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PubMed1988

Sample size.

Before undertaking a research comparison, investigators may wish to estimate the sample sizes needed to assure that the research is feasible and is worth the effort and expense. Such calculations require several decisions by the researchers: (1) the acceptable level of the type I error (P value), (2) the desired power of the test, (3) the difference between the samples that is considered to be important, and (4) the variability expected among the values to be studied. Some recipes for estimating approximate sample sizes are suggested.

Statistics as Topic↗
PubMed2003

On the use of population attributable fraction to determine sample size for case-control studies of gene-environment interaction.

Most methods for calculating the sample size needed to detect gene-environment interactions use odds ratios to measure the effect size. We show that for any combination of susceptible genotype prevalence and exposure prevalence and their associated risks, the odds ratio measuring strength of interaction corresponds to a population attributable fraction (PAF) because of interaction and vice versa. Simultaneous consideration of odds ratio for interaction and the associated PAF attributable to interaction provides additional insight to investigators evaluating the feasibility and public health relevance of a proposed study. We considered gene-environment interactions on a multiplicative scale, and assumed a dichotomous environmental exposure variable and a single two-allele disease-susceptibility locus. Our results show, for example, that for studies of exposures and genotypes that are common in a population (30%-50%), the PAF for interaction is large (>27%) even if the odds ratio for interaction is only moderate (approximately 2). If simultaneous estimates of interaction odds ratio and PAF indicate that the PAF is so large as to be implausible, the investigator may decide to reevaluate the study design based on detecting a more reasonable PAF. In this case, the associated odds ratio for interaction will be weaker and a considerably larger sample size may be needed.

Case-Control Studies↗
PubMed1991

Rates of detection of Salmonella and Campylobacter in meats in response to the sample size and the infection level of each species.

Pork, beef and chicken meat samples were collected from slaughter houses, poultry-processing plants and meat shops. Rates of incidence of Salmonella spp., Campylobacter jejuni and C. coli with respect to the sample size were compared and the most probable number for these species were determined. Salmonella spp. were detected in 69 (24.1%) of 286 chicken meat samples, in three (3.2%) of 94 pork samples, and in one (1.9%) of 52 beef samples. With chicken meat, the rates of detection were: 19.9% in 25-g, 15.7% in 10-g, and 12.2% in 1-g samples. The populations in most probable numbers, that gave positive results in 31 (20.8%) of 149 samples, ranged from 30 to 10(4) per 100 g, the majority (93.5%) being between 30 and 10(3) per 100 g. C. jejuni and C. coli were detected in 106 (67.9%) of 156 chicken meat samples, in two (2.1%) of 94 pork samples, and none of 52 beef samples. The results obtained with different sample sizes of chicken were compared. Positive rates were 55.8%, 39.7%, 27.6% in 10 g, 1 g, and 0.1 g, respectively. The most probable numbers in 107 (68.6%) positives out of 156 chicken samples examined ranged from 30 to 10(6) per 100 g: 46 (29.5%) contained between 10(2) and 10(3) per 100 g, 22 (14.1%) between 10(3) and 10(4) per 100 g, and the other 19 samples (12.2%) between 10(4) and 10(5) per 100 g.

Animals↗
PubMed2001

A simple procedure to compute the sample size needed to compare two independent groups when the population variances are unequal.

The usual methods of sample size determination which assume the homogeneity of within-group variances are not sufficiently robust against the violation of this assumption. A method using Satterthwaite's correction for unequal variances is given. It is shown that in the case of unequal variances the minimum total sample size is attained when the allocation ratio is equal to the proportion of the standard deviations.

Analysis of Variance↗
PubMed2005

A sample size formula for the supremum log-rank statistic.

An advantage of the supremum log-rank over the standard log-rank statistic is an increased sensitivity to a wider variety of stochastic ordering alternatives. In this article, we develop a formula for sample size computation for studies utilizing the supremum log-rank statistic. The idea is to base power on the proportional hazards alternative, so that the supremum log rank will have the same power as the standard log rank in the setting where the standard log rank is optimal. This results in a slight increase in sample size over that required for the standard log rank. For example, a 5.733% increase occurs for a two-sided test having type I error 0.05 and power 0.80. This slight increase in sample size is offset by the significant gains in power the supremum log-rank test achieves for a wide range of nonproportional hazards alternatives. A small simulation study is used for illustration. These results should facilitate the wider use of the supremum log-rank statistic in clinical trials.

Biometry↗
PubMedDate not supplied

Bayesian assessment of sample size for clinical trials of cost-effectiveness.

The authors present an analysis of the choice of sample sizes for demonstrating cost-effectiveness of a new treatment or procedure, when data on both cost and efficacy will be collected in a clinical trial. The Bayesian approach to statistics is employed, as well as a novel Bayesian criterion that provides insight into the sample size problem and offers a very flexible formulation.

