2012
DOI: 10.1080/07474946.2012.652014
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Boundary Crossing Random Walks, Clinical Trials, and Multinomial Sequential Estimation

Abstract: A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial random walks that are observed until they reach a boundary. Clinical trials are shown to be representable within this scheme and an application to the estimation of the multinomial probabilities following multinomial clinical trials is presented.

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Cited by 2 publications
(4 citation statements)
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“…We also end with caution against the use of the canonical joint distribution and the estimators given here in some settings. In particular, though we included an example with Bernoulli data to illustrate how the methodology can be applied in that setting, for such studies designs leveraging exact binomial densities and associated estimators should likely be preferred for all but the largest trial sample sizes (see, e.g., Porcher and Desseaux 5 for the single-arm case, while Bibbona and Rubba 47 provide relevant results for other designs). In addition, for time-to-event data in small-sample settings, direct simulation of study data and evaluation of estimator performance in this way (rather than using the canonical approximation) would be advisable.…”
Section: Discussionmentioning
confidence: 99%
“…We also end with caution against the use of the canonical joint distribution and the estimators given here in some settings. In particular, though we included an example with Bernoulli data to illustrate how the methodology can be applied in that setting, for such studies designs leveraging exact binomial densities and associated estimators should likely be preferred for all but the largest trial sample sizes (see, e.g., Porcher and Desseaux 5 for the single-arm case, while Bibbona and Rubba 47 provide relevant results for other designs). In addition, for time-to-event data in small-sample settings, direct simulation of study data and evaluation of estimator performance in this way (rather than using the canonical approximation) would be advisable.…”
Section: Discussionmentioning
confidence: 99%
“…In a few special cases, some ad‐hoc methods that were designed for sequential analysis were shown to provide unbiased estimators for a single trajectory of certain killed processes (Girshick et al. , 1946; Ferebee, 1983; Bibbona & Rubba, 2012). It would be useful to find unbiased estimators for non‐trivial diffusions also, and to provide a detailed comparison with the likelihood approach, especially for those experiments where only one trajectory is available.…”
Section: Discussionmentioning
confidence: 99%
“…This happens for the WD, but also for the OU process when the parameter β is known and only μ and σ are estimated (Bibbona et al. , 2008) and of some discrete models such as multidimensional random walks (Bibbona & Rubba, 2012). The same ‘optional sampling effect’ was noticed in MLE following a sequential test (Whitehead, 1986) in clinical trials (Jung & Kim, 2004) and is known for binomial samples since Girshick et al.…”
Section: Examplesmentioning
confidence: 99%
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