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PubMed1993

Sample size for beginners.

The common failure to include an estimation of sample size in grant proposals imposes a major handicap on applicants, particularly for those proposing work in any aspect of research in the health services. Members of research committees need evidence that a study is of adequate size for there to be a reasonable chance of a clear answer at the end. A simple illustrated explanation of the concepts in determining sample size should encourage the faint hearted to pay more attention to this increasingly important aspect of grantsmanship.

Analysis of Variance↗

PubMed1999

Approximate sample sizes for testing hypotheses about the ratio and difference of two means.

This article deals with a unifying approach to approximate sample size determination for different types of hypotheses formulated in terms of two means of normally distributed data. A simple approximation is given to the sample size required for testing hypotheses about the ratio of the means. The formula includes the situations of testing noninferiority, superiority, or equivalence. We present a more general formula that also covers hypotheses formulated in terms of the difference of means. We show that over a wide range of parameter values the approximation provides reliable sample sizes.

Controlled Clinical Trials as Topic↗

PubMed2005

Power and sample size calculations for genetic case/control studies using gene-centric SNP maps: application to human chromosomes 6, 21, and 22 in three populations.

Power and sample size calculations are critical parts of any research design for genetic association. We present a method that utilizes haplotype frequency information and average marker-marker linkage disequilibrium on SNPs typed in and around all genes on a chromosome. The test statistic used is the classic likelihood ratio test applied to haplotypes in case/control populations. Haplotype frequencies are computed through specification of genetic model parameters. Power is determined by computation of the test's non-centrality parameter. Power per gene is computed as a weighted average of the power assuming each haplotype is associated with the trait. We apply our method to genotype data from dense SNP maps across three entire chromosomes (6, 21, and 22) for three different human populations (African-American, Caucasian, Chinese), three different models of disease (additive, dominant, and multiplicative) and two trait allele frequencies (rare, common). We perform a regression analysis using these factors, average marker-marker disequilibrium, and the haplotype diversity across the gene region to determine which factors most significantly affect average power for a gene in our data. Also, as a 'proof of principle' calculation, we perform power and sample size calculations for all genes within 100 kb of the PSORS1 locus (chromosome 6) for a previously published association study of psoriasis. Results of our regression analysis indicate that four highly significant factors that determine average power to detect association are: disease model, average marker-marker disequilibrium, haplotype diversity, and the trait allele frequency. These findings may have important implications for the design of well-powered candidate gene association studies. Our power and sample size calculations for the PSORS1 gene appear consistent with published findings, namely that there is substantial power (>0.99) for most genes within 100 kb of the PSORS1 locus at the 0.01 significance level.

Black or African American↗

PubMedDate not supplied

Effectiveness research and implications for study design: sample size and statistical power.

Most clinical trials have started to incorporate more broadly defined outcome measures, such as health-related quality of life, to complement clinical status measures as well as direct costs and cost-effectiveness analyses. Contrasting a broad range of outcome and cost measures, we analyze the implications for sample sizes and study design using data from prior mental health and primary care studies that span a wide range of practice settings, patient populations, and geographic areas. While meaningful clinical symptomatic differences are often detectable with sample sizes of well under 100 per cell, detecting even large changes in health-related quality of life generally requires several hundred observations per cell. Reasonable precision in cost estimates usually requires sample sizes in the thousands. Very few clinical trials or observational effectiveness studies that incorporate quality of life or cost measures have such sample sizes, resulting in many (unreported) null findings and, due to publication biases favoring significant results, scientific publications that exaggerate true effects. It raises issues for the general direction of clinical trials and effectiveness studies, as well as for how cost and health-related quality of life results based on small studies should be dealt with in publications.

Clinical Trials as Topic↗

PubMed1992

Measurement of motor recovery after stroke. Outcome assessment and sample size requirements.

