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PubMed2006

Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method.

BACKGROUND: Cluster randomized trials are increasingly popular. In many of these trials, cluster sizes are unequal. This can affect trial power, but standard sample size formulae for these trials ignore this. Previous studies addressing this issue have mostly focused on continuous outcomes or methods that are sometimes difficult to use in practice. METHODS: We show how a simple formula can be used to judge the possible effect of unequal cluster sizes for various types of analyses and both continuous and binary outcomes. We explore the practical estimation of the coefficient of variation of cluster size required in this formula and demonstrate the formula's performance for a hypothetical but typical trial randomizing UK general practices. RESULTS: The simple formula provides a good estimate of sample size requirements for trials analysed using cluster-level analyses weighting by cluster size and a conservative estimate for other types of analyses. For trials randomizing UK general practices the coefficient of variation of cluster size depends on variation in practice list size, variation in incidence or prevalence of the medical condition under examination, and practice and patient recruitment strategies, and for many trials is expected to be approximately 0.65. Individual-level analyses can be noticeably more efficient than some cluster-level analyses in this context. CONCLUSIONS: When the coefficient of variation is <0.23, the effect of adjustment for variable cluster size on sample size is negligible. Most trials randomizing UK general practices and many other cluster randomized trials should account for variable cluster size in their sample size calculations.

Cluster Analysis↗
PubMed2003

Sample size calculations in surgery: are they done correctly?

BACKGROUND: Randomized controlled trials (RCTs) are considered the gold standard for evidence-based clinical research, but prior work has suggested that there may be poor reporting of sample sizes in the surgical literature. Sample size calculations are essential for planning a study to minimize both type I and type II errors. We hypothesized that sample size calculations may not be performed consistently in surgery studies and, therefore, many studies may be "underpowered." To address this issue, we reviewed RCTs published in the surgical literature to determine how often sample size calculations were reported and to analyze each study's ability to detect varying degrees of differences in outcomes. METHODS: A comprehensive MEDLINE search identified RCTs published in Annals of Surgery, Archives of Surgery, and Surgery between 1999 and 2002. Each study was evaluated by two independent reviewers. Sample size calculations were performed to determine whether they had 80% power to detect differences between treatment groups of 50% (large) and 20% (small), with one-sided test, alpha = 0.05. For the underpowered studies, the degree to which sample size would need to be increased was determined. RESULTS: One hundred twenty-seven RCT articles were identified; of these, 48 (38%) reported sample size calculations. Eighty-six (68%) studies reported positive treatment effect, whereas 41 (32%) found negative results. Sixty-three (50%) of the studies were appropriately powered to detect a 50% effect change, whereas 24 (19%) had the power to detect a 20% difference. Of the studies that were underpowered, more than half needed to increase sample size by more than 10-fold. CONCLUSIONS: The reporting of sample size calculations was not provided in more than 60% of recently published surgical RCTs. Moreover, only half of studies had sample sizes appropriate to detect large differences between treatment groups.

Data Interpretation, Statistical↗
PubMed2004

Sample size estimation in research with dependent measures and dichotomous outcomes.

I reviewed sample estimation methods for research designs involving nonindependent data and a dichotomous response variable to examine the importance of proper sample size estimation and the need to align methods of sample size estimation with planned methods of statistical analysis. Examples and references to published literature are provided in this article. When the method of sample size estimation is not in concert with the method of planned analysis, poor estimates may result. The effects of multiple measures over time also need to be considered. Proper sample size estimation is often overlooked. Alignment of the sample size estimation method with the planned analysis method, especially in studies involving nonindependent data, will produce appropriate estimates.

Computer Simulation↗
PubMed1992

Effects of sample size on the latency and amplitude of the auditory evoked response.

