Interim analysis of sequential estimation‐adjusted urn models with sample size re‐estimation

Author(s):  
Jun Yu ◽  
Dejian Lai
Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.


2006 ◽  
Vol 16 (1) ◽  
pp. 340-369 ◽  
Author(s):  
Li-X. Zhang ◽  
Feifang Hu ◽  
Siu Hung Cheung

1992 ◽  
Vol 71 (1) ◽  
pp. 3-14 ◽  
Author(s):  
John E. Overall ◽  
Robert S. Atlas

A statistical model for combining p values from multiple tests of significance is used to define rejection and acceptance regions for two-stage and three-stage sampling plans. Type I error rates, power, frequencies of early termination decisions, and expected sample sizes are compared. Both the two-stage and three-stage procedures provide appropriate protection against Type I errors. The two-stage sampling plan with its single interim analysis entails minimal loss in power and provides substantial reduction in expected sample size as compared with a conventional single end-of-study test of significance for which power is in the adequate range. The three-stage sampling plan with its two interim analyses introduces somewhat greater reduction in power, but it compensates with greater reduction in expected sample size. Either interim-analysis strategy is more efficient than a single end-of-study analysis in terms of power per unit of sample size.


Author(s):  
F. J. Anscombe

In a previous large-sample treatment of sequential estimation (1), it was shown that in certain circumstances, when there was only one unknown parameter in the distribution of the observations, an estimation formula valid for fixed sample sizes remained valid when the sample size was determined by a sequential stopping rule. The proof was heuristic, in that it depended on an application of the central limit theorem of which the justification was not obvious. Another proof has recently been given by Cox (2) (in the course of deriving a correction term to my result). Dr Cox pointed out to me that this work suggested that fixed-sample-size formulae might be valid generally for sequential sampling, provided the sample size was large. In establishing a proposition to that effect, I have now been able to by-pass some of the complexity of my previous approach by concentrating attention on a condition of ‘uniform continuity in probability’ to be satisfied by the statistic used. Theorem 1 is the basic result, which is applied in Theorem 2 to determine a sequential stopping rule giving required accuracy of estimation of an unknown parameter. Theorems 3–6 indicate some situations in which the uniform continuity condition postulated in Theorems 1 and 2 is satisfied. A few examples are discussed.


1998 ◽  
Vol 23 (6) ◽  
pp. 594-599 ◽  
Author(s):  
Gary E. Mccall ◽  
William C. Byrnes ◽  
Arthur L. Dickinson ◽  
Steven J. Fleck

This study aimed to determine the skeletal muscle fiber sample size required for a reliable, valid representation of an individual's average fiber area and capillary contacts (CC) per fiber. Biopsies were obtained from the biceps brachii of 11 college-age, recreational resistance-trained men in conjunction with a study investigating how muscle morphology changed after 12 weeks of resistance training. The effect of additional measurements on the rolling cumulative means for fiber area and CC per fiber was evaluated using sequential estimation analysis. Results showed that group cumulative mean and standard deviation had stabilized by 50 fiber measurements per individual for type I and II fibers and CC per fiber. Significant correlations (.96-.99; p < .05) existed between the 50th and 95th/100th cumulative individual means. These results indicate that a typical skeletal muscle needle biopsy would be sufficient to characterize type I and II fiber areas and CC per fiber of an individual in most subject populations, although the required sample size for characterizing fiber subtypes might be different. Key words: muscle biopsy; sequential estimation analysis


Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 614-614 ◽  
Author(s):  
Paul Richardson ◽  
Nancy Kernan ◽  
Marcie Tomblyn ◽  
Paul Martin ◽  
Sally Arai ◽  
...  

