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PubMed1989

Sample size and power based on the population attributable fraction.

Most methods for calculating sample size use the relative risk (RR) to indicate the strength of the association between exposure and disease. For measuring the public health importance of a possible association, the population attributable fraction (PAF)--the proportion of disease incidence in a population that is attributable to an exposure--is more appropriate. We determined sample size and power for detecting a specified PAF in both cohort and case-control studies and compared the results with those obtained using conventional estimates based on the relative risk. When an exposure is rare, a study that has little power to detect a small RR often has adequate power to detect a small PAF. On the other hand, for common exposures, even a relatively large study may have inadequate power to detect a small PAF. These comparisons emphasize the importance of selecting the most pertinent measure of association, either relative risk or population attributable fraction, when calculating power and sample size.

Epidemiologic Methods↗
PubMed1993

Exact conditional and unconditional sample size for pair-matched studies with binary outcome: a practical guide.

Tables of sample sizes for pair-matched studies with binary outcome are presented. They are based on conditional and unconditional approaches using the 'exact' (binomial) test. An approximate procedure is suggested to estimate the sample size for parameter values that do not correspond exactly with table entries. The procedure utilizes a minor modification of the large-sample formula given by Connett et al. A practical strategy for estimating the overall sample size in the presence of a nuisance parameter (the proportion of discordant pairs) is recommended. An example from a proposed clinical trial is given.

Binomial Distribution↗
PubMed2002

On the inappropriateness of an EM algorithm based procedure for blinded sample size re-estimation.

When planning a clinical trial the sample size calculation is commonly based on an a priori estimate of the variance of the outcome variable. Misspecification of the variance can have substantial impact on the power of the trial. It is therefore attractive to update the planning assumptions during the ongoing trial using an internal estimate of the variance. For this purpose, an EM algorithm based procedure for blinded variance estimation was proposed for normally distributed data. Various simulation studies suggest a number of appealing properties of this procedure. In contrast, we show that (i) the estimates provided by this procedure depend on the initialization, (ii) the stopping rule used is inadequate to guarantee that the algorithm converges against the maximum likelihood estimator, and (iii) the procedure corresponds to the special case of simple randomization which, however, in clinical trials is rarely applied. Further, we show that maximum likelihood estimation leads to no reasonable results for blinded sample size re-estimation due to bias and high variability. The problem is illustrated by a clinical trial in asthma.

Administration, Inhalation↗
PubMed2001

The effect of cluster randomization on sample size in prevention research.

BACKGROUND: This paper concerns the issue of cluster randomization in primary care practice intervention trials. We present information on the cluster effect of measuring the performance of various preventive maneuvers between groups of physicians based on a successful trial. We discuss the intracluster correlation coefficient of determining the required sample size and the implications for designing randomized controlled trials where groups of subjects (e.g., physicians in a group practice) are allocated at random. METHODS: We performed a cross-sectional study involving data from 46 participating practices with 106 physicians collected using self-administered questionnaires and a chart audit of 100 randomly selected charts per practice. The population was health service organizations (HSOs) located in Southern Ontario. We analyzed performance data for 13 preventive maneuvers determined by chart review and used analysis of variance to determine the intraclass correlation coefficient. An index of "up-to-datedness" was computed for each physician and practice as the number of a recommended preventive measure done divided by the number of eligible patients. An index called "inappropriateness" was computed in the same manner for the not-recommended measures. The intraclass correlation coefficients for 2 key study outcomes (up-to-datedness and inappropriateness) were also calculated and compared. RESULTS: The mean up-to-datedness score for the practices was 53.5% (95% confidence interval [CI], 51.0%-56.0%), and the mean inappropriateness score was 21.5% (95% CI, 18.1%-24.9%). The intraclass correlation for up-to-datedness was 0.0365 compared with inappropriateness at 0.1790. The intraclass correlation for preventive maneuvers ranged from 0.005 for blood pressure measurement to 0.66 for chest radiographs of smokers, and as a consequence required the sample size ranged from 20 to 42 physicians per group. CONCLUSIONS: Randomizing by practice clusters and analyzing at the level of the physician has important implications for sample size requirements. Larger intraclass correlations indicate interdependence among the physicians within a cluster; as a consequence, variability within clusters is reduced, and the required sample size increased. The key finding that many potential outcome measures perform differently in terms of the intracluster correlation reinforces the need for researchers to carefully consider the selection of outcome measures and adjust sample sizes accordingly when the unit of analysis and randomization are not the same.