Experiment I investigated the effects of sample size (500 to 1500 stimulus repetitions) on the auditory brainstem response as a function of intensity (20 to 80 dB nHL) on a group of 10 normally hearing subjects. There was little change in identifiability, reliability, latencies, or amplitudes of Waves I, III, and V as the sample size increased from 500 or 750 to 1500 repetitions. These results suggest that 500 to 750 repetitions may be adequate when methods similar to those in the present study are used, and that the common clinical practice of employing approximately 1500 repetitions may unnecessarily prolong testing. Experiment II employed 12 hearing-impaired subjects who were tested at 10 to 40 dB SL using sample sizes from 250 to 4500 stimulus repetitions. Identifiability of all waves increased as sample size increased from 250 to 4500 repetitions. The largest changes in identifiability occurred when sample size increased from 250 to 1500 or 3000 repetitions, with little improvement as sample size increased from 3000 to 4500 repetitions. Examiners should monitor averaged responses and terminate testing as soon as a wave is identified. Contrary to expectation, there was no systematic change in the standard error of measurement for latency (approximately 0.07 ms) as sample size increased from 250 to 4500 repetitions. The standard error of measurement for amplitude decreased from approximately 100 nV with 500 repetitions to approximately 45 nV at 3000 repetitions. The improvement in reliability with increasing sample size may be explained by a decrease in the variability of background noise. A systematic decrease in amplitude also was observed as sample size increased. This observation may be explained by a reduction in the residual noise levels or because of time jitter or adaptation within the auditory pathways. Nonetheless, investigators who wish to use ABR amplitude measures for diagnosis may benefit from using a relatively large sample size.

Adult↗
PubMed1987

Effective sample sizes for confidence intervals for survival probabilities.

We examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities. We compare the effective sample sizes of Cutler and Ederer and Peto et al., as well as a modified Cutler-Ederer effective sample size. We investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time. We note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric. We recommend the use of the Cutler-Ederer effective sample size in construction of upper confidence intervals and the Peto effective sample size in construction of lower confidence intervals. Two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes. This study also illustrates the need for caution in the application of simulation studies to real problems.

Bacterial Infections↗
PubMed2005

Ethics and sample size.

The belief is widespread that studies are unethical if their sample size is not large enough to ensure adequate power. The authors examine how sample size influences the balance that determines the ethical acceptability of a study: the balance between the burdens that participants accept and the clinical or scientific value that a study can be expected to produce. The average projected burden per participant remains constant as the sample size increases, but the projected study value does not increase as rapidly as the sample size if it is assumed to be proportional to power or inversely proportional to confidence interval width. This implies that the value per participant declines as the sample size increases and that smaller studies therefore have more favorable ratios of projected value to participant burden. The ethical treatment of study participants therefore does not require consideration of whether study power is less than the conventional goal of 80% or 90%. Lower power does not make a study unethical. The analysis addresses only ethical acceptability, not optimality; large studies may be desirable for other than ethical reasons.

Bias↗
PubMed2001

Unequal cluster sizes for trials in English and Welsh general practice: implications for sample size calculations.

Cluster randomized trials are often used in primary care settings. In the U.K., general practices are usually the unit of allocation. The effect of variability in practice list size on sample size calculations is demonstrated using the General Medical Services Statistics for England and Wales, 1997. Summary statistics and tables are given to help design such trials assuming that a fixed proportion of patients are to be recruited from each cluster. Three different weightings of the cluster means are compared: uniform, cluster size and minimum variance weights. Minimum variance weights are shown to be superior to uniform, particularly when clusters are small, and to cluster size weights, particularly when clusters are large. Where there are large numbers of participants per cluster and cluster size weights are used, the power actually falls as more patients are recruited to large clusters. When minimum variance weights are used the increase in the design effect due to variation in list size is small, regardless of the size of intracluster correlation coefficient or the number of participants per cluster, provided there is no loss of randomized units. When the expected number of participants per practice is low a greater loss in power comes from practices which fail to recruit patients. A method to estimate the likely effect and allow for it is presented.

Accidental Falls↗
PubMed1991

Minimising errors in clinical studies by proper selection of sample size.

In the planning of a clinical trial, the statistical aspects of the choice of sample size should be considered. The meaning of statistical terms such as Type I and Type II errors, significance and power are explained. Formulae are given for calculating the required sample size for parallel groups' designs (two independent samples) and matched pair or cross-over designs for both quantitative and qualitative responses. Samples size tables are given with instructions for their use and there are four worked examples. The sample size for a trial depends on the specification of the levels of significance and power and the size of the difference the trial is designed to detect, and these can be somewhat arbitrary. Furthermore, it is often necessary to estimate the standard deviation on the basis of limited information. Thus, the sample size required for a trial cannot be determined precisely, and there can be no exactly right or wrong sample size. However, sensible consideration of sample size should ensure that the trial is not so small as to make the results trivial, nor so large as to be unethical or a waste of resources.