BACKGROUND AND PURPOSE: The purpose of this study was to analyze recovery of motor function in a cohort of patients presenting with an acute occlusion in the carotid distribution. Analysis of recovery patterns is important for estimating patient care needs, establishing therapeutic plans, and estimating sample sizes for clinical intervention trials. METHODS: We prospectively measured the motor deficits of 104 stroke patients over a 6-month period to identify earliest measures that would predict subsequent motor recovery. Motor function was measured with the Fugl-Meyer Assessment. Fifty-four patients were randomly assigned to a training set for model development; 50 patients were assigned to a test set for model validation. In a second analysis, patients were stratified on basis of time and stroke severity. The sample size required to detect a 50% improvement in residual motor function was calculated for each level of impairment and at three points in time. RESULTS: At baseline the initial Fugl-Meyer motor scores accounted for only half the variance in 6-month motor function (r2 = 0.53, p less than 0.001). After 5 days, both the 5-day motor and sensory scores explained 74% of the variance (p less than 0.001). After 30 days, the 30-day motor score explained 86% of the variance (p less than 0.001). Application of these best models to the test set confirmed the results obtained with the training set. Sample-size calculations revealed that as severity and time since stroke increased, sample sizes required to detect a 50% improvement in residual motor deficits decreased. CONCLUSIONS: Most of the variability in motor recovery can be explained by 30 days after stroke. These findings have important implications for clinical practice and research.

Activities of Daily Living↗

PubMed2002

Sample size re-estimation in cluster randomization trials.

Cluster randomization trials in which families are the unit of allocation are commonly adopted for the evaluation of disease prevention interventions. Sample size estimation for cluster randomization trials depends on parameters that quantify the variability within and between clusters and the variability in cluster size. Accurate advance estimates of these nuisance parameters may be difficult to obtain and misspecification may lead to an underpowered study. Since families are typically recruited over time, we propose using a portion of the data to estimate the nuisance parameters and to re-estimate sample size based on the estimates. This extends the standard internal pilot study methods to the setting of cluster randomization trials. The effect of this design on the power, significance level and sample size is analysed via simulation and is shown to provide a flexible and practical approach to cluster randomization trials.

Cluster Analysis↗

PubMed1999

Sample size calculations for trials in health services research.

The current orthodox way of estimating sample size for a trial is through a power calculation based on a significance test. It therefore carries the assumption that this test should be the centerpiece of the statistical analysis. However, it is increasingly the case that confidence intervals are preferred to significance tests in summarising the results of trials, particularly in health services research. We believe that the way sample size is estimated should reflect this change and focus on the width of the confidence interval rather than on the outcome of a significance test. Such a method of estimation is described here and shown to have additional advantages of simplicity and transparency, enabling a more informed debate about the proposed size of trials.

Confidence Intervals↗

PubMed1999

Surveying physicians to determine the minimal important difference: implications for sample-size calculation.

The minimal important difference (MID) is the smallest benefit of treatment that would result in clinicians recommending it to their patients. The MID is necessary to calculate sample size for randomized clinical trials, but its chosen value is often arbitrary. This study set out to determine the practicability of surveying physicians to elicit the MID for clinical trial sample-size calculation. Using a mail survey, we elicited the MID of different physician specialties (family medicine, internal medicine, vascular surgery) for using propranolol to slow abdominal aortic aneurysm (AAA) growth assuming that propranolol was efficacious in this condition. We used different outcome measures (growth rate or proportion of patients requiring surgery) and different methods of data presentation for the proportion of patients requiring surgery (absolute risk reduction or number needed to treat). The MID varied significantly by physician specialty, experience with AAA and propranolol, and the method used to elicit the MID. Consequently, sample-size calculations using these various MIDs varied from 116 to 3015. Future attempts to elicit the MID need to consider carefully who is surveyed, how data are presented, and how opinions are elicited.

Adrenergic beta-Antagonists↗

PubMed2005

A new approach to sample size calculation for reference interval studies.

A new criterion is proposed for determining the sample size required for a study performed for the purpose of establishing reference intervals. The basic idea behind the criterion is to compare the empirical coverage (i.e. the probability content) of the reference region obtained from the sample with its target value (e.g. 95 per cent) and to set suitable limits delta1, delta2 to the difference between both quantities which must not be exceeded with sufficiently large probability beta (e.g. beta=90 per cent). For the most frequently used parametric and distribution-free methods of estimating univariate reference limits, implicit formulae are derived relating the sample size to the design parameters delta1, delta2 and beta. For symmetric specification of (delta1, delta2), explicit approximation formulae for the computation of n are given. Exact values obtained by means of suitable numerical techniques are presented in a set of tables covering specifications of delta1, delta2 and beta which can be recommended for real applications. The tables can be used both for one- and two-sided reference intervals.