Humans↗
PubMed2001

Sample size determination for studies of gene-environment interaction.

BACKGROUND: The search for interaction effects is common in epidemiological studies, but the power of such studies is a major concern. This is a practical issue as many future studies will wish to investigate potential gene-gene and gene-environment interactions and therefore need to be planned on the basis of appropriate sample size calculations. METHODS: The underlying model considered in this paper is a simple linear regression and relating a continuous outcome to a continuously distributed exposure variable. RESULTS: The slope of the regression line is taken to be dependent on genotype, and the ratio of the slopes for each genotype is considered as the interaction parameter. Sample size is affected by the allele frequency and whether the genetic model is dominant or recessive. It is also critically dependent upon the size of the association between exposure and outcome, and the strength of the interaction term. The link between these determinants is graphically displayed to allow sample size and power to be estimated. An example of the analysis of the association between physical activity and glucose intolerance demonstrates how information from previous studies can be used to determine the sample size required to examine gene-environment interactions. CONCLUSIONS: The formulae allowing the computation of the sample size required to study the interaction between a continuous environmental exposure and a genetic factor on a continuous outcome variable should have a practical utility in assisting the design of studies of appropriate power.

Effect Modifier, Epidemiologic↗
PubMed2006

[Aspects of sample size determination and power calculation illustrated on examples from rehabilitation research].

Often it is reported in medical studies that an expected effect could not be detected. This may be the case if the sample size had been too small to detect an effect which actually exists. This often is due to the fact that sound sample size estimation had been omitted prior to the study outset. As a result, it is not known how many persons should have been involved in the study to detect this effect if present. On the other hand, if sample size estimation has not been realized, more persons than needed might be included in the study. This is problematic for economic and in particular for ethical reasons. The aim of this paper is to point out the principles of sample size estimation as well as to emphasize its importance not only in general but also in medical rehabilitation research.

Clinical Trials as Topic↗
PubMed2004

Sample size for detecting differentially expressed genes in microarray experiments.

BACKGROUND: Microarray experiments are often performed with a small number of biological replicates, resulting in low statistical power for detecting differentially expressed genes and concomitant high false positive rates. While increasing sample size can increase statistical power and decrease error rates, with too many samples, valuable resources are not used efficiently. The issue of how many replicates are required in a typical experimental system needs to be addressed. Of particular interest is the difference in required sample sizes for similar experiments in inbred vs. outbred populations (e.g. mouse and rat vs. human). RESULTS: We hypothesize that if all other factors (assay protocol, microarray platform, data pre-processing) were equal, fewer individuals would be needed for the same statistical power using inbred animals as opposed to unrelated human subjects, as genetic effects on gene expression will be removed in the inbred populations. We apply the same normalization algorithm and estimate the variance of gene expression for a variety of cDNA data sets (humans, inbred mice and rats) comparing two conditions. Using one sample, paired sample or two independent sample t-tests, we calculate the sample sizes required to detect a 1.5-, 2-, and 4-fold changes in expression level as a function of false positive rate, power and percentage of genes that have a standard deviation below a given percentile. CONCLUSIONS: Factors that affect power and sample size calculations include variability of the population, the desired detectable differences, the power to detect the differences, and an acceptable error rate. In addition, experimental design, technical variability and data pre-processing play a role in the power of the statistical tests in microarrays. We show that the number of samples required for detecting a 2-fold change with 90% probability and a p-value of 0.01 in humans is much larger than the number of samples commonly used in present day studies, and that far fewer individuals are needed for the same statistical power when using inbred animals rather than unrelated human subjects.

Animals↗
PubMedDate not supplied

Key methodological features of randomized controlled trials of Alzheimer's disease therapy. Minimal clinically important difference, sample size and trial duration.

