Boundary Crossing Random Walks, Clinical Trials, and Multinomial Sequential Estimation

Bibbona, Enrico; Rubba, Alessandro

doi:10.1080/07474946.2012.652014

Cited by 2 publications

(4 citation statements)

References 18 publications

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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%

Point estimation following a two-stage group sequential trial

Grayling

Wason

2022

Stat Methods Med Res

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Repeated testing in a group sequential trial can result in bias in the maximum likelihood estimate of the unknown parameter of interest. Many authors have therefore proposed adjusted point estimation procedures, which attempt to reduce such bias. Here, we describe nine possible point estimators within a common general framework for a two-stage group sequential trial. We then contrast their performance in five example trial settings, examining their conditional and marginal biases and residual mean square error. By focusing on the case of a trial with a single interim analysis, additional new results aiding the determination of the estimators are given. Our findings demonstrate that the uniform minimum variance unbiased estimator, whilst being marginally unbiased, often has large conditional bias and residual mean square error. If one is concerned solely about inference on progression to the second trial stage, the conditional uniform minimum variance unbiased estimator may be preferred. Two estimators, termed mean adjusted estimators, which attempt to reduce the marginal bias, arguably perform best in terms of the marginal residual mean square error. In all, one should choose an estimator accounting for its conditional and marginal biases and residual mean square error; the most suitable estimator will depend on relative desires to minimise each of these factors. If one cares solely about the conditional and marginal biases, the conditional maximum likelihood estimate may be preferred provided lower and upper stopping boundaries are included. If the conditional and marginal residual mean square error are also of concern, two mean adjusted estimators perform well.

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Section: Discussionmentioning

confidence: 99%

Point estimation following a two-stage group sequential trial

Grayling

Wason

2022

Stat Methods Med Res

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“…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%

“…the blood pressure or some substance in the blood, but only when it is between some critical limits, whereafter the subject enters a major crisis. The same problem also occurs whenever parameter estimation follows some sequential data acquisition, for example a sequential test (Whitehead, 1986) or a clinical trial (Jung & Kim, 2004; Bibbona & Rubba, 2012). Sequential estimation for i.i.d.…”

Section: Introductionmentioning

confidence: 99%

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Estimation in Discretely Observed Diffusions Killed at a Threshold

Bibbona¹,

Ditlevsen²

2012

Scandinavian J Statistics

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Abstract. Parameter estimation in diffusion processes from discrete observations up to a first‐passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein–Uhlenbeck model for biological relevant parameters can be up to 25–100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first‐passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analysed.

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Boundary Crossing Random Walks, Clinical Trials, and Multinomial Sequential Estimation

Cited by 2 publications

References 18 publications

Point estimation following a two-stage group sequential trial

Point estimation following a two-stage group sequential trial

Estimation in Discretely Observed Diffusions Killed at a Threshold

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