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PubMed1998

Sample size calculations for paired or matched ordinal data.

The problem of calculating the number of subjects in a paired or matched study in which the outcome variable is ordinal is discussed. A common approach in the case of a two category variable is to calculate the required number of discordant pairs, and then divide this by the expected proportion of discordant pairs to obtain the total sample size. An approximate solution for the number of discordant pairs is proposed for ordinal data and compared to sample sizes estimated through simulation. It is shown that the sample sizes are underestimated when the number of categories is two, but that the approximation improves as the number of categories increases. Comparison of the required discordant sample size when there are two categories with the required sample size for more than two categories would suggest that the loss of power is not great if a categorical variable is collapsed into only two categories. However, the total sample size required is likely to be greater with only two categories, since the expected proportion of discordant to concordant pairs increases. Since the expected number of discordant pairs is likely to decrease as the number of categories increases, this suggests that as a rule of thumb the required discordant sample size for the two category case be used as an approximation to the total required sample size when the number of categories is greater than two.

Clinical Trials as Topic↗
PubMed2001

A SAS macro for sample size re-estimation.

The assessment of sample size in clinical trials comparing means requires a variance estimate of the main efficacy variable. If no reliable information about the variance of the key response is available at the beginning of a clinical trial, the use of data from the first 'few' patients entered in the trial ('internal pilot') may be appropriate to estimate the variance and thus to recalculate the required sample size. A SAS macro that implements the EM algorithm for carrying out and simulating such interim power evaluations without unblinding the treatment status is presented.

Algorithms↗
PubMedDate not supplied

Power and sample size calculations for stochastic cost-effectiveness analysis.

As the data for economic analyses are increasingly collected prospectively alongside clinical trials, many commentators have highlighted that the sample sizes in such trials should be based on the requirements for the economic analysis as well as those for the clinical evaluation. However, issues associated with sample size calculations for economic analysis have yet to receive the rigorous attention given to sample size calculation for clinical evaluation. In particular, no sample size formula for cost-effectiveness analysis is available for analysts hoping either to calculate the required sample size at the design stage of a study or to calculate the power a given size of clinical trial will generate for cost-effectiveness analysis. Building on the recent literature for calculating confidence intervals for cost-effectiveness ratios, the authors explore possible techniques for deriving a sample size formula for cost-effectiveness analysis based on simple combination of the confidence limits on costs and effects.

Clinical Trials as Topic↗
PubMed1992

Optimum sample size determination in stratified case-control studies with cost considerations.

We investigate sample size determination for Cochran's test for stratified case-control studies when samples of cases and controls are allocated to maximize the asymptotic efficiency of Cochran's test subject to fixed total cost with cost per control varying by strata. We consider two situations typical of strata-matched case-control studies: when one samples both cases and controls and when cases are given and one samples controls. In each situation we develop and study an asymptotic method for finding the sample size required for a specific power under the optimum allocation proposed by Nam and Fears. Also, for the second situation, we investigate an asymptotic method for determining the common ratio, k, in one-to-k strata-matched case-control studies without cost consideration for a given power. When cases are given, neither the optimum nor the standard control sample sizes appear in a closed form; we present numerical methods for calculating these sample sizes and illustrate them with examples. We find the reduction in total cost obtained under the optimum allocation compared to standard allocation more pronounced as the differences in stratum-specific costs of sampling controls increase.

Adult↗
PubMedDate not supplied

[Practical aspects regarding sample size in clinical research].

BACKGROUND: The knowledge of the right sample size let us to be sure if the published results in medical papers had a suitable design and a proper conclusion according to the statistics analysis. To estimate the sample size we must consider the type I error, type II error, variance, the size of the effect, significance and power of the test. To decide what kind of mathematics formula will be used, we must define what kind of study we have, it means if its a prevalence study, a means values one or a comparative one. In this paper we explain some basic topics of statistics and we describe four simple samples of estimation of sample size.

Sample Size↗
PubMed2004

Sample size estimates for atrial fibrillation endpoints.

This article reviews the current sample size requirements for studies evaluating the efficacy of atrial therapies. Sample sizes for several study designs and endpoints are presented. However, emphasis is given to studies conducted in patients with implantable devices in the light of new available data from recent trials involving such patients. Studies utilizing mortality require >5,000 patients followed for at least 2 years. Symptomatic episode recurrence represents a possible alternate endpoint but still requires >400 patients followed for 1 year. Parallel design studies for device atrial fibrillation (AF) burden and frequency endpoints were found to be of little value because they would require thousands of patients. In contrast, cross-over studies utilizing device AF burden or AF frequency endpoints provide the best option in terms of sample size and study duration. A 30% therapy efficacy (reduction in AF burden or frequency) can be detected with just a little over 100 patients followed for 6 months. Therefore, cross-over studies with device-based endpoints are a viable option to evaluate and screen possible new rhythm control treatments before evaluating their effect on clinical outcome variables that may require larger trials with longer follow-up times.