Clinical Trials as Topic↗
PubMed2006

Adaptive, group sequential and decision theoretic approaches to sample size determination.

This paper presents two adaptive methods for sample size re-estimation within a unified group sequential framework. The conceptual and practical distinction between these adaptive modifications and more traditional sample size changes due to revised estimates of nuisance parameters is highlighted. The motivation for the adaptive designs is discussed. Having established that adaptive sample size modifications can be made without inflating the type 1 error, the paper concludes with a novel decision theoretic approach for determining the magnitude of the sample size modification.

Clinical Trials as Topic↗
PubMed1995

On the use of a pilot sample for sample size determination.

To compute the sample size needed to achieve the planned power for a t-test, one needs an estimate of the population standard deviation sigma. If one uses the sample standard deviation from a small pilot study as an estimate of sigma, it is quite likely that the actual power for the planned study will be less than the planned power. Monte Carlo simulations indicate that using a 100(1-gamma) per cent upper one-sided confidence limit on sigma will provide a sample size sufficient to achieve the planned power in at least 100(1-gamma) per cent of such trials.

Clinical Trials as Topic↗
PubMed1996

Sample size and statistical power in [15O]H2O studies of human cognition.

Determining the appropriate sample size is a crucial component of positron emission tomography (PET) studies. Power calculations, the traditional method for determining sample size, were developed for hypothesis-testing approaches to data analysis. This method for determining sample size is challenged by the complexities of PET data analysis: use of exploratory analysis strategies, search for multiple correlated nodes on interlinked networks, and analysis of large numbers of pixels that may have correlated values due to both anatomical and functional dependence. We examine the effects of variable sample size in a study of human memory, comparing large (n = 33), medium (n = 16,17), small (n = 11, 11, 11), and very small (n = 6,6,7,7,7) samples. Results from the large sample are assumed to be the "gold standard." The primary criterion for assessing sample size is replicability. This is evaluated using a hierarchically ordered group of parameters: pattern of peaks, location of peaks, number of peaks, size (volume) of peaks, and intensity of the associated t (or z) statistic. As sample size decreases, false negatives begin to appear, with some loss of pattern and peak detection; there is no corresponding increase in false positives. The results suggest that good replicability occurs with a sample size of 10-20 subjects in studies of human cognition that use paired subtraction comparisons of single experimental/baseline conditions with blood flow differences ranging from 4 to 13%.

Adult↗
PubMed2000

Sample size for ophthalmology studies.

Knowledge and the usage of actual sample size formulae are a necessity as validity of the inferences from research studies is often dependent on this. This paper explains how sample sizes are calculated. The concept of sampling variation is explained to emphasize the need for its proper calculation. Sample size formulae are explained with examples to provide researchers with a means of calculating the sample sizes for the commonly used study designs. Ophthalmic data are used as examples. It is perceived that this will improve the quality of inferences drawn from ophthalmic research studies.

Humans↗
PubMed2003

Sample size calculation for studies on temporomandibular disorders.

Sample size calculation is a fundamental step for the validity and the usefulness of results from a study. Nevertheless, as demonstrated by some papers in the literature, such calculation is often ignored. Despite the lack of papers on this topic, it is probable that this shortcoming also affects studies on temporomandibular disorders. Therefore, the aim of this paper was to provide some basic rules to calculate the sample size necessary for different types of studies, both longitudinal and transversal, on those pathologies. Some examples of the application of such rules for different types of studies have also been provided, in order to make a full comprehension easier. In fact, the systematic application of those rules is strongly requested for the effective usefulness of results. Furthermore, an analysis of the statistical power of past studies on temporomandibular disorders could be useful to evaluate if our epidemiological and clinical-therapeutic knowledge of temporomandibular disorders is effectively based upon studies conducted with the appropriate sample size.

