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PubMed2005

Sample sizes and negative studies in clinical vaccine research.

Negative studies of vaccine adverse events occur with some frequency in the published literature. They serve important roles in fending off claims posed by the anti-vaccine movement and in reinforcing public health efforts to prevent diseases. Still, negative studies frequently suffer from concerns of adequate sample size. The double-significance Neyman-Pearson formula for sample size calculation that is now in vogue results in immense sample sizes that can lead to illogical interpretations. The late Professor Alvan R. Feinstein, the father of quantitative clinical epidemiology, proposed a more logical approach that would reduce the confusion and call for more moderate sample sizes. Understanding the issues involved in sample size calculations is important to those who design clinical vaccine studies. The implications of the calculations have far-reaching effects upon elements of feasibility such as the expense of the study, the ability to recruit adequate numbers, and even whether the study will be done at all.

Biometry↗

PubMed2006

Using design effects from previous cluster surveys to guide sample size calculation in emergency settings.

A good estimate of the design effect is critical for calculating the most efficient sample size for cluster surveys. We reviewed the design effects for seven nutrition and health outcomes from nine population-based cluster surveys conducted in emergency settings. Most of the design effects for outcomes in children, and one-half of the design effects for crude mortality, were below two. A reassessment of mortality data from Kosovo and Badghis, Afghanistan revealed that, given the same number of clusters, changing sample size had a relatively small impact on the precision of the estimate of mortality. We concluded that, in most surveys, assuming a design effect of 1.5 for acute malnutrition in children and two or less for crude mortality would produce a more efficient sample size. In addition, enhancing the sample size in cluster surveys without increasing the number of clusters may not result in substantial improvements in precision.

Afghanistan↗

PubMed1992

Correlated binomial variates: properties of estimator of intraclass correlation and its effect on sample size calculation.

In group randomized studies, the sample size calculations are complicated by within group (worksite, community, etc.) correlation. We compare by simulation the moment method and the more standard ANOVA method of estimating the intraclass correlation. We find the former is less biased for a small to moderate number of clusters but the difference disappears when the appropriate degree of freedom is used for the ANOVA estimator. We propose a simulation approach for sample size determination and illustrate it with an example.

Analysis of Variance↗

PubMed1979

Sample-size estimation: a sensitivity analysis in the context of a clinical trial for treatment of mild hypertension.

The effectiveness of treatment for mild hypertension (diastolic pressures of 85 to 105 mm Hg) has not been conclusively demonstrated. Both the costs of a carefully designed clinical trial and the likelihood that it will produce definitive answers will depend importantly on the sample size. This paper presents sample-size estimates under a variety of assumptions regarding the characteristics of the population to be studied, the degree of blood pressure control to be achieved, and the health benefits to be expected. Under a central set of assumptions, the estimated sample size per group is 22,700 with death as an endpoint and 14,000 with morbid events (CHD and stroke) as endpoints. As individual assumptions are varied one at a time, required sample sizes range from 10,900 to 101,100 and from 6,800 to 63,100 for the respective endpoints. Results are most sensitive to the degree of blood pressure control actually achieved to the expected health benefits from blood pressure control. They are also highly sensitive to the sex composition of the population and to expected dropout rates. The choice of sample size will depend on the decision maker's assessment of the likelihood that each assumption will be fulfilled and on the degree of willingness to risk an inconclusive study result. By making explicit the effect of variation in each assumption, decision making is rendered more susceptible to critical examination by outside reviewers.

Adult↗

PubMed2003

Reducing sample sizes in genome scans: group sequential study designs with futility stops.