Atrial Fibrillation↗
PubMed1995

Sample size and statistical power in reproductive research.

The calculation of sample size should be an integral part of the planning stages of all research projects to avoid wasting time, money, and valuable resources. The necessary information for sample size calculations includes the alpha (type I) error level, the beta (type II) error, delta (or the difference you would like to be able to detect), and, for continuous variables, the variance. We review these terms and outline their importance in the calculation of sample size and statistical power. When necessary, the investigator should seek expertise and advice to perform these calculations.

Female↗
PubMed2006

The effect of sample size in studies of soil microbial community structure.

Replicate soil samples of 0.01, 0.1, 0.25, 1.0 and 10.0 g were taken from a single, large, homogenized sample from a field maintained as continuous meadow. The samples were processed for direct enumeration of bacterial cells and community structure assays by DGGE analysis of PCR-amplified 16S-rDNA fragments from whole community extracts. The goal was to determine the sample size or size range that produced the most consistent results (i.e., mean values) and the lowest variance. Enumeration data were analyzed by ANOVA, and the community composition fingerprints were analyzed by discriminant analysis (DA). Acceptable results were obtained for sample sizes from 0.1 to 1.0 g for both enumeration and community fingerprinting, but the size that yielded the best results for both measures was 0.25 g. The results suggest that for well homogenized silt loam soils with moderate organic matter concentrations, this sample size should produce high quality consistent results. For soils that differ in organic concentrations or clay content, a reconnaissance survey similar to the present examination is recommended.

Bacteria↗
PubMed1993

Sample size required for various methods of assessing bone status in commercial leghorn hens.

A study was conducted to determine the appropriate sample size required for various methods used to assess tibial bone status in commercial Leghorn hens. The methods used were in vivo bone mineral content (BMC), in vivo bone density (BD), in vitro BMC, in vitro BD, tibia bone breaking strength (TBS), and percentage bone ash (BA). Dietary total P levels of .4, .45, .5, .55, and .7% were used as treatment source of variation. Twenty hens were sampled randomly to represent each dietary treatment. The CV for each bone status comparison method was estimated and was used in a procedure to estimate the sample size requirement for detecting a difference of delta between treatments. The sample size required to detect the difference between treatment means varied depending on 1) the method used to compare bone status 2) the difference between the treatment means to be detected as significant (delta); and 3) the level of significance (alpha) assumed. The sample size required for various methods are tabulated at .01, .05, and .1 level of significance and for 2.5, 5,7.5, 10, 15, and 20% delta. To detect an actual difference of 5% from the mean to be significant, at the .05 level of significance, a sample size of 44, 22, 31, 23, 47, and 85 hens per treatment would be necessary for in vivo BMC, in vivo BD, in vitro BMC, in vitro BD, TBS, and BA methods, respectively. The estimated sample size values would help researchers in designing experiments that involve bone status comparison of commercial Leghorn hens.

Animals↗
PubMed2003

Sample size calculations for population- and family-based case-control association studies on marker genotypes.

Most previous sample size calculations for case-control studies to detect genetic associations with disease assumed that the disease gene locus is known, whereas, in fact, markers are used. We calculated sample sizes for unmatched case-control and sibling case-control studies to detect an association between a biallelic marker and a disease governed by a putative biallelic disease locus. Required sample sizes increase with increasing discrepancy between the marker and disease allele frequencies, and with less-than-maximal linkage disequilibrium between the marker and disease alleles. Qualitatively similar results were found for studies of parent offspring triads based on the transmission disequilibrium test (Abel and Müller-Myhsok, 1998, Am. J. Hum. Genet. 63:664-667; Tu and Whittemore, 1999, Am. J. Hum. Genet. 64:641-649). We also studied other factors affecting required sample size, including attributable risk for the disease allele, inheritance mechanism, disease prevalence, and for sibling case-control designs, extragenetic familial aggregation of disease and recombination. The large sample-size requirements represent a formidable challenge to studies of this type.

Alleles↗
PubMed1990

Sample size requirements for interval estimation of the odds ratio.

Sample sizes are calculated for unmatched case-control (or cohort) studies where the goal is interval estimation of the odds ratio. The procedure used gives the smallest sample size for which a 100(1-alpha)% confidence interval for the log odds ratio will not exceed a specified width with specified probability (1-gamma). Tables of sample sizes for various choices of parameter values are presented. Considerable disagreement is found with a published method which has as its basis expected cell counts.

Case-Control Studies↗
PubMed2006

Sample size calculation in survival trials accounting for time-varying relationship between noncompliance and risk of outcome event.

