymer sirolimus eluting Combo™ stent in an all-comers population with coronary artery disease undergoing percutaneous coronary intervention (PCI). The SORT OUT XI study was a randomized, multicenter, single blinded, all-comer, 2-arm, noninferiority trial comparing the biodegradable polymer biolimus A9 BioMatrix Alpha™ stent to the biodegradable polymer sirolimus eluting Combo™ stent in three Danish University Hospitals in Western Denmark. The composite primary endpoint was target lesion failure (TLF) within 12 months. TLF was defined as composite of cardiac death, myocardial infarction not related to other than index lesion or target lesion revascularization. Clinically driven event detection was used and no planned follow up was performed. With a sample size of 1,564 patients in each treatment arm, a 2-group large-sample normal approximation test of proportions with a 1-sided 5% significance level will have 90% power to detect noninferiority with a predetermined noninferiority margin of 2.1%. The trial ran from August 14, 2019 to March 19, 2023. A total of 3141 patients were enrolled and randomized 1:1 to Combo™ stent (n=1,573) and BioMatrix Alpha™ stent (n=1,568). Conclusion The SORT OUT XI trial will assess if the biolimus A9 eluting BioMAtrix Alpha™ stent is noninferior to the dual-therapy Combo™ stent with respect to target lesion failure. (ClinicalTrials.gov NCT03952273).

The Locommotion Study (MMY4001): A Prospective, Multinational Study of Real-Life Current Standards of Care in Patients with Relapsed and/or Refractory Multiple Myeloma Who Received at Least 3 Prior Lines of Therapy Including PI, IMiD, and CD38 Monoclonal Antibody Treatment and Documented Disease Progression

The Locommotion Study (MMY4001): A Prospective, Multinational Study of Real-Life Current Standards of Care in Patients with Relapsed and/or Refractory Multiple Myeloma Who Received at Least 3 Prior Lines of Therapy Including PI, IMiD, and CD38 Monoclonal Antibody Treatment and Documented Disease Progression

Interval estimation for Wiener processes based on accelerated degradation test data

Degradation is a primary cause of failures for many materials and products. Although stochastic processes have been widely applied to degradation data, there is a lack of efficient and accurate methods for interval estimation of model parameters and reliability characteristics given limited degradation data. Using the method of generalized pivotal quantities, this study develops interval estimation procedures for fixed-effects and mixed-effects Wiener degradation processes based on accelerated degradation test data. The fixed-effects processes are common for mature products and the mixed-effects model is capable of capturing heterogeneities in an immature product. The constructed confidence intervals are shown to have exact, or asymptotically exact, frequentist coverage probabilities. Extensive simulations are conducted to compare the proposed procedures to other competing methods, including the large sample normal approximation, and the bootstrap. The simulation results reveal that the proposed intervals have satisfactory performance in terms of the coverage probability and the average interval length. The proposed interval estimation procedures are successfully applied to accelerated degradation data from commercial white LEDs.

Randomized clinical comparison of the dual-therapy CD34 antibody-covered sirolimus-eluting Combo stent with the sirolimus-eluting Orsiro stent in patients treated with percutaneous coronary intervention: Rationale and study design of the Scandinavian Organization for Randomized Trials with Clinical Outcome (SORT OUT) X trial

The Combo stent (OrbusNeich, Hoevelaken, the Netherlands) combining an abluminal, bioabsorbable polymer eluting sirolimus with a luminal CD34+ antibody to capture endothelial progenitor cells has been developed to further improve safety and efficacy of coronary interventions. We have designed a large-scale registry-based randomized clinical trial to compare the Combo stent to the Orsiro stent (Biotronik, Bülach, Switzerland) in patients undergoing percutaneous coronary intervention. The SORT OUT X study will randomly assign 3,140 patients to treatment with Combo or Orsiro stents at 3 sites in Western Denmark. Patients are eligible if they are ≥18 years old, have chronic stable coronary artery disease or acute coronary syndromes, and have ≥1 coronary lesion with >50% diameter stenosis requiring treatment with a drug-eluting stent. The primary end point target lesion failure is a composite of cardiac death, myocardial infarction (not related to other than index lesion), or target lesion revascularization within 12 months. Clinically driven event detection will be derived from validated Danish registries. An event rate of 4.2% is assumed in each stent group. With a sample size of 1,570 patients in each treatment arm, a 2-group large-sample normal approximation test of proportions with a 1-sided 5% significance level will have 90% power to detect noninferiority of the Combo stent compared with the Orsiro stent with a predetermined noninferiority margin of 2.1%. The SORT OUT X trial will determine whether the dual-therapy Combo stent is noninferior to the Orsiro stent with respect to clinically driven events (ClinicalTrials.govNCT03216733).