Group sequential study designs can greatly facilitate analyses of genetic linkage in complex traits. We recently proposed designs allowing stopping investigations early if the result is significant (König et al. [2001] Am. J. Hum. Genet. 69:590-600), thereby decreasing average sample sizes under the alternative hypothesis. However, average sample sizes were slightly increased under the null hypothesis. We now present designs where the analysis of markers is additionally stopped in case of futility, i.e., if the probability for significant results is sufficiently low. These sequential designs are applied to linkage analyses of single loci. We calculated sample sizes, time points, and critical boundaries for all analyses for 2- and 3-stage designs at an overall significance level of 0.0001. To confirm the validity of asymptotic approximations, Monte Carlo simulations were performed. The utility is demonstrated analyzing genome scan data provided for the Genetic Analysis Workshop 12. Application of the novel sequential designs yields tremendous decreases in average sample sizes, regardless of the size of the underlying genetic effect at investigated loci. Depending on the applied design, almost half of the sample size is spared on average. These enormous savings are expected to have a special impact on costs and time of large-scale studies such as genome scans.

Genetic Linkage↗

PubMed2001

Clinical trials of multiple sclerosis monitored with enhanced MRI: new sample size calculations based on large data sets.

OBJECTIVE: A new parametric simulation procedure based on the negative binomial (NB) model was used to evaluate the sample sizes needed to achieve optimal statistical powers for parallel groups (with (PGB) and without (PG) a baseline correction scan). It was also used for baseline versus treatment (BVT) design clinical trials in relapsing-remitting (RR) and secondary progressive (SP) multiple sclerosis (MS), when using the number of new enhancing lesions seen on monthly MRI of the brain as the measure of outcome. METHODS: MRI data obtained from 120 untreated patients with RRMS selected for the presence of MRI activity at baseline, 66 untreated and unselected patients with RRMS, and 81 untreated and unselected patients with SPMS were fitted using an NB distribution. All these patients were scanned monthly for at least 6 months and were all from the placebo arms of three large scale clinical trials and one natural history study. The statistical powers were calculated for durations of follow up of 3 and 6 months. RESULTS: The frequency of new enhancing lesions in patients with SPMS was lower, but not significantly different, from that seen in unselected patients with RRMS. As expected, enhancement was more frequent in patients with RRMS selected for MRI activity at baseline than in the other two patient groups. As a consequence, the estimated sample sizes needed to detect treatment efficacy in selected patients with RRMS were smaller than those of unselected patients with RRMS and those with SPMS. Baseline correction was also seen to reduce the sample sizes of PG design trials. An increased number of scans reduced the sample sizes needed to perform BVT trials, whereas the gain in power was less evident in PG and PGB trials. CONCLUSION: This study provides reliable estimates of the sample sizes needed to perform MRI monitored clinical trials in the major MS clinical phenotypes, which should be useful for planning future studies.

Adult↗

PubMed2003

Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant.

An approach to sample size planning for multiple regression is presented that emphasizes accuracy in parameter estimation (AIPE). The AIPE approach yields precise estimates of population parameters by providing necessary sample sizes in order for the likely widths of confidence intervals to be sufficiently narrow. One AIPE method yields a sample size such that the expected width of the confidence interval around the standardized population regression coefficient is equal to the width specified. An enhanced formulation ensures, with some stipulated probability, that the width of the confidence interval will be no larger than the width specified. Issues involving standardized regression coefficients and random predictors are discussed, as are the philosophical differences between AIPE and the power analytic approaches to sample size planning.

Humans↗

PubMed2004

The effect of sample size for estimating Rasch/IRT parameters with dichotomous items.

Thirteen samples were randomly drawn from the normative database for the latest edition of Knox's Cube Test-Revised (KCT-R). Parameter estimates for the Rasch model and two and three parameter logistic models were derived and compared. Sample size influenced these estimates as might be expected. Rasch parameter estimates consistently showed the smallest values by sample size using a goodness of fit index.

Data Interpretation, Statistical↗

PubMed1999

Power and sample size calculations in case-control studies of gene-environment interactions: comments on different approaches.

