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PubMed2004

Sample-size requirements for comparisons of two groups on repeated observations of a binary outcome.

When preparing a research protocol, an investigator must be as careful in projecting sample-size requirements as in specifying hypotheses. In this article, tables are presented that provide estimates of sample-size requirements for statistical power of 0.80 with two-tailed alpha-levels of 0.05 in studies with a balanced design that plan to compare two groups on time-averaged, repeated observations of a binary outcome. The estimates, which are based on the algorithm of Diggle, Heagerty, Liang, and Zeger, are a function of several features of the study, including the response rates for each group, the number of repeated observations per participant, and the strength of the association among observations within participants as quantified with an intraclass correlation coefficient.

Algorithms↗
PubMed1991

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↗
PubMed1987

Estimating sample size for longitudinal studies of age-related cognitive decline.

Cross-sectional age-group norms for cognitive tests reveal a progressive age-related decline. There is current interest in the possibility of developing interventions that forestall the normal cognitive decline in elderly adults. This raises new research design issues, one of which is the estimation of appropriate sample sizes for longitudinal studies when only cross-sectional data are presently available. Formulae for estimating change parameters from cross-sectional data are presented in this article. Based on age-related changes in cross-sectional norms for the Wechsler Adult Intelligence Scale (WAIS), the sample sizes required for controlled intervention studies of 1 to 3 years duration are very large. If cognitive decline within individuals is not as great as the decline evident in cross-sectional norms, the required sample sizes will be even larger.

Aged↗
PubMed2004

Sample sizes based on exact unconditional tests for phase II clinical trials with historical controls.

Investigated in the setting of phase II clinical trials is the two-sample binomial problem of testing H0: pe = pc H1: pe > pc, where pe and pc are the unknown target population response rates for the experimental and control groups, respectively, using the usual Z-statistic with pooled variance estimator. The cornerstones that make this paper unique are as follows. First, the emphasis is on determining the sample size given that the control group information has already been collected (historical control). Second, exact unconditional inference, rather than an asymptotic method, is utilized. Sample size tables, contrasting the exact and asymptotic methods, are provided. Although asymptotic results were usually fairly close to the exact results, some important differences were observed.

Clinical Trials, Phase II as Topic↗
PubMed2005

Simple nomograms to calculate sample size in diagnostic studies.

OBJECTIVES: To produce an easily understood and accessible tool for use by researchers in diagnostic studies. Diagnostic studies should have sample size calculations performed, but in practice, they are performed infrequently. This may be due to a reluctance on the part of researchers to use mathematical formulae. METHODS: Using a spreadsheet, we derived nomograms for calculating the number of patients required to determine the precision of a test's sensitivity or specificity. RESULTS: The nomograms could be easily used to determine the sensitivity and specificity of a test. CONCLUSIONS: In addition to being easy to use, the nomogram allows deduction of a missing parameter (number of patients, confidence intervals, prevalence, or sensitivity/specificity) if the other three are known. The nomogram can also be used retrospectively by the reader of published research as a rough estimating tool for sample size calculations.

Diagnostic Techniques and Procedures↗
PubMed1999

Estimating sample sizes for continuous, binary, and ordinal outcomes in paired comparisons: practical hints.

Paired data occur in crossover trials and matched case-control studies, and it is rare to find studies reporting sample size calculations associated with these types of studies, despite recommendations from editors that sample size calculations should be justified. In this article we describe some simple formulas and strategies for calculating the number of patients that should be entered into a matched or paired study when the outcome measures are continuous, binary, or ordinal.

Aged↗
PubMed1994

Presentation of the intrasubject coefficient of variation for sample size planning in bioequivalence studies.

Bioequivalence studies are generally performed as crossover studies and, therefore, information on the intrasubject coefficient of variation is needed for sample size planning. Unfortunately, this information is usually not presented in publications on bioequivalence studies, and only the pooled inter- and intrasubject coefficient of variation for either test or reference formulation is reported. Thus, the essential information for sample size planning of future studies is not made available to other researchers. In order to overcome such shortcomings, the presentation of results from bioequivalence studies should routinely include the intrasubject coefficient of variation. For the relevant coefficients of variation, theoretical background together with modes of calculation and presentation are given in this communication with particular emphasis on the multiplicative model.

Humans↗
PubMed1998

Sample size required for the accurate determination of fiber area and capillarity of human skeletal muscle.