Interval estimation for k-out-of-n load-sharing systems

ABSTRACTLoad-sharing systems are commonly seen in industry; e.g., water pumps in a cooling system. In a load-sharing system, the stress level on each surviving component increases as components fail. The load-sharing nature of the component failure process creates difficulties in statistical inference for the system. This article develops two interval procedures for failure data from load-sharing systems. We assume that the component lifetime under each stress level follows an exponential distribution, a common distribution in reliability engineering. A log-linear link function is used to model the relationship between the stress levels and component lifetimes. In the two proposed interval procedures, we construct confidence intervals for the model parameters by using pivotal quantities and generalized pivotal quantities. Interval estimation for important reliability characteristics including the mean lifetime and the reliability of the load-sharing system is also discussed. A simulation study shows that the confidence intervals produced from the proposed procedures are more accurate compared with traditional approximate interval procedures, such as the large sample normal approximation and the bootstrap. A numerical example is used to demonstrate the performance of the proposed procedures.

Bayesian Life Test Planning for Log-Location-Scale Family of Distributions

This paper describes Bayesian methods for life test planning with censored data from a log-location-scale distribution when prior information of the distribution parameters is available. We use a Bayesian criterion based on the estimation precision of a distribution quantile. A large-sample normal approximation gives a simplified, easy-to-interpret, yet valid approach to this planning problem, where in general no closed-form solutions are available. To illustrate this approach, we present numerical investigations using the Weibull distribution with type II censoring. We also assess the effects of prior distribution choice. A simulation approach of the same Bayesian problem is also presented as a tool for visualization and validation. The validation results generally are consistent with those from the large-sample approximation approach.

Randomized comparison of a sirolimus-eluting Orsiro stent with a biolimus-eluting Nobori stent in patients treated with percutaneous coronary intervention: Rationale and study design of the Scandinavian Organization for Randomized Trials with Clinical Outcome VII trial

Third-generation coronary drug-eluting stents (DES) with biodegradable polymers have been designed to improve safety and efficacy. We designed a large scale registry-based randomized clinical trial to compare 2 third-generation DES: a thin strut, cobalt-chromium DES with silicon carbide-coating releasing sirolimus from a biodegradable polymer (O-SES, Orsiro; Biotronik, Bülach, Switzerland) with the stainless steel biodegradable polymer biolimus-eluting Nobori stents (N-BES, Nobori; Terumo, Tokyo, Japan) in an all-comer patient population. The multicenter SORT OUT VII trial (NCT01879358) randomly assigned 2,530 patients to treatment with biodegradable polymer O-SES or biodegradable polymer N-BES at 3 sites in Western Denmark. Patients were eligible, if they were ≥18 years old; had chronic stable coronary artery disease or acute coronary syndromes; and ≥1 coronary lesion with >50% diameter stenosis, requiring treatment with a DES. The primary end point target lesion failure is a composite of cardiac death, myocardial infarction (not related to other than index lesion), or target lesion revascularization within 12 months. Clinically, driven event detection based on Danish registries will be used. An event rate of 6.5% is assumed in each stent group. With a sample size of 1,157 patients in each treatment arm, a 2-group large-sample normal approximation test of proportions with a 1-sided 5% significance level will have 90% power to detect noninferiority of the O-SES compared with the N-BES with a predetermined noninferiority margin of 3.0%. The SORT OUT VII trial will determine whether the biodegradable polymers O-SES is noninferior to the N-BES with respect to driven event.

Confidence intervals for intraclass correlation coefficients in a nonlinear dose-response meta-analysis.

This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the heterogeneity across studies. To interpret the size of heterogeneity, an accurate estimate of ICC and its confidence interval is required. The goal is to apply a recently proposed generic beta-approach for construction the confidence intervals on ICCs for linear mixed effects models to nonlinear mixed effects models using four estimation methods. These estimation methods are the maximum likelihood, second-order generalized estimating equations and two two-step procedures. The beta-approach is compared with a large sample normal approximation (delta method) and bootstrapping. The confidence intervals based on the delta method and the nonparametric percentile bootstrap with various resampling strategies failed in our settings. The beta-approach demonstrates good coverages with both two-step estimation methods and consequently, it is recommended for the computation of confidence interval for ICCs in nonlinear mixed effects models for small studies.

