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On random sample size, ignorability, ancillarity, completeness, separability, and degeneracy: Sequential trials, random sample sizes, and missing data

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The vast majority of settings for which frequentist statistical properties are derived assume a fixed, a priori known sample size. Familiar properties then follow, such as, for example, the consistency, asymptotic
normality, and efficiency of the sample average for the mean parameter, under a wide range of conditions.
We are concerned here with the alternative situation in which the sample size is itself a random variable
which may depend on the data being collected. Further, the rule governing this may be deterministic or
probabilistic. There are many important practical examples of such settings, including missing data,
sequential trials, and informative cluster size. It is well known that special issues can arise when
evaluating the properties of statistical procedures under such sampling schemes, and much has been
written about specific areas (Grambsch P. Sequential sampling based on the observed Fisher
information to guarantee the accuracy of the maximum likelihood estimator. Ann Stat 1983; 11: 68–77;
Barndorff-Nielsen O and Cox DR. The effect of sampling rules on likelihood statistics. Int Stat Rev 1984;
52: 309–326). Our aim is to place these various related examples into a single framework derived from
the joint modeling of the outcomes and sampling process and so derive generic results that in turn provide
insight, and in some cases practical consequences, for different settings. It is shown that, even in the
simplest case of estimating a mean, some of the results appear counterintuitive. In many examples, the
sample average may exhibit small sample bias and, even when it is unbiased, may not be optimal. Indeed,
there may be no minimum variance unbiased estimator for the mean. Such results follow directly from key
attributes such as non-ancillarity of the sample size and incompleteness of the minimal sufficient statistic of the sample size and sample sum. Although our results have direct and obvious implications for estimation
following group sequential trials, there are also ramifications for a range of other settings, such as random
cluster sizes, censored time-to-event data, and the joint modeling of longitudinal and time-to-event data.
Here, we use the simplest group sequential setting to develop and explicate the main results. Some implications for random sample sizes and missing data are also considered. Consequences for other
related settings will be considered elsewhere.

Keywords: Frequentist inference, generalized sample average, informative cluster size, joint modeling, likelihood inference, missing at random, random cluster size

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Informasi Detail

Judul Seri

Statistical Methods in Medical Research

No. Panggil

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Penerbit

New York : SAGE., 2014

Deskripsi Fisik

Statistical Methods in Medical Research 2014, Vol. 23(1) 11–41

Bahasa

English

ISBN/ISSN

DOI: 10.1177/0962280

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

2014, Vol. 23(1)

Subjek

METODOLOGI PENELITIAN

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

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