Power and sample size considerations are critical for the design of epidemiologic studies of gene-environment interactions. Hwang et al. (Am J Epidemiol 1994;140:1029-37) and Foppa and Spiegelman (Am J Epidemiol 1997;146:596-604) have presented power and sample size calculations for case-control studies of gene-environment interactions. Comparisons of calculations using these approaches and an approach for general multivariate regression models for the odds ratio previously published by Lubin and Gail (Am J Epidemiol 1990; 131:552-66) have revealed substantial differences under some scenarios. These differences are the result of a highly restrictive characterization of the null hypothesis in Hwang et al. and Foppa and Spiegelman, which results in an underestimation of sample size and overestimation of power for the test of a gene-environment interaction. A computer program to perform sample size and power calculations to detect additive or multiplicative models of gene-environment interactions using the Lubin and Gail approach will be available free of charge in the near future from the National Cancer Institute.

Case-Control Studies↗

PubMed1991

Ankylosing spondylitis antirheumatic drug trials. II. Tables for calculating sample size for clinical trials.

The calculation of sample size requires knowledge of the standard deviation (SD) of index variables. Unfortunately, there are no published lists of standard deviations and it is exceedingly difficult to locate variance estimates based on relevant populations. We used standardized procedures to determine in 60 patients with ankylosing spondylitis (AS) the SD of key outcome measures recommended in current Food Drug Administration and European League Against Rheumatism guidelines for AS clinical trials. We anticipate that these tables will be useful to clinical researchers in selecting outcome measures as well as for calculating sample size requirements for future clinical studies in AS.

Analysis of Variance↗

PubMed1992

Osteoarthritis antirheumatic drug trials. II. Tables for calculating sample size for clinical trials.

The calculation of sample size for clinical trials requires knowledge of the standard deviation (SD) of index variables. There are no published lists of SD and it is difficult to locate variance estimates based on relevant populations. In this study we used standardized procedures to determine in 60 patients with osteoarthritis (OA) of the knee the standard deviation of key outcome measures recommended in current Food and Drug Administration and European League Against Rheumatism guidelines for OA clinical trials. These tables will be useful to clinical researchers in selecting outcome measures as well as for calculating sample size requirements for future clinical studies in OA.

Clinical Trials as Topic↗

PubMed2005

FDR-controlling testing procedures and sample size determination for microarrays.

Microarrays are used increasingly to identify genes that are truly differentially expressed in tissues under different conditions. Planning such studies requires establishing a sample size that will ensure adequate statistical power. For microarray analyses, false discovery rate (FDR) is considered to be an appropriate error measure. Several FDR-controlling procedures have been developed. How these procedures perform for such analyses has not been evaluated thoroughly under realistic assumptions. In order to develop a method of determining sample sizes for these procedures, it needs to be established whether these procedures really control the FDR below the pre-specified level so that the determined sample size indeed provides adequate power. To answer this question, we first conducted simulation studies. Our simulation results showed that these procedures do control the FDR at most situations but under-control the FDR when the proportion of positive genes is small, the most likely scenarios. Thus, these existing procedures can overestimate the power and underestimate the sample size. Accordingly, we developed a simulation-based method to provide more accurate estimates for power and sample size.

Algorithms↗

PubMed1999

Misclassification in case-control studies of gene-environment interactions: assessment of bias and sample size.

In studies of gene-environment interactions, exposure misclassification can lead to bias in the estimation of an interaction effect and increased sample size. The magnitude of the bias and the consequent increase in sample size for fixed misclassification probabilities are highly dependent on the prevalence of the misclassified factor and on the interaction model. This paper describes a relatively simple approach to assess the impact of misclassification on bias in the estimation of multiplicative or additive interactions and on sample size requirements. Applications of this method illustrate that even small errors in the assessment of environmental or genetic factors can result in biased interaction parameters and substantially increased sample size requirements that can compromise the feasibility of the study. Also, an example is provided where nondifferential misclassification biases an additive interaction parameter away from the null value, even under conditions where a multiplicative interaction parameter will always be biased toward the null value. Efforts to improve the accuracy in measuring both genetic and environmental factors are critical for the valid assessment of gene-environment interactions in case-control studies.

Benzo(a)pyrene↗

PubMed2007

Sample size determination for logistic regression revisited.