Sample size determination for the parallel model in a survey with sensitive questions

Recently, a new non-randomized parallel design is proposed by Tian (2013) for surveys with sensitive topics. However, the sample size formulae associated with testing hypotheses for the parallel model are not yet available. As a crucial component in surveys, the sample size formulae with the parallel design are developed in this paper by using the power analysis method for both the one- and two-sample problems. We consider both the one- and two-sample problems. The asymptotic power functions and the corresponding sample size formulae for both the one- and two-sided tests based on the large-sample normal approximation are derived. The performance is assessed through comparing the asymptotic power with the exact power and reporting the ratio of the sample sizes with the parallel model and the design of direct questioning. We numerically compare the sample sizes needed for the parallel design with those required for the crosswise and triangular models. Two theoretical justifications are also provided. An example from a survey on ‘sexual practices’ in San Francisco, Las Vegas and Portland is used to illustrate the proposed methods.

Large-sample normal approximation and relevant sensitivity in linear seismic fragility analysis with hierarchically modeled stiffness properties

This paper investigates the potential of the large-sample normal approximation to Bayesian posterior distributions in linear seismic fragility analysis. With the stiffness properties modeled hierarchically, the prior information on the parameters involved in the relevant probability distributions can be updated based on the latest stiffness data acquired, leading to the posterior distributions of these parameters. Using large-sample Bayesian techniques, the posterior distributions may be approximated by normal distributions. The stochastic characteristics of some parameters in the normal distributions are first presented. Specifically, the relationships of the pertinent coefficients of variation and percentage points to the number of the observations for the stiffness properties are examined; a sensitivity analysis with respect to the number of observations is implemented; and the effect of some included distribution types on the stochastic characteristics is analyzed through defined factors. The seismic fragility analysis of a shear frame is then carried out, and comparisons are made between the fragilities from the underlying model and those from the approximate model. The results of the study could be useful in formulating related structural design strategies, provided that adequate amount of the latest stiffness data can be made available through techniques such as structural health monitoring. • Hierarchically modeled stiffness properties. • Large-sample Bayesian techniques in linear seismic fragility analysis. • Comprehensive quantification work relevant to the stochastic characteristics. • Detailed sensitivity analysis with respect to the number of observations. • Illustrated convenient and straightforward application of the formulated approximate model.

Statistical Aspects of Forest Harvesting: Price -Weighted Apportionment Index and Related Inference

Price-Weighted Apportionment Index measures the fit between log demand distribution and log output distribution. We present the asymptotic sampling distribution of Price-Weighted Apportionment Index by assuming a multinomial distribution for the outcome variables. Our results are based mainly on large-sample normal approximation.

Laparoscopic radioisotope-guided sentinel lymph node mapping and excision of the rectum—an experimental study

Patients with a low-risk T1 rectal carcinoma can undergo the therapy of a local excision. In these patients the lymph node (LN) status remains unknown. There is a potential risk of up to 7% for nodal metastasis. To investigate the possibility of using the sentinel lymph node (SLN) concept, an experimental study on pigs was undertaken. The objective was to laparoscopically identify and extract SLNs from the rectum using a radioisotope (RI). The experiment was conducted in 30 pigs, since the sample size calculation indicated that with 30 animals a two-sided 95% confidence interval for a single proportion using the large sample normal approximation would extend at most 0.107 from the observed proportion of 0.9. One milliliter of a mixture of the RI Technetium 99 m (Tc99 m) and patent blue V dye was administered in the rectum endoscopically and after the lapse of 1 h, we laparoscopically identified and excised all SLNs using a laparoscopic gamma camera probe. We found in all operated pigs (n = 30) at least one SLN (lymph node with highest measured counts per second (cps)). In mean we detected 1.6 SLN (range one to three SLNs). In 28 cases, the SLN concept was successful. Sensitivity for detecting SLNs was 93% (n = 28/30), the probe count rate ranged from 600-10,000 cps with a median of 3,800. Minimal invasive mapping and excision of SLN of the rectum using a RI is feasible. The sensitivity for detecting SLN was high (93%). The application of this procedure on humans seems to be possible.

Sample size determination for the non-randomised triangular model for sensitive questions in a survey

Sample size determination is an essential component in public health survey designs on sensitive topics (e.g. drug abuse, homosexuality, induced abortions and pre or extramarital sex). Recently, non-randomised models have been shown to be an efficient and cost effective design when comparing with randomised response models. However, sample size formulae for such non-randomised designs are not yet available. In this article, we derive sample size formulae for the non-randomised triangular design based on the power analysis approach. We first consider the one-sample problem. Power functions and their corresponding sample size formulae for the one- and two-sided tests based on the large-sample normal approximation are derived. The performance of the sample size formulae is evaluated in terms of (i) the accuracy of the power values based on the estimated sample sizes and (ii) the sample size ratio of the non-randomised triangular design and the design of direct questioning (DDQ). We also numerically compare the sample sizes required for the randomised Warner design with those required for the DDQ and the non-randomised triangular design. Theoretical justification is provided. Furthermore, we extend the one-sample problem to the two-sample problem. An example based on an induced abortion study in Taiwan is presented to illustrate the proposed methods.