Clinical Trials as Topic↗
PubMed1989

Sample size tables for logistic regression.

Sample size tables are presented for epidemiologic studies which extend the use of Whittemore's formula. The tables are easy to use for both simple and multiple logistic regressions. Monte Carlo simulations are performed which show three important results. Firstly, the sample size tables are suitable for studies with either high or low event proportions. Secondly, although the tables can be inaccurate for risk factors having double exponential distributions, they are reasonably adequate for normal distributions and exponential distributions. Finally, the power of a study varies both with the number of events and the number of individuals at risk.

Adult↗
PubMed1996

Sample size of randomized double-blind trials 1976-1991.

OBJECTIVE: To study whether sample size of randomized trials has increased over recent years. DESIGN: A systematic review of randomized trials published in 1976, 1981, 1986, or 1991 which were double-blind, had active treatments in both arms, were not of a crossover design, were published in English as full articles, and which had clinical outcomes. RESULTS: We included 386 references. The median total sample size increased from 46 in 1976 to 71 in 1991 (p<0.0001). Sample size was not related to journal impact factor (p = 0.40). The median sample size and impact factor for 106 trials in gastroenterology, cardiology or oncology were larger than for other specialties, 83 vs 60 (p = 0.01) and 1.5 vs 1.2 (p = 0.04), respectively. The use of binary outcomes increased with time (p = 0.00001) as did the proportion of trials with significant results (p = 0.001). CONCLUSION: Although increased, most sample sizes are still too small since several hundred patients are needed to be reasonably sure not to overlook a 25% improvement over standard therapy. A more profound change in sample size could be obtained if the bodies responsible for approving trials rejected small trials, apart from exceptional circumstances, such as very rare diseases.

Double-Blind Method↗
PubMed1986

Sample sizes in the multivariate analysis of repeated measurements.

Determination of sample sizes for comparing two or more treatments in repeated measurements experiments is considered. Multivariate normality of the individual's vector of repeated measures is assumed. Particular emphasis is placed on applications wherein the error variance-covariance matrix is arbitrary positive-definite. Sample size determination is based on power considerations associated with Hotelling's T2 test and the desire to detect a specified difference between any pair of treatment means. Tabulated sample sizes are given in the case of an equal variance-unequal covariance structure. The utility of these sample sizes is also demonstrated for a more general variance-covariance structure. Applications of these sample sizes are illustrated with two examples.

Analysis of Variance↗
PubMedDate not supplied

Approaches to sample size calculation in comparative studies.

The questions 'what should be the minimum study subjects' and 'how these subjects should be enrolled in the study' are two aspects that are considered at the design stage. Regardless of research question and the study design adopted, these two questions are an integral part of any research proposal. No matter how well a study is conducted and statistically analysed using sophisticated statistical methods/softwares, if the study size is inadequate, concluding statements will have inadequate power and such statements may be misleading and harmful to both target population and the scientific community. There is no substitute/shortcut to an adequate study size as no statistical methods are available to adjust for an inadequate study size. Though a larger sample size will result in higher precision in estimates, however, it may not be desirable in terms of cost, time and the efforts. In medical sciences, majority of research questions pertain to comparing outcome measures in two or more than two groups. Focus of this article is on the number of study subjects required in a study and an attempt is made to review the ingredients required to calculate the sample size in situations commonly encountered by researchers in medical sciences. Formulae for the specific situations are provided with worked out examples.

Child↗
PubMedDate not supplied

[Determination of the sample size and distribution of the ABO and Rh blood groups in Botucatu, Sã Paulo, Brazil (author's transl)].

In the present paper some statistical aspects referred to the distribution of the ABO and Rh blood groups were studied. The sample included 4,037 data, about white and no white persons, of both sexes, living in Botucatu. The results are presented with a calculation of the frequencies of the alleles responsible for the polymorphisms studied, the sample frequencies of the blood groups and their populations confidence-intervals estimates. The possibles interdependences for sex and color with the blood groups were verified by the chi2 test. The principal aim of the present study was to determine the ideal sample size. It was elaborated a table where are given populations sizes, samples sizes and the percentual relations between these values.

ABO Blood-Group System↗