This study aimed to determine the skeletal muscle fiber sample size required for a reliable, valid representation of an individual's average fiber area and capillary contacts (CC) per fiber. Biopsies were obtained from the biceps brachii of 11 college-age, recreational resistance-trained men in conjunction with a study investigating how muscle morphology changed after 12 weeks of resistance training. The effect of additional measurements on the rolling cumulative means for fiber area and CC per fiber was evaluated using sequential estimation analysis. Results showed that group cumulative mean and standard deviation had stabilized by 50 fiber measurements per individual for type I and II fibers and CC per fiber. Significant correlations (.96-.99; p < .05) existed between the 50th and 95th/100th cumulative individual means. These results indicate that a typical skeletal muscle needle biopsy would be sufficient to characterize type I and II fiber areas and CC per fiber of an individual in most subject populations, although the required sample size for characterizing fiber subtypes might be different.

Adult↗
PubMed1994

Sample size calculations for single group post-marketing cohort studies.

In pharmacoepidemiology, single group cohort is the most frequently proposed design to determine if the incidence rate of an adverse drug reaction among the exposed differs from a reference value. In many situations, the number of events expected in the cohort is too small to conduct sample size calculations based on the normal distribution. This paper proposes, for a single group cohort study, calculations and tables derived from the Poisson distribution. The results are based on a one-sided test with a 0.05 significance level and a power of 0.9 and 0.8. Two parameters have to be specified a priori: the expected incidence of the event under the null hypothesis and the minimum risk ratio to be detected. The required sample size and the critical number of events to reject the null hypothesis are directly derived from the tables. Results show that the normal approximation may lead to an underestimation of the required sample size.

Cohort Studies↗
PubMed1984

Sample size graphs for "proving the null hypothesis".

Sample size graphs are given for clinical trials designed to test whether an experimental therapy is as effective as a standard therapy. We assume a dichotomous outcome variable and a one-sided test of the hypothesis that the probability of success with standard therapy is greater than the probability of success with experimental therapy by at least some specified amount delta. Graphs are given for significance level alpha = 0.01, 0.025, 0.05; type II error beta = 0.10, 0.20; and delta = 0.10, 0.20.

Clinical Trials as Topic↗
PubMed2002

A note on sample size calculation in bioequivalence trials.

Based on fundamental pharmacokinetic relationships, a multiplicative model is commonly used in bioequivalence trials. With regard to the parametric analysis, this implies the assumption of a lognormal distribution. Statistical methods for sample size calculation has been consolidated over the last years. Recently, methods for sample size calculation in the additive model, i.e., under normality assumption, were presented. Hence, these methods are reviewed from a statistical and regulatory point of view.

Models, Biological↗
PubMed1993

HIV vaccine trials: some design issues including sample size calculation.

Anticipating the availability of one or more candidate HIV vaccines for efficacy testing in the next few years, public health agencies are now planning for the conduct of large-scale efficacy trials. We expect these trials to be randomized, double-blind, placebo-controlled studies with prevention of infection as the primary goal. We discuss in detail factors that influence sample size. Factors most influential are the incidence rate of HIV infection in the study population and the minimum efficacy at which a vaccine is still considered acceptable. The smaller either of these factors is, the larger the sample size will be. The desire to complete trials quickly, the gradual accrual of benefit from vaccination, the inaccuracies of assays to detect infection, the need to counsel participants to avoid exposure to HIV, and loss to follow-up all tend to drive up sample size. To illustrate, 83 subjects per study arm suffice to detect 90% efficacy in a population with a 7% annual risk of infection. This assumes a 3-year study with accrual completed in 1 year, no loss to follow-up, and Types I and II error rates of 5 and 10%, respectively. In contrast, 4,254 subjects per arm are required to identify a 60% effective vaccine in a population with a 1% annual risk. The study is also shortened to 2 years, assumes a 5% annual loss to follow-up, and supposes that the full benefit of vaccination is achieved in 6 months. The most realistic assumptions indicate that trials are very likely to require several thousand participants. Limitations of the proposed designs are also discussed.

Clinical Trials as Topic↗
PubMed1985

Applicability of sample size calculations based on a comparison of proportions for use with the logrank test.

The asymptotic relative efficiency of a test of proportions versus the logrank test is calculated for various clinical trial designs that are used to compare the survival of two treatment groups. The asymptotic relative efficiency is shown to be a reasonable guide to the relative sample sizes required for the logrank and proportions test. It is shown that the efficiency of the proportions test is near 1.0 for designs corresponding to typical studies of cardiovascular disease, for which the duration of the experiment is short compared to mean survival. This result is of practical importance, because sample size calculations based on the comparison of proportions are available to cover many contingencies, including a delay in the onset of full treatment effectiveness, whereas similar calculations have not been published for the logrank statistic. On the other hand, the efficiency of the proportions test can drop to 72% or less for trials in which the accrual period exceeds the mean survival, as is often the case in trials to treat cancer. In such cases, sample size calculations for the proportions test would be [(1/0.72) - 1] = 39% larger than required for the logrank test. Thus, power calculations specifically tailored to the logrank test should be used for studies with a duration comparable to mean survival, if one intends to employ the logrank statistic.