BACKGROUND: The results of clinical trials are routinely presented in terms of statistical significance, which may or may not indicate clinical significance. Analysis of the minimal clinically important difference (MCID) of cognitive scales has received little attention to date. OBJECTIVES: By reviewing the key methodological features (sample size, duration, statistical and clinical significance) of clinical trials examining the efficacy of tacrine in the treatment of Alzheimer's disease (AD), we assessed their ability to detect clinically important changes in cognition. DESIGN: The value for the MCID of the Mini-Mental State Examination (MMSE) was determined by surveying specialists in neurology and geriatric medicine. This value was then used to interpret the clinical significance of the results of published randomized controlled trials (RCTs) assessing the efficacy of tacrine in the treatment of AD and to retrospectively determine their optimal sample size and trial duration. RESULTS: The mean survey MCID for the MMSE was 3.72 (95% confidence interval 3.50-3.95) points. Only 2 of 12 tacrine RCTs using the MMSE found a statistically significant difference in MMSE scores for patients taking tacrine compared with those taking placebo. These improvements were not clinically significant when compared with the survey MMSE MCID. For parallel trials of tacrine in AD, the smallest sample size and minimum trial duration required to demonstrate a clinically significant difference were calculated to be 53 subjects and 1 year, respectively. Five of the 7 parallel trials met the required sample size; however, none of them met the criteria for trial duration. CONCLUSIONS: When using the MMSE as an outcome measure, no tacrine trial reported results that were clinically significant as perceived by clinicians working with dementia patients. Application of a range of plausible MCIDs to the parallel design RCTs also demonstrated that 2 of 7 of these trials did not have sufficient sample size, and none had sufficient duration of treatment to reliably detect clinically meaningful changes in cognition. Future clinical trials in this area will need to incorporate the evolving knowledge of MCIDs in order to increase their chance of detecting clinically relevant results. CopyrightCopyright 1999S.KargerAG,Basel

Aged↗
PubMed2005

Sample size determination for the false discovery rate.

MOTIVATION: There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). RESULTS: We propose and develop the anticipated FDR (aFDR) as a conceptual tool for determining sample size. We derive mathematical expressions for the aFDR and anticipated average statistical power. These expressions are used to develop a general algorithm to determine sample size. We provide specific details on how to implement the algorithm for a k-group (k > or = 2) comparisons. The algorithm performs well for k-group comparisons in a series of traditional simulations and in a real-data simulation conducted by resampling from a large, publicly available dataset. AVAILABILITY: Documented S-plus and R code libraries are freely available from www.stjuderesearch.org/depts/biostats.

Algorithms↗
PubMed2002

Sample size calculation for rank tests comparing K survival distributions.

Rank tests, such as logrank or Wilcoxon rank sum tests, have been popularly used to compare survival distributions of two or more groups in the presence of right censoring. However, there has been little research on sample size calculation methods for rank tests to compare more than two groups. An existing method is based on a crude approximation, which tends to underestimate sample size, i.e., the calculated sample size has lower power than projected. In this paper we propose an asymptotically correct method and an approximate method for sample size calculation. The proposed methods are compared to other methods through simulation studies.

Algorithms↗
PubMed2004

Bayesian sample size determination for prevalence and diagnostic test studies in the absence of a gold standard test.

Planning studies involving diagnostic tests is complicated by the fact that virtually no test provides perfectly accurate results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be taken into account, whether the primary goal of the study is to estimate the prevalence of a disease in a population or to investigate the properties of a new diagnostic test. Previous work on sample size requirements for estimating the prevalence of disease in the case of a single imperfect test showed very large discrepancies in size when compared to methods that assume a perfect test. In this article we extend these methods to include two conditionally independent imperfect tests, and apply several different criteria for Bayesian sample size determination to the design of such studies. We consider both disease prevalence studies and studies designed to estimate the sensitivity and specificity of diagnostic tests. As the problem is typically nonidentifiable, we investigate the limits on the accuracy of parameter estimation as the sample size approaches infinity. Through two examples from infectious diseases, we illustrate the changes in sample sizes that arise when two tests are applied to individuals in a study rather than a single test. Although smaller sample sizes are often found in the two-test situation, they can still be prohibitively large unless accurate information is available about the sensitivities and specificities of the tests being used.

Bayes Theorem↗
PubMed2003

Practical midcourse sample size modification in clinical trials.

Power calculations are very important in the planning of a well-designed clinical trial. Sometimes there is limited information available before the trial, making it highly desirable to adjust the sample size after seeing actual trial data. Indeed, there has been a recent proliferation of papers promising great flexibility in midcourse correction of sample size and other design features, such as choice of primary endpoint. We point out the difficulty in accurately estimating the treatment effect midway through a trial, and we encourage the use of a simple, conservative approach whereby sample size can be increased but not decreased from what was originally planned. We show how to compute the p value and confidence interval for this two-stage procedure. If the original sample size is maintained, analysis of the data is the same as for a fixed sample procedure.

Bayes Theorem↗
PubMed2004

Bayesian sample size calculations in phase II clinical trials using informative conjugate priors.