There is no consensus on the approach to compute the power and sample size with logistic regression. Some authors use the likelihood ratio test; some use the test on proportions; some suggest various approximations to handle the multivariate case. We advocate the use of the Wald test since the Z-score is routinely used for statistical significance testing of regression coefficients. The null-variance formula became popular from early studies, which contradicts modern software, which utilizes the method of maximum likelihood estimation (MLE), when the variance of the MLE is estimated at the MLE, not at the null. We derive general Wald-based power and sample size formulas for logistic regression and then apply them to binary exposure and confounder to obtain a closed-form expression. These formulas are applied to minimize the total sample size in a case-control study to achieve a given power by optimizing the ratio of controls to cases. Approximately, the optimal number of controls to cases is equal to the square root of the alternative odds ratio. Our sample size and power calculations can be carried out online at www.dartmouth.edu/ approximately eugened.

Clinical Trials as Topic↗

PubMed1994

Implications of measurement error in exposure for the sample sizes of case-control studies.

In this paper, recent results describing the effects of measurement error on estimation of the association between an exposure and a disease are applied to sample size calculation in case-control studies. Models of the relation between true exposure and a surrogate exposure measure assessed with error are used to derive equations for sample size determination. The results show that the sample size of a study based on an exposure variable which is measured with error must be larger by a factor of 1/rho 2 than if exposure were measured without error, where rho is the correlation between the true exposure and the surrogate exposure measure. Review of the magnitude of measurement error in dietary assessments suggests that failure to account for measurement error in sample size determination for case-control studies of diet and disease could lead to marked underestimation of the required sample size.

Bias↗

PubMed1999

Sample Size Requirements of a Mixture Analysis Method with Applications in Systematic Biology.

The available information on sample size requirements of mixture analysis methods is insufficient to permit a precise evaluation of the potential problems facing practical applications of mixture analysis. We use results from Monte Carlo simulation to assess the sample size requirements of a simple mixture analysis method under conditions relevant to biological applications of mixture analysis. The mixture model used includes two univariate normal components with equal variances but assumes that the researcher is ignorant as to the equality of the variances. The method used relies on the EM algorithm to compute the maximum likelihood estimates of the mixture parameters, and the likelihood ratio test to assess the number of components in the mixtures. Our results suggest that sample sizes close to 500 or 1000 data may be required to adequately solve mixtures commonly found in biology. Sample sizes of 500 or 1000 are difficult to achieve. However, use of this MA method may be a reasonable option when the researcher deals with problems which are intractable by other means. Copyright 1999 Academic Press.

Journal Article↗

PubMed1991

To increase power in randomized clinical trials without increasing sample size.

The power of a randomized clinical trial (RCT) depends on two factors: sample size and effect size. Most psychiatric research design strategies focus on increasing sample size, despite major problems in recruiting large numbers of subjects or funding such costly studies. It is possible to increase power in RCTs in a variety of ways without increasing sample size, in essence by increasing effect size by decreasing within-group variance. Such strategies are presented and discussed.

Humans↗

PubMed2001

Sample size and statistical power of randomised, controlled trials in orthopaedics.

We reviewed all 717 manuscripts published in the 1997 issues of the British and American volumes of the Journal of Bone and Joint Surgery and in Clinical Orthopaedics and Related Research, from which 33 randomised, controlled trials were identified. The results and sample sizes were used to calculate the statistical power of the study to distinguish small (0.2 of standard deviation), medium (0.5 of standard deviation), and large (0.8 of standard deviation) effect sizes. Of the 33 manuscripts analysed, only three studies (9%) described calculations of sample size. To perform post-hoc power assessments and estimations of deficiencies of sample size, the standard effect sizes of Cohen (small, medium and large) were calculated. Of the 25 studies which reported negative results, none had adequate power (beta < 0.2) to detect a small effect size and 12 (48%) lacked the power necessary to detect a large effect size. Of the 25 studies which did not have an adequate size of sample to detect small differences, the average used was only 10% of the required number Our findings suggest that randomised, controlled trials in clinical orthopaedic research utilise sample sizes which are too small to ensure statistical significance for what may be clinically important results.

Humans↗