Abstract Introduction: Veno-occlusive disease (VOD) with multi-organ failure (MOF) has an extremely poor prognosis, with mortality at day (D) +100 after SCT ≥80%. A prior randomized phase 2 study (n=150) comparing 2 doses of defibrotide (DF) demonstrated complete response (CR) in 46% of patients (pts) with severe VOD, and D+100 survivorship of 41%. CR with DF therapy correlated closely with survival, with >90% of pts achieving a CR living to D+100 post SCT, and best dose of DF was 25 mg/kg/day. A large, multi-center, international phase 3 trial is now being conducted, comparing the use of DF (6.25 mg/kg IV q6h) in pts with VOD/MOF post SCT to a rigorous historical control. Methods: Eligible pts (adult and pediatric) met Baltimore criteria (total bilirubin ≥ 2.0 mg/dL; and ≥ 2 of the following: hepatomegaly, ascites or 5% weight gain) by D +21 and were diagnosed with either severe renal or pulmonary dysfunction by D +28. Exclusion criteria included pre-existing cirrhosis, viral hepatitis, GvHD involving liver or gut, clinically significant bleeding or inability to maintain blood pressure except with multiple pressors. To create the comparator arm, each site performed a retrospective screen of SCT pts: cohorts of 133 pts were sequentially reviewed. All pts who met Baltimore criteria and had MOF were subsequently assessed by 2 independent experts blinded to outcome data (CR, survival and/or autopsy information) to confirm eligibility. Projected sample size (80 in each group) was based on an estimated 20% survivorship to D+100 in the historical control arm compared to 40% in the DF-treated group. Interim analysis (after 40 pts were enrolled) is being performed to confirm treatment difference and sample size. Results: In the DF-treated group, 52 pts have been enrolled across 36 sites to date. The interim analysis of D+100 survival and CR is in process and final analysis will follow upon study completion. For the historical control database, 4065 charts have been reviewed to date. In the treatment arm, toxicities related to DF have been minimal and generally manageable, although 2 pts with intercurrent severe coagulopathy, sepsis and platelet-refractory progressive VOD/MOF experienced serious hemorrhage (CNS and GI). Conclusions: This phase 3 study of DF for the treatment of severe VOD post SCT is the first comparative study of its kind in this life-threatening disease. DF has been generally well tolerated and toxicity has been consistent with prior studies, with CR rate and D+100 survival data pending. Results from this novel design should provide validation of DF as therapy for established VOD/MOF in pts with a high risk of mortality and for whom no effective alternative treatment exists.


2000 ◽  
Vol 139 (4) ◽  
pp. 0161-0165
Author(s):  
Susan S. Ellenberg

2007 ◽  
Vol 25 (18_suppl) ◽  
pp. 6513-6513
Author(s):  
R. A. Wilcox ◽  
G. H. Guyatt ◽  
V. M. Montori

6513 Background: Investigators finding a large treatment effect in an interim analysis may terminate a randomized trial (RCT) earlier than planned. A systematic review (Montori et. al., JAMA 2005; 294: 2203–2209) found that RCTs stopped early for benefit are poorly reported and may overestimate the true treatment affect. The extent to which RCTs in oncology stopped early for benefit share similar concerns remains unclear. Methods: We selected RCTs in oncology which had been reported in the original systematic review and reviewed the study characteristics, features related to the decision to monitor and stop the study early (sample size, interim analyses, monitoring and stopping rules), and the number of events and the estimated treatment effects. Results: We found 29 RCTs in malignant hematology (n=6) and oncology (n=23), 52% published in 2000–2004 and 41% in 3 high-impact medical journals (New England Journal of Medicine, Lancet, JAMA). The majority (79%) of trials reported a planned sample size and, on average, recruited 67% of the planned sample size (SD 31%). RCTs reported (1) the planned sample size (n=20), (2) the interim analysis at which the study was terminated (n=16), and (3) whether the decision to stop the study prematurely was informed by a stopping rule (n=16); only 13 reported all three. There was a highly significant correlation between the number of events and the treatment effect (r=0.68, p=0.0007). The odds of finding a large treatment effect (a relative risk < median of 0.54, IQR 0.3–0.7) when studies stopped after a few events (no. events < median of 54 events, IQR 22–125) was 6.2 times greater than when studies stopped later. Conclusions: RCTs in oncology stopped early for benefit tend to report large treatment effects that may overestimate the true treatment effect, particularly when the number of events driving study termination is small. Also, information pertinent to the decision to stop early was inconsistently reported. Clinicians and policymakers should interpret such studies with caution, especially when information about the decision to stop early is not provided and few events occurred. No significant financial relationships to disclose.


2003 ◽  
Vol 37 (3) ◽  
pp. 317-320 ◽  
Author(s):  
Simon Kirby ◽  
Scott McBride ◽  
Lohita Puvanarajan

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