A number of researchers have discussed phase II clinical trials from a Bayesian perspective. A recent article by Tan and Machin focuses on sample size calculations, which they determine by specifying a diffuse prior distribution and then calculating a posterior probability that the true response will exceed a prespecified target. In this article, we extend these sample size calculations to include informative prior distributions using various strategies that allow researchers with both optimistic and pessimistic priors direct involvement in the sample size decision making. We select the informative priors via multiple methods determined by the mean, median or mode of the conjugate prior. These cases can result in varying sample sizes.

Bayes Theorem↗
PubMed1995

Sample size determination in stratified trials to establish the equivalence of two treatments.

When designing a trial to establish that a new treatment is as effective as a standard one, the conventional test procedure and sample size based on a null hypothesis of no difference between two treatments is inappropriate. Several authors have investigated test statistics and corresponding sample sizes based on the null hypothesis that the standard treatment is more effective than the new by at least some specific value for a single 2 x 2 table. This paper considers a trial that involves several 2 x 2 tables and presents an approximate formula for the sample size required to obtain a given power of a one-tailed score test for a null hypothesis of a specific common non-zero difference between two treatments across strata. I show that the sample size for a trial based on an unstratified test is always larger than that based on a stratified test when the design is balanced.

Clinical Trials as Topic↗
PubMed1992

Sample size calculations for ophthalmologic studies.

Sample size calculations are shown for some common ophthalmologic study designs in which two treatments are to be compared. Included are the following three designs: 1, only one eye per subject; 2, both eyes, with each eye assigned to a different treatment; and 3, both eyes undergoing a common treatment. Continuous and binary outcomes are considered. The correlation between eyes is accounted for in the computations using a simple correction factor. For design 3, the formulas allow for a mixture of single-eye and double-eye eligible subjects. A computer program that performs the calculations is available.

Humans↗
PubMed1988

Sample sizes based on the log-rank statistic in complex clinical trials.

The log-rank test is frequently used to compare survival curves. While sample size estimation for comparison of binomial proportions has been adapted to typical clinical trial conditions such as noncompliance, lag time, and staggered entry, the estimation of sample size when the log-rank statistic is to be used has not been generalized to these types of clinical trial conditions. This paper presents a method of estimating sample sizes for the comparison of survival curves by the log-rank statistic in the presence of unrestricted rates of noncompliance, lag time, and so forth. The method applies to stratified trials in which the above conditions may vary across the different strata, and does not assume proportional hazards. Power and duration, as well as sample sizes, can be estimated. The method also produces estimates for binomial proportions and the Tarone-Ware class of statistics.

Clinical Trials as Topic↗
PubMed2000

[Planning sample size in ophthalmologic studies].

An essential aspect in the cooperation of clinic and biometry consists in designing of studies, e.g. during the preparation of grant applications or for review by official drug surveillance institutions. A central aspect in study planning is the design-adequate and well-documented prediction of sample size, which should be recommended for any intended study. Based on several examples for sample size planning in study designs, which are of common relevance for ophthalmology, guidelines are derived to enable clinical researchers to perform sample size planning on their own. The latter can be based on the various available software packages for sample size prediction.

Bias↗
PubMed2006

A general approach for sample size and statistical power calculations assessing of interventions using a mixture model in the presence of detection limits.

A zero-inflated log-normal mixture model (which assumes that the data has a probability mass at zero and a continuous response for values greater than zero) with left censoring due to assay measurements falling below detection limits has been applied to compare treatment groups in randomized clinical trials and observational cohort studies. The sample size calculation (for a given type I error rate and a desired statistical power) has not been studied for this type of data under the assumption of equal proportions of true zeros in the treatment and control groups. In this article, we derive the sample sizes based on the expected differences between the non-zero values of individuals in treatment and control groups. Methods for calculation of statistical power are also presented. When computing the sample sizes, caution is needed as some irregularities occur, namely that the location parameter is sometimes underestimated due to the mixture distribution and left censoring. In such cases, the aforementioned methods fail. We calculated the required sample size for a recent randomized chemoprevention trial estimating the effect of oltipraz on reducing aflatoxin. A Monte Carlo simulation study was also conducted to investigate the performance of the proposed methods. The simulation results illustrate that the proposed methods provide adequate sample size estimates. However, when the aforementioned irregularity occurs, our methods are restricted and further research is needed.

Anticarcinogenic Agents↗