Humans↗
PubMed2006

Optimization of sample size in controlled experiments: the CLAST rule.

Sequential rules are explored in the context of null hypothesis significance testing. Several studies have demonstrated that the fixed-sample stopping rule, in which the sample size used by researchers is determined in advance, is less practical and less efficient than sequential stopping rules. It is proposed that a sequential stopping rule called CLAST (composite limited adaptive sequential test) is a superior variant of COAST (composite open adaptive sequential test), a sequential rule proposed by Frick (1998). Simulation studies are conducted to test the efficiency of the proposed rule in terms of sample size and power. Two statistical tests are used: the one-tailed t test of mean differences with two matched samples, and the chi-square independence test for twofold contingency tables. The results show that the CLAST rule is more efficient than the COAST rule and reflects more realistically the practice of experimental psychology researchers.

Behavioral Research↗
PubMed2004

Incorporating the sampling variation of the disease prevalence when calculating the sample size in a study to determine the diagnostic accuracy of a test.

During the design stage of a study to assess the population sensitivity (P(S)) (or specificity) of a diagnostic test, the number of subjects (N) who will be administered both a gold standard test and a new test needs to be calculated. A common approach is to calculate the number of cases (n) with a specific disease or condition as diagnosed by the gold standard test first, and then to determine N based on the prevalence or incidence rate of the disease (P(P)) in the population, calculated as N=n/P(P). Due to sampling variation, given the sample size N, the number of cases having the disease identified by the gold standard test could be less than N x P(P). In this case, the study would be under-powered and may fail to produce an unbiased and precise estimate. In this study, we investigated this possibility for a situation where the required sample size is calculated using the confidence interval approach. When the sampling variation is considered, the variance of the sample sensitivity is slightly inflated, but its confidence interval width becomes widely dispersed. In order to reach the originally designed precision, adjustment in the sample size, N, is needed and suggested in this paper.

Cross-Sectional Studies↗
PubMed1998

Sample size determination for phase II clinical trials based on Bayesian decision theory.

This paper describes an application of Bayesian decision theory to the determination of sample size for phase II clinical studies. The approach uses the method of backward induction to obtain group sequential designs that are optimal with respect to some specified gain function. A gain function is proposed focussing on the financial costs of, and potential profits from, the drug development programme. On the basis of this gain function, the optimal procedure is also compared with an alternative Bayesian procedure proposed by Thall and Simon. The latter method, which tightly controls type I error rate, is shown to lead to an expected gain considerably smaller than that from the optimal test. Gain functions with respect to which Thall and Simon's boundary is optimal are sought and it is shown that these can only be of the form considered, that is, with constant cost for phase III study and cost of the phase II study proportional to the sample size, if potential profit increases over time.

Bayes Theorem↗
PubMed2000

Sample size to test for interaction between a specific exposure and a second risk factor in a pair-matched case-control study.

We discuss a sample size calculation for a pair-matched case-control study to test for interaction between a specific exposure and a second risk factor. The second risk factor could be either binary or continuous. An algorithm for the calculation of sample size is suggested which is based on a logistic regression model that relates the logarithm of the disease-exposure odds ratio to the second risk factor. This problem is motivated by a study comparing the prevalence of GP-IIIa Pl(A2) polymorphism (the exposure) in individuals with and without myocardial infarction (case-control). One of the hypotheses in this study is whether or not there is an interaction between the prevalence of GP-IIIa Pl(A2) polymorphism and a second risk factor such as smoking status and homocysteine level. We introduce the algorithm in detail with several numerical examples.

Algorithms↗
PubMed1996

Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity.

Careful consideration of statistical issues related to the choice of a sample size is critical for achieving meaningful results in research studies designed to evaluate diagnostic tests. When assessing the ability of a diagnostic test to screen for disease, the parameters sensitivity, specificity, and predictive values are of interest. Study sample size requirements can be calculated based on a clinically acceptable degree of precision, the hypothesized values of sensitivity and specificity, and the estimated prevalence of disease in the target population. The simple methods and tables in this paper guide the researcher when deciding how many subjects to sample in a study designed to estimate both the sensitivity and the specificity of a diagnostic test, given a specified precision and estimated disease prevalence.

Bias↗