Bayes Theorem↗
PubMed2003

Sample size estimates for determining treatment effects in high-risk patients with early relapsing-remitting multiple sclerosis.

BACKGROUND: Risk factors for short-term progression in early relapsing remitting MS have been identified recently. Previously we determined potential risk factors for rapid progression of early relapsing remitting MS and identified three groups of high-risk patients. These non-mutually exclusive groups of patients were drawn from a consecutively studied sample of 98 patients with newly diagnosed MS. High-risk patients had a history of either poor recovery from initial attacks, more than two attacks in the first two years of disease, or a combination of at least four other risk factors. OBJECTIVE: To determine differences in sample sizes required to show a meaningful treatment effect when using a high-risk sample versus a random sample of patients. METHODS: Power analyses were used to calculate the different sample sizes needed for hypothetical treatment trials. RESULTS: We found that substantially smaller numbers of patients should be needed to show a significant treatment effect by employing these high-risk groups of patients as compared to a random population of MS patients (e.g., 58% reduction in sample size in one model). CONCLUSION: The use of patients at higher risk of progression to perform drug treatment trials can be considered as a means to reduce the number of patients needed to show a significant treatment effect for patients with very early MS.

Aged↗
PubMed2000

Sample size and multiple regression analysis.

Despite the development of procedures for calculating sample size as a function of relevant effect size parameters, rules of thumb tend to persist in designs of multiple regression studies. One explanation for their persistence may be the difficulty in formulating a reasonable a priori value of an effect size to be detected. This article presents methods for calculating effect sizes in multiple regression from a variety of perspectives and also introduces a new method based on an exchangeability structure among predictor variables. No single method is deemed superior, but rather examples show that a combination of methods is likely to be most valuable in many situations. A simulation provides a 2nd explanation for why rules of thumb for choosing sample size have persisted but also shows that the outcome of such underpowered studies will be a literature consisting of seemingly contradictory results.

Child↗
PubMed2005

A comment on sampling error in the standardized mean difference with unequal sample sizes: avoiding potential errors in meta-analytic and primary research.

The authors discuss potential confusion in conducting primary studies and meta-analyses on the basis of differences between groups. First, the authors show that a formula for the sampling error of the standardized mean difference (d) that is based on equal group sample sizes can produce substantially biased results if applied with markedly unequal group sizes. Second, the authors show that the same concerns are present when primary analyses or meta-analyses are conducted with point-biserial correlations, as the point-biserial correlation (r) is a transformation of d. Third, the authors examine the practice of correcting a point-biserial r for unequal sample sizes and note that such correction would also increase the sampling error of the corrected r. Correcting rs for unequal sample sizes, but using the standard formula for sampling error in uncorrected r, can result in bias. The authors offer a set of recommendations for conducting meta-analyses of group differences.

Humans↗
PubMed2002

Sample size and optimal designs in stratified comparative trials to establish the equivalence of treatment effects among two ethnic groups.

When a new investigational medicine is intended to be applied to populations with different ethnic backgrounds, a stratified comparative phase III trial using ethnic groups as strata may be conducted to assess the influence of ethnic factors on clinical outcomes of this new medicine. In this paper, based on a binomial model with odds ratio as the measure of the treatment effect, we derive the score test and the associated sample size formula for establishing the equivalence/noninferiority of the treatment effects of a medicine among two ethnic groups. A simplified test together with its sample size formula are also given. Taking into account the sample size, cost, and power of testing, respectively, we derive the optimal design parameters, i.e., the allocation among treatment groups and ethnic groups, based on the simplified test.

Algorithms↗
PubMed2001

Sample size requirements for case-control study designs.

BACKGROUND: Published formulas for case-control designs provide sample sizes required to determine that a given disease-exposure odds ratio is significantly different from one, adjusting for a potential confounder and possible interaction. RESULTS: The formulas are extended from one control per case to F controls per case and adjusted for a potential multi-category confounder in unmatched or matched designs. Interactive FORTRAN programs are described which compute the formulas. The effect of potential disease-exposure-confounder interaction may be explored. CONCLUSIONS: Software is now available for computing adjusted sample sizes for case-control designs.

Case-Control Studies↗
PubMed1996

[Criterion quality and estimation of the expected sample size in sequential analysis of linkage].

It is shown that, when conducting sequential testing of linkage in pedigree samples, (1) type I and type II errors observed are less than expected and (2) the generally accepted method for determining the average sample size, E(N), required for sequential analysis of linkage, underestimates it. A less biased approximation of E(N) is proposed. A wide scattering of actual sample sizes required for completion of sequential analysis is demonstrated, which puts practical use of E(N) into question.

Evaluation Studies as Topic↗
PubMed2003

Technical variability and required sample size of helminth egg isolation procedures.