Alanine Transaminase↗

PubMed2000

Sample size determination for testing whether an identified treatment is best.

Laska and Meisner (1989, Biometrics 45, 1139-1151) dealt with the problem of testing whether an identified treatment belonging to a set of k + 1 treatments is better than each of the other k treatments. They calculated sample size tables for k = 2 when using multiple t-tests or Wilcoxon-Mann-Whitney tests, both under normality assumptions. In this paper, we provide sample size formulas as well as tables for sample size determination for k > or = 2 when t-tests under normality or Wilcoxon-Mann-Whitney tests under general distribution assumptions are used.

Biometry↗

PubMed1993

Diagnosis of meniscal tears of the knee with MR imaging: effect of observer variation and sample size on sensitivity and specificity.

OBJECTIVE: A wide range in the efficacy of MR imaging for the diagnosis of meniscal tears of the knee has been reported. To evaluate two possible causes for this variation, we studied how sensitivity and specificity are affected when different observers and sample sizes are used. MATERIALS AND METHODS: Two hundred MR examinations of the knee in patients for whom the results of arthroscopy were available were used for the study. One hundred eight medial meniscal tears and 58 lateral meniscal tears were found at arthroscopy. The sensitivity and specificity for detection of meniscal tears were determined for the original interpretations and retrospective evaluations by three observers. Comparisons were also made between sample sizes of 25 and 100. chi 2 analysis was used for unmatched data sets and McNemar's statistic was used for matched sets. RESULTS: For the 200 examinations, the sensitivity was 0.89-0.93 for medial meniscal tears and 0.79-0.83 for lateral meniscal tears. The specificity was 0.86 for medial meniscal tears and 0.90-0.92 for lateral meniscal tears. Sensitivity and specificity varied widely among different observers and different sample sizes. However, we found no significant difference between any of the comparisons at the p < .05 level. The largest interobserver variation occurred in the detection of lateral meniscal tears, with a sensitivity of 0.71 for one observer and 0.88 for another observer (p = .16). The largest variation between sets of 100 examinations was a change in sensitivity for detection of lateral meniscal tears from 0.74 to 0.88 for the original interpretations (p = .10). For the sample sets of 25 cases, the variation was even larger, with the sensitivity for detection of lateral meniscal tears varying from 0.5 for one set to 1.0 for another. CONCLUSION: We conclude that chance variation related to sample size can cause large but not statistically significant variations in sensitivity and specificity in this setting. These variations are of sufficient magnitude to explain many of the differences in reported sensitivity and specificity for MR imaging in the diagnosis of meniscal tears. We found no significant difference in observer performance.

Adolescent↗

PubMed1992

Significance testing in mutagen screening: the dependence of statistical power on the control sample size.

The continuous accumulation of control data in multicellular mutagen screening systems prompted us to study the dependence of the statistical power on the size of the control sample (for fixed control values). Two widely used screening systems were chosen: dicentric chromosomes in human lymphocytes and recessive sex-linked lethals in Drosophila melanogaster. The power increases rapidly at first as the control sample size increases, then levels off at a few tens of thousands of control units tested and thereafter remains almost constant up to the historical control. The practical implications from our study are discussed.

Animals↗

PubMed2005

Electronic sorting and recovery of single live cells from microlitre sized samples.

Sorting and recovering specific live cells from samples containing less than a few thousand cells have become major hurdles in rare cell exploration such as stem cell research, cell therapy and cell based diagnostics. We describe here a new technology based on a microelectronic chip integrating an array of over 100,000 independent electrodes and sensors which allow individual and parallel single cell manipulation of up to 10,000 cells while maintaining viability and proliferation capabilities. Manipulation is carried out using dynamic dielectrophoretic traps controlled by an electronic interface. We also demonstrate the capabilities of the chip by sorting and recovering individual live fluorescent cells from an unlabeled population.

Cell Proliferation↗

PubMed2003

Power and sample size for ordered categorical data.

We propose a new method for computing power and sample size for linear rank tests of differences between two ordered multinomial populations. The method is flexible in that it is applicable to any general alternative hypothesis and for any choice of rank scores. We show that the method, though asymptotic, closely approximates existing exact methods. At the same time it overcomes the computational limitations of the exact methods. This advantage makes our asymptotic approach more practical for sample size computations at the planning stages of a large study. We illustrate the method with data arising from both proportional and non-proportional odds models in the two ordered multinomial setting.