BACKGROUND: Most methods of sample size calculations for survival trials adjust the estimated outcome event rates for noncompliance based on the assumption that non-compliance is independent of the risk of the outcome event although there has been published evidence that noncompliers are often at a higher risk than compliers. More recent work has started to consider the situations of informative noncompliance and different risks for noncompliers. However, the possibility of a time-varying association between noncompliance and risk has been ignored. Our analysis indicated a strong time-varying relationship between noncompliance defined as permanent discontinuation of study treatments and risk of the outcome event in the CONVINCE trial. PURPOSE: The purpose of this research is to develop methods for the log-rank sample size calculations for two-arm clinical trials that allow for the relationship between risk and noncompliance to vary over time and to study how sample size requirements vary with different patterns of the time relationship. METHODS: The method developed takes Lakatos' Markov chain approach as a basis, modifying it to incorporate time dynamics, and emphasizing permanent discontinuation of study medication as the form of noncompliance to be considered. RESULTS: Results with our method show that sample size depends on the relative rates of noncompliance in the two arms, the hazard for the outcome event following non-compliance, whether it involves switching to the hazard of the opposite arm or is common to both arms, and whether noncompliance occurs early or late in the trial. These factors interact with each other in complex ways, precluding simple summaries. LIMITATIONS: This research focuses on two-arm clinical trials with time to event as primary outcome measure. The method developed is not directly applicable to trials with more complicated designs and/or trials with other types of primary outcome. CONCLUSIONS: The pattern of the relationship between noncompliance and risk can have a dramatic impact on the sample size and power calculations in survival studies. The method introduced provides a useful tool for investigators to explore the optimal sample size accounting for various dynamic associations between noncompliance and risk.

Clinical Trials as Topic↗
PubMed2004

Sample size determination for comparing several survival curves with unequal allocations.

Ahnn and Anderson derived sample size formulae for unstratified and stratified designs assuming equal allocation of subjects to three or more treatment groups. We generalize the sample size formulae to allow for unequal allocation. In addition, we define the overall probability of death to be equal to one minus the censored proportion for the stratified design. This definition also leads to a slightly different definition of the non-centrality parameter than that of Ahnn and Anderson for the stratified case. Assuming proportional hazards, sample sizes are determined for a prespecified power, significance level, hazard ratios, allocation of subjects to several treatment groups, and known censored proportion. In the proportional hazards setting, three cases are considered: (1) exponential failures--exponential censoring, (2) exponential failures--uniform censoring, and (3) Weibull failures (assuming same shape parameter for all groups)--uniform censoring. In all three cases of the unstratified case, it is assumed that the censoring distribution is the same for all of the treatment groups. For the stratified log-rank test, it is assumed the same censoring distribution across the treatment groups and the strata. Further, formulae have been developed to provide approximate powers for the test, based upon the first two or first four-moments of the asymptotic distribution. We observe the following two major findings based on the simulations. First, the simulated power of the log-rank test does not depend on the censoring mechanism. Second, for a significance level of 0.05 and power of 0.80, the required sample size n is independent of the censoring pattern. Moreover, there is very close agreement between the exact (asymptotic) and simulated powers when a sequence of alternatives is close to the null hypothesis. Two-moment and four-moment power series approximations also yield powers in close agreement with the exact (asymptotic) power. With unequal allocations, our simulations show that the empirical powers are consistently above the target value of prespecified power of 0.80 when 50 per cent of the patients are allocated to the treatment group with the smallest hazard.

Antineoplastic Agents↗
PubMed2006

Sample size calculations for disease freedom and prevalence estimation surveys.

We developed a Bayesian approach to sample size calculations for studies designed to estimate disease prevalence that uses a hierarchical model for estimating the proportion of infected clusters (cluster-level prevalence) within a country or region. The clusters may, for instance, be villages within a region, cities within a state, or herds within a country. Our model allows for clusters with zero prevalence and for variability in prevalences among infected clusters. Moreover, uncertainty about diagnostic test accuracy and within-cluster prevalences is accounted for in the model. A predictive approach is used to address the issue of sample size selection in human and animal health surveys. We present sample size calculations for surveys designed to substantiate freedom of a region from an infectious agent (disease freedom surveys) and for surveys designed to estimate cluster-level prevalence of an endemic disease (prevalence estimation surveys). In disease freedom surveys, for instance, assuming the cluster-level prevalence for a particular infectious agent in the region is greater than a maximum acceptable threshold, a sample size combination consisting of the number of clusters sampled and number of subjects sampled per cluster can be determined for which authorities conducting the survey detect this excessive cluster-level prevalence with high predictive probability. The method is straightforward to implement using the Splus/R library emBedBUGS together with WinBUGS.

