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Determining the effective sample size of a parametric prior.

ABSTRACT: We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the logarithm of each distribution, and the posterior minimizing the distance defines the effective sample size of the prior. For cases where the distance cannot be computed analytically, we provide a numerical approximation based on Monte Carlo simulation. We provide general guidelines for application, illustrate the method in several standard cases where the answer seems obvious, and then apply it to some nonstandard settings.

SUBMITTER: Morita S

PROVIDER: S-EPMC3081791 | biostudies-literature | 2008 Jun

REPOSITORIES: biostudies-literature

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Determining the effective sample size of a parametric prior.

Morita Satoshi S Thall Peter F PF Müller Peter P

Biometrics 20070830 2

We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the l ...[more]

PMID: 17764481

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Project description:BackgroundThe current CONSORT guidelines for reporting pilot trials do not recommend hypothesis testing of clinical outcomes on the basis that a pilot trial is under-powered to detect such differences and this is the aim of the main trial. It states that primary evaluation should focus on descriptive analysis of feasibility/process outcomes (e.g. recruitment, adherence, treatment fidelity). Whilst the argument for not testing clinical outcomes is justifiable, the same does not necessarily apply to feasibility/process outcomes, where differences may be large and detectable with small samples. Moreover, there remains much ambiguity around sample size for pilot trials.MethodsMany pilot trials adopt a 'traffic light' system for evaluating progression to the main trial determined by a set of criteria set up a priori. We construct a hypothesis testing approach for binary feasibility outcomes focused around this system that tests against being in the RED zone (unacceptable outcome) based on an expectation of being in the GREEN zone (acceptable outcome) and choose the sample size to give high power to reject being in the RED zone if the GREEN zone holds true. Pilot point estimates falling in the RED zone will be statistically non-significant and in the GREEN zone will be significant; the AMBER zone designates potentially acceptable outcome and statistical tests may be significant or non-significant.ResultsFor example, in relation to treatment fidelity, if we assume the upper boundary of the RED zone is 50% and the lower boundary of the GREEN zone is 75% (designating unacceptable and acceptable treatment fidelity, respectively), the sample size required for analysis given 90% power and one-sided 5% alpha would be around n = 34 (intervention group alone). Observed treatment fidelity in the range of 0-17 participants (0-50%) will fall into the RED zone and be statistically non-significant, 18-25 (51-74%) fall into AMBER and may or may not be significant and 26-34 (75-100%) fall into GREEN and will be significant indicating acceptable fidelity.DiscussionIn general, several key process outcomes are assessed for progression to a main trial; a composite approach would require appraising the rules of progression across all these outcomes. This methodology provides a formal framework for hypothesis testing and sample size indication around process outcome evaluation for pilot RCTs.

Project description:Eradication or local extinction of the human parasite Schistosoma mansoni is a goal for many control programs. Population genetic analyses are helping to evaluate and guide these efforts, yet what to sample, how to sample and how densely to sample is not well established. We determined the S. mansoni allele frequency profile of nearly all infected inhabitants in two small Brazilian communities and created sub-samples representing 5-50% of all detected human infections (infrapopulations). Samples were selected at random with replacement, and each size class was replicated 100 times. Mean pairwise differentiation for all infrapopulations (Di) and the variance effective population size (Ne) were calculated for each sample. Prior to community-wide treatment, the true mean Di was moderate (0.095-0.123) and Ne large (>30,000). Most samples of <50% of those infected produced estimates outside of 5% of the true value. For estimates within 10%, sample sizes of >15% of all infrapopulations were required. At the 3 year follow-up after treatment, the Di increased and Ne was reduced by >15 fold. At this time sampling of >30-45% was needed to achieve the same accuracy. Following a second treatment and 4 years from baseline, the Di further increased and Ne decreased with little change in the sampling effort required. Extensive sampling is required for accurate estimates of these important population parameters. Characteristics such as population census size, infection prevalence, the community's treatment history and the degree of infrapopulation differentiation should be taken into account. The intensity of infection was weakly correlated with the ability of a single infrapopulation to represent the component population (Dic), indicating a tendency toward random acquisition of parasite genotypes. This also suggests that targeted sampling from those most heavily infected will better represent the genetic diversity of the whole community than a random sample of infrapopulations.

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Determining the effective sample size of a parametric prior.

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Determining the effective sample size of a parametric prior.

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