Biometry↗

PubMed1993

Sample sizes for event rate equivalence trials using prior information.

Trials for demonstrating the 'equivalence' of active standard and test treatments generally require large sample sizes that depend on the definition of 'equivalence' and the overall event rate when the outcome is incidence of an event such as mortality. The planning of sample sizes for such trials requires specification of a value for the overall event rate. This value often will reflect the outcomes of previous trials of the standard treatment, and is subject to uncertainty that needs some accommodation, to protect against an inadequate sample. Bayes and Empirical Bayes methods can be used to incorporate information from one or more previous trials into the sample size calculation when equivalence means high confidence that the event rate ratio is less than some specified value.

Angiotensin-Converting Enzyme Inhibitors↗

PubMed2006

Sample sizes for identifying the key types of container occupied by dengue-vector pupae: the use of entropy in analyses of compositional data.

A method has been developed for estimating the sample sizes needed to identify categories that comprise a large proportion of a compositional data-set. The method is to be used in the design of surveys of mosquito pupae, for identifying the key container types from which the majority of adult dengue vectors emerge. Although a finite-population correction was devised for estimating the mean of a negative binomial distribution, other complications of parametric approaches make them unlikely to yield methods simple enough to be practically applicable. The Shannon-Wiener index was therefore investigated as a more useful alternative, at the cost of theoretical generalizability, in an approach based on re-sampling methods in conjunction with the use of entropy. This index can be used to summarize the degree to which pupae are either concentrated in a few container types, or dispersed among many. An empirical relationship between the index and the repeatability of surveys of differing sample sizes was observed. A step-wise rule, based on the entropy of the cumulative data, was devised for determining the sample size, in terms of the number of houses positive for pupae, at which a pupal survey might reasonably be stopped.

Aedes↗

PubMed1980

Some considerations for the planning of total-community prevention trials--when is sample size adequate?

Despite the large accumulated experience of statisticians with sample-size calculations for clinical trials, little information is available on extending this methodology to total community trials, in which the units of randomization are total communities and surveillance methods are used to assess event rates. As in clinical trials, the asymptotic formula for total sample size is used. However, the assumptions underlying the usual method of computing the expected T-year even rate for the experimental group, pe, are no longer valid in total community trials: all emigrants (dropouts) from large communities cannot practically be identified or followed. Immigrants, similar to dropouts in clinical trials in that they are exposed to the treatment for only a portion of the period but are followed to the end of the study, present an additional problem. This paper presents a method for the computation of pe in total community trials, taking into account in- and out-migration as well as the determinants usually considered in clinical trials. Sample computations are presented, and general problems of design, execution and data analysis of total community prevention trials are briefly discussed.

Clinical Trials as Topic↗

PubMed1987

The beta error and sample size determination in clinical trials in emergency medicine.

In the analysis of a clinical trial an investigator may fail to discern a statistically significant difference in outcome between control and experimental groups, when in fact one exists. Failure to demonstrate such a difference when it actually exists is known as "type II" error, and its probability of occurring is termed "beta." The purpose of our study was to determine the distribution of beta errors in negative trials in the Journal of the American College of Emergency Physicians (JACEP) (1972-1979) and Annals of Emergency Medicine (1980-1984). All negative comparative clinical trials appearing in JACEP and Annals from volume 1 (1972) to volume 13 (1984) were surveyed and were eligible for inclusion in the study. A trial was defined as negative if the investigator specifically stated that there was no significant difference in outcome between the experimental and control groups. For each negative trial the following parameters were calculated: beta error, based on the sample size used and the difference determined to be important to detect clinically; sample size required to detect a clinically meaningful difference as determined by the authors of this study; and minimum true difference that had to be detected in the trial at a beta equal to 0.20, to discern a statistically significant result. For the 13 years surveyed, we found 21 endpoints in 14 negative trials that were analyzable. Only one of the trials (7.1%) addressed the issues of beta errors and sample size determination. In the remaining 13 negative trials, the calculated beta error ranged from .60 to .97. For the endpoints analyzed, a sample size of up to 450 times larger than that used would have been required to detect a clinically important difference.(ABSTRACT TRUNCATED AT 250 WORDS)

Clinical Trials as Topic↗