Measurements of parasite load are often very variable. This implies that little confidence can be attached to single measurements of parasite numbers and egg concentrations, and that many measurements are required for the detection of differences between groups of hosts or parasites. For studies that aim to detect these differences, it is important to increase the precision (closeness of repeated measures to each other) of parasite numbers, because it determines the number of samples that is needed to find significant differences among groups. In this study, sample sizes required to detect group differences were estimated using nematode egg counts of faecal samples of dairy cattle. They were found to be much lower for a centrifugation technique than for the widely used McMaster technique in replicate samples, in spite of a generally similar mean FEC. For example, the sample size required to detect FEC differences between groups of 10, 50, and 250 eggs per gram (EPG) were 46, 25, and 27 for the McMaster technique and 8, 5, and 12 for the SSF method, respectively. Interestingly, sample sizes required for faeces with a relatively high egg concentration (approximately 1000 EPG) were also considerably lower than for the McMaster technique in spite of a higher mean EPG of the latter method. This implies that technical variation can be reduced considerably by simple methods of egg isolation. Given that the range of egg concentration is similar for a number of nematodes of livestock and human helminths, a reduction of technical error will aid studies with many group comparisons such as vaccination strategies against parasites with typically low FECs and studies of the genetics of host resistance. It may also lead to improved guidelines for measures related to public health.

Animals↗
PubMed2003

Confidence intervals and sample size calculations for studies of film-reading performance.

The relaxation of restrictions on the type of professions that can report films has resulted in radiographers and other healthcare professionals becoming increasingly involved in image interpretation in areas such as mammography, ultrasound and plain-film radiography. Little attention, however, has been given to sample size determinations concerning film-reading performance characteristics such as sensitivity, specificity and accuracy. Illustrated with hypothetical examples, this paper begins by considering standard errors and confidence intervals for performance characteristics and then discusses methods for determining sample size for studies of film-reading performance. Used appropriately, these approaches should result in studies that produce estimates of film-reading performance with adequate precision and enable investigators to optimize the sample size in their studies for the question they seek to answer.

Clinical Competence↗
PubMed2006

Sample size determination for matched-pair equivalence trials using rate ratio.

In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point. These statistics can be implemented through sample-based, constrained least squares estimation and constrained maximum likelihood (CML) estimation methods. Sample size formulae based on the CML estimation method are developed. We consider formulae that control a prespecified power or confidence width. Our simulation studies show that statistics based on the CML estimation method generally outperform other statistics and methods with respect to actual type I error rate and average width of confidence intervals. Also, the corresponding sample size formulae are valid asymptotically in the sense that the exact power and actual coverage probability for the estimated sample size are generally close to their prespecified values. The methods are illustrated with a real example from a clinical laboratory study.

Biometry↗
PubMed2003

Sample sizes for comparing means of two lifetime distributions with type II censored data: application in an aging intervention study.

Sample size determination is a very important part of planning for clinical trials. Most clinical trials do not follow all their subjects to the terminal event, resulting in censored observations. This article presents a method of computing sample sizes required to achieve adequate statistical power to compare the means of two lifetime distributions when both samples are subject to type II censoring. Our approach is based on the location-scale family of log-transformed lifetime distributions as compared to that based on the log-rank test and the family of proportional hazards. Specific applications to log-normal distribution and Weibull distribution are also discussed.

Aging↗
PubMed2002

Sample size considerations in observational health care quality studies.

A common objective in health care quality studies involves measuring and comparing the quality of care delivered to cohorts of patients by different health care providers. The data used for inference involve observations on units grouped within clusters, such as patients treated within hospitals. Unlike cluster randomization trials where often clusters are randomized to interventions to learn about individuals, the target of inference in health quality studies is the cluster. Furthermore, randomization is often not performed and the resulting biases may invalidate standard tests. In this paper, we discuss approaches to sample size determination in the design of observational health quality studies when the outcome is binary. Methods for calculating sample size using marginal models are briefly reviewed, but the focus is on hierarchical binomial models. Sample size in unbalanced clusters and stratified designs are characterized. We draw upon the experiences that have arisen from a study funded by the Agency for Healthcare Research and Quality involving assessment of quality of care for patients with cardiovascular disease. If researchers are interested in comparing clusters, hierarchical models are preferred.

Anti-Inflammatory Agents, Non-Steroidal↗
PubMed2005

Sample size and power analysis for endometrial safety studies.

Endometrial safety studies are required for the approval of progestin components. The Committee for Proprietary Medicinal Products requirement is the actual percentage below 2% and the upper limit of the one-sided exact 95% confidence interval not more than 2% above the point estimate. The more recent U.S. Food and Drug Administration requirement is the actual percentage < or = 1% and the upper limit of the one-sided exact 95% confidence interval < or =4%. I studied the sample size and power needed to satisfy both requirements based on the exact confidence intervals for the binomial parameter and the Poisson parameter. I discovered that a larger sample size does not always lead to a higher power. I presented a best sample size that satisfies both requirements and recommended that the patient enrollment should be closely monitored during the study.

Aged↗