A Berry-Esseen theorem for hypergeometric probabilities under minimal conditions

In this paper, we consider simple random sampling without replacement from a dichotomous finite population and derive a necessary and sufficient condition on the finite population parameters for a valid large sample Normal approximation to Hypergeometric probabilities. We then obtain lower and upper bounds on the difference between the Normal and the Hypergeometric distributions solely under this necessary and sufficient condition.

Approximating the distribution of the two-stage least squares estimator when the concentration parameter is small

This paper presents a new approximation to the exact sampling distribution of the instrumental variables estimator in simultaneous equations models. It differs from many of the approximations currently available, Edgeworth expansions for example, in that it is specifically designed to work well when the concentration parameter is small. The approximation is remarkable in that simultaneously: (i) it has an extremely simple final form; (ii) in situations for which it is designed it is typically much more accurate than is the large sample normal approximation; and (iii) it is able to capture most of those stylized facts that characterize lack of identification and weak instrument scenarios. The development leading to the approximation is also novel in that it introduces techniques of some independent interest not seen in this literature hitherto.

Bayesian Methods for Planning Accelerated Life Tests

This article describes Bayesian methods for accelerated life test planning with one accelerating variable, when the acceleration model is linear in the parameters, based on censored data from a log-location-scale distribution. We use a Bayesian criterion based on estimation precision of a distribution quantile at a specified use condition to find optimum test plans. We also show how to compute optimized compromise plans that satisfy practical constraints. A large-sample normal approximation provides an easy-to-interpret yet useful simplification to this planning problem. We present a numerical example using the Weibull distribution with type I censoring to illustrate the methods and to examine the effects of the prior distribution, censoring, and sample size. The general equivalence theorem is used to verify that the numerically optimized test plans are globally optimum. The resulting optimum plans are also evaluated using simulation.

Wilcoxon‐type rank‐sum precedence tests: large‐sample approximation and evaluation

AbstractWilcoxon‐type rank‐sum precedence tests are useful alternatives to the precedence life‐test proposed for testing the hypothesis that two lifetime distribution functions are equal. In this paper, we first derive the exact power function under the Lehmann alternative for these tests. We also note that the large‐sample normal approximation for the null distribution is not satisfactory in case of small or moderate sample sizes. Then, we develop an Edgeworth expansion to approximate the significance probabilities. Comparison of normal approximation and Edgeworth approximation for various sample sizes are provided. Finally, an example is presented for illustration. Copyright © 2002 John Wiley & Sons, Ltd.

Bayesian Inference for Some Mixture Problems in Quality and Reliability

This is an expository paper dealing with Bayesian inference for three important mixture problems in quality and reliability. The traditional approach for estimation in these situations is the method of maximum likelihood. The corresponding inference based on large-sample theory can, however, be misleading in situations where the large-sample normal approximation is not adequate. The Bayesian approach, on the other hand, has been viewed as computationally intractable due to the complex nature of mixture models. Recent advances in Bayesian computational methods have alleviated this problem considerably. We illustrate the use of data augmentation methods for doing Bayesian inference in these applications. While the framework is formally Bayesian in nature, it can also be viewed as a computational device for calculating the likelihood function and doing likelihood-based inference. An additional advantage of data augmentation methods is that no further complications arise when failure time data are grouped or censored.

Exact Statistical Inference for Group Sequential Trials

This paper considers clinical trials comparing two treatments with dichotomous responses where the data are examined periodically for early evidence of treatment difference. The existing group sequential methods for such trials are based on the large-sample normal approximation to the joint distribution of the estimators of treatment difference over interim analyses. We demonstrate through extensive numerical studies that, for small and even moderate-sized trials, these approximate procedures may lead to tests with supranominal size (mainly when unpooled estimators of variance are used) and confidence intervals with under-nominal coverage probability. We then study exact methods for group sequential testing, repeated interval estimation, and interval estimation following sequential testing. The new procedures can accommodate any treatment allocation rules. An example using real data is provided.

KENDALL'S TAU AND CONTINGENCY TABLES

SummaryKendall's tau is a coefficient of concordance between two rankings of n objects. Its definition and large sample normal approximation are easily extended to the case where one of the rankings contains ties. In this paper, definition and normal approximation are extended further to the case where both rankings contain ties. The results are applied to give a fully distribution‐free test for two‐way contingency tables with ordered categories.