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How many more? Sample size determination in studies of morphological integration and evolvability.

ABSTRACT: 1. The variational properties of living organisms are an important component of current evolutionary theory. As a consequence, researchers working on the field of multivariate evolution have increasingly used integration and evolvability statistics as a way of capturing the potentially complex patterns of trait association and their effects over evolutionary trajectories. Little attention has been paid, however, to the cascading effects that inaccurate estimates of trait covariance have on these widely used evolutionary statistics. 2. Here, we analyze the relationship between sampling effort and inaccuracy in evolvability and integration statistics calculated from 10-trait matrices with varying patterns of covariation and magnitudes of integration. We then extrapolate our initial approach to different numbers of traits and different magnitudes of integration and estimate general equations relating the inaccuracy of the statistics of interest to sampling effort. We validate our equations using a dataset of cranial traits, and use them to make sample size recommendations. 3. Our results suggest that highly inaccurate estimates of evolvability and integration statistics resulting from small sample sizes are likely common in the literature, given the sampling effort necessary to properly estimate them. We also show that patterns of covariation have no effect on the sampling properties of these statistics, but overall magnitudes of integration interact with sample size and lead to varying degrees of bias, imprecision, and inaccuracy. 4. Finally, we provide R functions that can be used to calculate recommended sample sizes or to simply estimate the level of inaccuracy that should be expected in these statistics, given a sampling design.

SUBMITTER: Grabowski M

PROVIDER: S-EPMC5423670 | biostudies-literature | 2017 May

REPOSITORIES: biostudies-literature

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How many more? Sample size determination in studies of morphological integration and evolvability.

Grabowski Mark M Porto Arthur A

Methods in ecology and evolution 20161107 5

1. The variational properties of living organisms are an important component of current evolutionary theory. As a consequence, researchers working on the field of multivariate evolution have increasingly used integration and evolvability statistics as a way of capturing the potentially complex patterns of trait association and their effects over evolutionary trajectories. Little attention has been paid, however, to the cascading effects that inaccurate estimates of trait covariance have on these ...[more]

PMID: 28503291

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Project description:BACKGROUND: Research for developing search strategies to retrieve high-quality clinical journal articles from MEDLINE is expensive and time-consuming. The objective of this study was to determine the minimal number of high-quality articles in a journal subset that would need to be hand-searched to update or create new MEDLINE search strategies for treatment, diagnosis, and prognosis studies. METHODS: The desired width of the 95% confidence intervals (W) for the lowest sensitivity among existing search strategies was used to calculate the number of high-quality articles needed to reliably update search strategies. New search strategies were derived in journal subsets formed by 2 approaches: random sampling of journals and top journals (having the most high-quality articles). The new strategies were tested in both the original large journal database and in a low-yielding journal (having few high-quality articles) subset. RESULTS: For treatment studies, if W was 10% or less for the lowest sensitivity among our existing search strategies, a subset of 15 randomly selected journals or 2 top journals were adequate for updating search strategies, based on each approach having at least 99 high-quality articles. The new strategies derived in 15 randomly selected journals or 2 top journals performed well in the original large journal database. Nevertheless, the new search strategies developed using the random sampling approach performed better than those developed using the top journal approach in a low-yielding journal subset. For studies of diagnosis and prognosis, no journal subset had enough high-quality articles to achieve the expected W (10%). CONCLUSION: The approach of randomly sampling a small subset of journals that includes sufficient high-quality articles is an efficient way to update or create search strategies for high-quality articles on therapy in MEDLINE. The concentrations of diagnosis and prognosis articles are too low for this approach.

Project description:BackgroundBefore conducting a microarray experiment, one important issue that needs to be determined is the number of arrays required in order to have adequate power to identify differentially expressed genes. This paper discusses some crucial issues in the problem formulation, parameter specifications, and approaches that are commonly proposed for sample size estimation in microarray experiments. Common methods for sample size estimation are formulated as the minimum sample size necessary to achieve a specified sensitivity (proportion of detected truly differentially expressed genes) on average at a specified false discovery rate (FDR) level and specified expected proportion (pi1) of the true differentially expression genes in the array. Unfortunately, the probability of detecting the specified sensitivity in such a formulation can be low. We formulate the sample size problem as the number of arrays needed to achieve a specified sensitivity with 95% probability at the specified significance level. A permutation method using a small pilot dataset to estimate sample size is proposed. This method accounts for correlation and effect size heterogeneity among genes.ResultsA sample size estimate based on the common formulation, to achieve the desired sensitivity on average, can be calculated using a univariate method without taking the correlation among genes into consideration. This formulation of sample size problem is inadequate because the probability of detecting the specified sensitivity can be lower than 50%. On the other hand, the needed sample size calculated by the proposed permutation method will ensure detecting at least the desired sensitivity with 95% probability. The method is shown to perform well for a real example dataset using a small pilot dataset with 4-6 samples per group.ConclusionsWe recommend that the sample size problem should be formulated to detect a specified proportion of differentially expressed genes with 95% probability. This formulation ensures finding the desired proportion of true positives with high probability. The proposed permutation method takes the correlation structure and effect size heterogeneity into consideration and works well using only a small pilot dataset.

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How many more? Sample size determination in studies of morphological integration and evolvability.

Publications

How many more? Sample size determination in studies of morphological integration and evolvability.

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