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Sample size estimation for comparing two or more treatment groups in clinical trials.

Methods for estimating required sample size for comparing two population means have been published. Most involve the use of complicated formulae and tables. These methods are limited to comparing two groups. Although techniques exist to determine sample sizes for comparing more than two groups, they are intrinsically far more complicated. A simple linear nomogram is proposed as a solution to these problems, and its use is illustrated with examples of parallel group, ordered parallel group and factorial designs.

Algorithms

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

Methodological issues concerning the sensitive query in AIDS/alcohol research: sample size estimates for randomized response procedures.

Quantification of sample size requirements for two common models of the RRT as compared to conventional survey techniques demonstrates that Campbell is fundamentally correct. However, the absolute increase in sample size necessitated by either model of the RRT is not of such a magnitude as to make use of the method always impractical. Where the appropriate sample size exists, it may well be the method of choice for selected issues pertaining to AIDS and alcohol research.

Acquired Immunodeficiency Syndrome

Sixteen S-squared over D-squared: a relation for crude sample size estimates.

I suggest for memorization an equation for calculating approximate sample size requirements intended only for a specific set of values (80 per cent power for a two-tailed alpha = 0.05 test) which seems to occur often in biopharmaceutical research. After presenting the formula in terms of variance estimate s2 and effect size d, I derive a few alternative forms and then discuss the accuracy of the approximation and other properties as well as examples of its use.

Drug Evaluation

Likelihood ratios with confidence: sample size estimation for diagnostic test studies.

Confidence intervals are important summary measures that provide useful information from clinical investigations, especially when comparing data from different populations or sites. Studies of a diagnostic test should include both point estimates and confidence intervals for the tests' sensitivity and specificity. Equally important measures of a test's efficiency are likelihood ratios at each test outcome level. We present a method for calculating likelihood ratio confidence intervals for tests that have positive or negative results, tests with non-positive/non-negative results, and tests reported on an ordinal outcome scale. In addition, we demonstrate a sample size estimation procedure for diagnostic test studies based on the desired likelihood ratio confidence interval. The renewed interest in confidence intervals in the medical literature is important, and should be extended to studies analyzing diagnostic tests.

Epidemiology

A goodness-of-fit approach to inference procedures for the kappa statistic: confidence interval construction, significance-testing and sample size estimation.

We propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome. The procedure is based on a chi-square goodness-of-fit test as applied to a model frequently used for clustered binary data. The procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures. The procedure also has use for significance-testing and the planning of corresponding sample size requirements.

Confidence Intervals

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

Sample sizes for estimation of exposure-specific disease rates in population-based case-control studies.

This paper discusses sample sizes for estimation of exposure-specific disease rates for population-based case-control studies. Neutra and Drolette's confidence limits, which are based on the approximate normality of the logarithm of the ratio of independent binomial exposure rates, are used to determine the sample sizes required for precise estimation of exposure-specific disease rates. It is shown that, for large sample sizes, the disease rate in the exposed population is more precisely estimated than the disease rate in the unexposed population when more than 50% of the cases are exposed, and that the converse is true when fewer than 50% of the cases are exposed. Expressions are derived for the optimal case and control sample sizes that ensure the required level of precision and minimize the total study size. The optimum control-to-case ratio is found to be equal to the square root of the exposure odds ratio. The optimum number of cases and the total study size are found to be smaller for precise estimation of the disease rate in the exposed population than for precise estimation of the exposure odds ratio when the disease is rare.

Humans

The efficacy of psychotropic drugs: implications for power analysis.

The estimation of the correct sample size to successfully test a hypothesis has become critical. A common approach to this problem is for the investigating team to complete a pilot study of a few patients to establish the "active drug-placebo" difference, using this "effect size" to perform the power analysis for sample size estimation. Given the variability evident in the effect size from completed and published studies, the pilot study approach may not be entirely dependable. The authors propose a method to obtain this initial "active drug-placebo" difference, in the field of psychotropic drug research. They apply meta-analysis to statistically summarize effect sizes obtained from an exhaustive review of the literature for a specific psychotropic drug in a given clinical condition. All double-blind, random assignment studies are used to calculate the effect size; therefore, no selection bias exists. These literature-based effect sizes are then used to perform the traditional power analysis for sample size estimation. The authors propose these estimations as a convenient reference source for future clinical investigators.

Humans

Statistical significance and statistical power in hypothesis testing.

Experimental design requires estimation of the sample size required to produce a meaningful conclusion. Often, experimental results are performed with sample sizes which are inappropriate to adequately support the conclusions made. In this paper, two factors which are involved in sample size estimation are detailed--namely type I (alpha) and type II (beta) error. Type I error can be considered a "false positive" result while type II error can be considered a "false negative" result. Obviously, both types of error should be avoided. The choice of values for alpha and beta is based on an investigator's understanding of the experimental system, not on arbitrary statistical rules. Examples relating to the choice of alpha and beta are presented, along with a series of suggestions for use in experimental design.

Research Design

[Estimation of sample size in randomized controlled clinical trials--elimination of various systematic biases by the utilization of computer network system].

