Dataset Information

Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.

ABSTRACT: Often, sample size is not fixed by design. A key example is a sequential trial with a stopping rule, where stopping is based on what has been observed at an interim look. While such designs are used for time and cost efficiency, and hypothesis testing theory has been well developed, estimation following a sequential trial is a challenging, still controversial problem. Progress has been made in the literature, predominantly for normal outcomes and/or for a deterministic stopping rule. Here, we place these settings in a broader context of outcomes following an exponential family distribution and, with a stochastic stopping rule that includes a deterministic rule and completely random sample size as special cases. It is shown that the estimation problem is usually simpler than often thought. In particular, it is established that the ordinary sample average is a very sensible choice, contrary to commonly encountered statements. We study (1) The so-called incompleteness property of the sufficient statistics, (2) A general class of linear estimators, and (3) Joint and conditional likelihood estimation. Apart from the general exponential family setting, normal and binary outcomes are considered as key examples. While our results hold for a general number of looks, for ease of exposition, we focus on the simple yet generic setting of two possible sample sizes, N=n or N=2n.

SUBMITTER: Milanzi E

PROVIDER: S-EPMC4861245 | biostudies-literature | 2016 Feb

REPOSITORIES: biostudies-literature

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Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.

Milanzi Elasma E Molenberghs Geert G Alonso Ariel A Kenward Michael G MG Verbeke Geert G Tsiatis Anastasios A AA Davidian Marie M

Journal of biometrics & biostatistics 20160125 1

Often, sample size is not fixed by design. A key example is a sequential trial with a stopping rule, where stopping is based on what has been observed at an interim look. While such designs are used for time and cost efficiency, and hypothesis testing theory has been well developed, estimation following a sequential trial is a challenging, still controversial problem. Progress has been made in the literature, predominantly for normal outcomes and/or for a deterministic stopping rule. Here, we pl ...[more]

PMID: 27175309

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Project description:BackgroundRe-randomisation trials involve re-enrolling and re-randomising patients for each new treatment episode they experience. They are often used when interest lies in the average effect of an intervention across all the episodes for which it would be used in practice. Re-randomisation trials are often analysed using independence estimators, where a working independence correlation structure is used. However, research into independence estimators in the context of re-randomisation has been limited.MethodsWe performed a simulation study to evaluate the use of independence estimators in re-randomisation trials. We focussed on a continuous outcome, and the setting where treatment allocation does not affect occurrence of subsequent episodes. We evaluated different treatment effect mechanisms (e.g. by allowing the treatment effect to vary across episodes, or to become less effective on re-use, etc), and different non-enrolment mechanisms (e.g. where patients who experience a poor outcome are less likely to re-enrol for their second episode). We evaluated four different independence estimators, each corresponding to a different estimand (per-episode and per-patient approaches, and added-benefit and policy-benefit approaches).ResultsWe found that independence estimators were unbiased for the per-episode added-benefit estimand in all scenarios we considered. We found independence estimators targeting other estimands (per-patient or policy-benefit) were unbiased, except when there was differential non-enrolment between treatment groups (i.e. when different types of patients from each treatment group decide to re-enrol for subsequent episodes). We found the use of robust standard errors provided close to nominal coverage in all settings where the estimator was unbiased.ConclusionsCareful choice of estimand can ensure re-randomisation trials are addressing clinically relevant questions. Independence estimators are a useful approach, and should be considered as the default estimator until the statistical properties of alternative estimators are thoroughly evaluated.

Dataset Information

Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.

Publications

Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.

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