|Title||Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.|
|Publication Type||Journal Article|
|Year of Publication||2016|
|Authors||Milanzi, Elasma, Geert Molenberghs, Ariel Alonso, Michael G. Kenward, Geert Verbeke, Anastasios A. Tsiatis, and Marie Davidian|
|Journal||J Biom Biostat|
|Date Published||2016 Feb|
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.
|Alternate Journal||J Biom Biostat|
|Original Publication||Properties of estimators in exponential family settings with observation-based stopping rules.|
|PubMed Central ID||PMC4861245|
|Grant List||P01 CA142538 / CA / NCI NIH HHS / United States |
R01 CA051962 / CA / NCI NIH HHS / United States
R01 CA085848 / CA / NCI NIH HHS / United States
R37 AI031789 / AI / NIAID NIH HHS / United States
Properties of Estimators in Exponential Family Settings with Observation-based Stopping Rules.