Although sample size calculation is mandatory in clinical trials, the power of most of the published small size clinical studies, was only about 0.25 instead of 0.80 which is normally required in a standard randomized controlled trial. This phenomenon is probably due to the publication bias. In a cancer clinical study, the ideal sample size needed in a trial exceeds over a thousand, when significance level was fixed under 0.05 and treatment difference is estimated from 10 to 15%. In such cases, evaluation of a new treatment in less common cancers or in a specified strata become unfeasible. Although statistically plausible clinical trial is difficult, small trials of newly advocated treatment is likely to be performed elsewhere, and presentation of these haphazard results might propagate a wrong information about the new treatment. To prevent the dissemination of these biased results, 1) preregistration of all planned clinical trials to an authorized organization before the initiation of the trial, 2) randomization of the patients entered in the trial from the first case, and 3) registration of all available data of the patients and meta-analysis of preregistered multiple trials, should be the most effective counterplans. In order to achieve those functions, installation of a computer assisted coordinating center is considered to be the best solution for the proper evaluation of the clinical trial as well as for the evaluation of a new treatment. With the collaboration of regional affiliating hospitals, a pilot study have started to establish a computer network system.

Database Management Systems

An iterative approach to the analysis of EM autoradiographs. II. Estimates of sample sizes and confidence limits.

The errors inherent in EM autoradiography are discussed and certain of them deemed to be of particular practical significance in the quantitative assessment of preparations. A method is described for estimating the standard errors attributable to each of several sources of variation and thence for obtaining the overall standard error value to be attached to relative activity estimates obtained in the method of Downs & Williams (1978). In an appendix, a fully worked example is given illustrating clearly the strategy of the method and the magnitudes of error estimates that are to be attached to the final specific activity values.

Autoradiography

On sample sizes to estimate the protective efficacy of a vaccine.

To estimate vaccine protective efficacy, defined as VE = 1 - ARV/ARU where ARV is the disease attack rate in the vaccinated group and ARU is the disease attack rate in the controls, investigators have used both cohort and case-control designs. For each design, we present a method for calculation of the sample size required to provide an approximate confidence interval for VE of predetermined width and probability of coverage. The required sample size is a function of the desired width of the confidence interval, the probability of coverage, the assumed VE, and, for cohort designs, the assumed disease attack rate in the controls, and for case-control designs, the assumed vaccine exposure prevalence for the controls.

Child, Preschool

Variability of indexes for myocardial ischemia: a comparison of exercise treadmill test, ambulatory electrocardiographic monitoring and symptoms of myocardial ischemia.

Fifty-four patients with chronic stable angina were studied to determine and compare weekly variability of indexes for the detection of myocardial ischemia. All patients underwent three single-blind placebo periods, each lasting 1 week. An exercise treadmill test, 24 h ambulatory electrocardiographic (Holter) monitoring (analyzed blindly) and an accurate diary of anginal attacks and nitroglycerin use were obtained at the end of each placebo period. An unbalanced, completely random component of variance analysis was used to calculate a component for within subject variability and a component for among subject variability. The coefficient of variation and percent variation (within subjects) of onset of chest pain during exercise were 19% and 30%, respectively; the corresponding values were 28% and 33% for onset of 1 mm ST depression, 15% and 15% for exercise duration, 44% and 27% for number of ischemic episodes/24 h, 56% and 43% for anginal frequency and 55% and 27% for nitroglycerin consumption, respectively. With use of this statistical method and variation within subjects, the change in the value of each variable necessary to exceed those attributable to spontaneous variation was determined. The trade-off between repeated measurements and number of subjects, the sample size estimated for planning studies and the minimal sample size for using various designs were also determined. Although the data indicate that all indexes for myocardial ischemia, both during exercise and during daily activity, vary considerably, but the exercise variables have less variability and are more reproducible.(ABSTRACT TRUNCATED AT 250 WORDS)

Ambulatory Care

A simplified general method for cluster-sample surveys of health in developing countries.

General guidelines are presented for the use of cluster-sample surveys for health surveys in developing countries. The emphasis is on methods which can be used by practitioners with little statistical expertise and no background in sampling. A simple self-weighting design is used, based on that used by the World Health Organization's Expanded Programme on Immunization (EPI). Topics covered include sample design, methods of random selection of areas and households, sample-size calculation and the estimation of proportions, ratios and means with standard errors appropriate to the design. Extensions are discussed, including stratification and multiple stages of selection. Particular attention is paid to allowing for the structure of the survey in estimating sample size, using the design effect and the rate of homogeneity. Guidance is given on possible values for these parameters. A spreadsheet is included for the calculation of standard errors.

Child

Measurement error in assessing the size of posterior subcapsular cataracts from retroillumination photographs.

Twenty-six eyes with posterior subcapsular opacities of various sizes were photographed with the Neitz-Kawara Retroillumination camera. The outline of the opacity in a single photograph of each opacity was traced onto a transparent plastic overlay twice by two independent outliners. Two methods were used to estimate the area within the outlines of the opacities. In the first, a transparent overlay with a standard grid was used to count the number of boxes within the outlines. The second method used computer planimetry to estimate the area within the tracings. We estimated the measurement error associated with a single outlining of an opacity and the contribution of the measurement error to overall sample size requirements in studies comparing the mean areas of posterior subcapsular opacities. Variability in the measurement techniques contributed fewer than 20 additional subjects to overall sample size estimates, a small contribution to total sample size requirements in most studies. An outliner's inherent variability in outlining an opacity was a much larger contributor to the measurement error than was variability in assessing the area of the outline of the opacity. While within outliner variability was similar for the two persons outlining the opacities, there were systematic differences in the way the two traced the outlines. Variability from the use of separate photographs of the same opacity taken by different photographers was minimal.

Cataract