Animals↗
PubMedDate not supplied

Assessment of the Gould-Shih procedure for sample size re-estimation.

The power of a clinical trial is partly dependent upon its sample size. With continuous data, the sample size needed to attain a desired power is a function of the within-group standard deviation. An estimate of this standard deviation can be obtained during the trial itself based upon interim data; the estimate is then used to re-estimate the sample size. Gould and Shih proposed a method, based on the EM algorithm, which they claim produces a maximum likelihood estimate of the within-group standard deviation while preserving the blind, and that the estimate is quite satisfactory. However, others have claimed that the method can produce non-unique and/or severe underestimates of the true within-group standard deviation. Here the method is thoroughly examined to resolve the conflicting claims and, via simulation, to assess its validity and the properties of its estimates. The results show that the apparent non-uniqueness of the method's estimate is due to an apparently innocuous alteration that Gould and Shih made to the EM algorithm. When this alteration is removed, the method is valid in that it produces the maximum likelihood estimate of the within-group standard deviation (and also of the within-group means). However, the estimate is negatively biased and has a large standard deviation. The simulations show that with a standardized difference of 1 or less, which is typical in most clinical trials, the standard deviation from the combined samples ignoring the groups is a better estimator, despite its obvious positive bias.

Algorithms↗
PubMed2005

Power and sample size of therapeutic trials in procedural dermatology: how many patients are enough?

BACKGROUND: Many new devices and therapeutic interventions are continually introduced in cutaneous surgery. The efficacy of these new techniques must be compared with that of preexisting standards so that patients can be appropriately counseled. OBJECTIVES: The purpose of this article is to (1) review methods for estimating sample size and power, (2) estimate the range of sample sizes sufficient to ensure that true differences are not missed in clinical trials of new procedural dermatologic therapies, and (3) consider the reasons why the sample size may be too small in procedural dermatology trials and how this problem can be addressed. METHODS: (1) Selective review of textbooks and other relevant literature, presentation of a brief tutorial describing sample size and power determination for therapeutic clinical trials comparing two groups with continuous outcomes variables; (2) implementation of standard formulae and assumptions to estimate sample size in cutaneous surgery therapeutic trials. RESULTS: Assuming that one group receives a standard surgical intervention and another group undergoes a new technique, to identify a moderate difference in efficacy between groups, at least 50 to 200 subjects will need to be enrolled if conventional strategies are used to reduce the likelihood of finding a difference that does not really exist (Type I error), as well as the likelihood of missing a true difference (Type II error). CONCLUSION: By face validity, it is apparent that most efficacy comparisons in procedural dermatology have low sample size and a concomitant risk of failing to detect actual differences between therapeutic arms. Owing to the limitations that restrict surgeons from frequently performing large randomized controlled trials in procedural dermatology, meta-analyses may be needed to pool the results of smaller studies. When it is critically important that differences between groups be accurately identified, dermatologic surgeons may consider eschewing smaller trials in favor of collaborating on larger trials with an adequate sample size.

Dermatology↗
PubMed2003

Simple procedures for blinded sample size adjustment that do not affect the type I error rate.

For normally distributed data, determination of the appropriate sample size requires a knowledge of the variance. Because of the uncertainty in the planning phase, two-stage procedures are attractive where the variance is reestimated from a subsample and the sample size is adjusted if necessary. From a regulatory viewpoint, preserving blindness and maintaining the ability to calculate or control the type I error rate are essential. Recently, a number of proposals have been made for sample size adjustment procedures in the t-test situation. Unfortunately, none of these methods satisfy both these requirements. We show through analytical computations that the type I error rate of the t-test is not affected if simple blind variance estimators are used for sample size recalculation. Furthermore, the results for the expected power of the procedures demonstrate that the methods are effective in ensuring the desired power even under initial misspecification of the variance. A method is discussed that can be applied in a more general setting and that assumes analysis with a permutation test. This procedure maintains the significance level for any design situation and arbitrary blind sample size recalculation strategy.

Anxiety Disorders↗
PubMed1990

Sample size determination for case-control studies: the influence of the joint distribution of exposure and confounder.

In case-control studies, the results about how the exposure distribution affects sample size are well known. This paper extends previous results by incorporating the effect of a confounder into the calculation of sample size for a desired size and power of a statistical test. The paper also includes a quantitative discussion on the influence of the joint distribution for exposure to a putative cause and a a confounder on required sample sizes. The results show that, to detect a specified alternative for a given size and power, the required sample size decreases as either the variance of exposure or the effect of exposure on disease increases. The required sample size, however, increases as either the variance of the confounder or the effect of the confounder on disease increases. Generally, the higher is the absolute value of the simple correlation between the exposure and the confounder, the larger is the required sample size.

Analysis of Variance↗