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PubMed1995

On the sample size for one-sided equivalence of sensitivities based upon McNemar's test.

In this paper we formalize the problem of testing the one-sided equivalence in the sensitivities of two medical diagnostic tests under a matched-pair study design. We derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests. We calculate upper boundary and midpoint sample sizes. Results of a Monte Carlo simulation study that compares the proposed sample size formulae with that of Lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper.

Binomial Distribution↗
PubMed2004

Centile charts II: alternative nonparametric approach for establishing time-specific reference centiles and assessment of the sample size required.

BACKGROUND: Reference intervals, and more generally centile estimates, are used to characterize a reference population for the purposes of interpreting an individual patient's clinical measurement. We describe methods of calculating reference intervals where these centiles vary with a covariate, usually age or time. METHODS: The US Food and Drug Administration and the IFCC have made recommendations on two approaches: the parametric approach, which models the structural characteristics of the data set with a theoretical distribution, and the nonparametric approach, which makes no particular assumption about this structure. In this report we propose a nonparametric procedure that relies on the principles of regression and show how sample size determination can be assessed. We also show how the sample size calculation is influenced by the distribution of the times measured. RESULTS: We illustrated our method on three data sets and compared the results for our proposed nonparametric method with parametric estimates. We showed that the bias is reduced and that the nonparametric method is less likely to produce fluctuating profiles. CONCLUSIONS: To achieve adequate precision the sample size needs to be larger than 120, as has often been recommended. If there is doubt about the parametric model, then threshold sample sizes may need to be as high as 500.

Adolescent↗
PubMed2006

Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: what sample size is needed for valid results?

Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait-multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M-1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M-1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean- and variance-adjusted chi(2) test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the chi(2) approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait-method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good -- albeit slightly liberal -- chi(2) approximation and stable and reliable parameter estimates for models of reasonable complexity (2-4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait-method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.

Humans↗
PubMed1997

Sample size required for predefined linkage decision quality.

A method for estimating the sample size required to attain a predefined linkage decision quality (type I and type II errors) is proposed using the linkage test power estimate developed by Ginsburg et al. [(1996) Genet Epidemiol 13:355-366]. The method is applicable for samples of arbitrarily structured pedigrees collected via proband. Comparison of different ascertainment schemes and pedigree structures by their consequent minimal sample size was performed. For recessive and dominant inheritance with complete penetrance, the relative ranks of the ascertainment schemes are invariant regardless of the true recombination fraction value and the trait and marker gene frequencies, which enables one to point out the better scheme. The feasibility of evaluating a sampling strategy by the cost of pedigree collection is also considered, and comparison between these two methods of sample planning is performed.

Gene Frequency↗
PubMed1996

The effects of sample size and variability on the correlation coefficient.

The purpose of the study was to investigate the effects of variability as a function of sample size on the Pearson product-moment correlation coefficient (PCC) under the assumption of a perfect relationship between two variables. The effects of sample size (subjects/trials) and variability on the PCC were demonstrated using a computer model. The model was also used to evaluate selected examples taken from the literature. The results indicated that variability in excess of 10% of the range for each variable resulted in a mean reduction of the shared variance by 50% or greater. Although sample size did not affect the mean PCC, it did have a dramatic effect on extreme percentile values producing unreliable results. These results indicate that a small PCC value can be an artifact of variability. It is suggested, therefore, that one should be cautious when stating conclusions regarding the relationship between two variables without having knowledge of the associated variabilities.

Humans↗
PubMed1994

Attentional effects on concurrent psychophysical discriminations: investigations of a sample-size model.

In two experiments, a concurrent discrimination paradigm was used to study the effects of visual attention on psychophysical judgments and the consistency of these effects with a sample-size model in which attention influences the variance of the internal representation used to make psychophysical judgments. Two pairs of lines were presented simultaneously--one on each side of fixation--and subjects had to indicate for each pair separately whether or not the lines had the same length. Attention was manipulated by instructing subjects to pay 100%, 75%, 50%, 25%, or 0% of their attention to the discrimination on one side, with the complementary amount of attention to the other side. In the first experiment, the relationship between attention and discrimination accuracy was consistent with the sample-size model both when attentional allocation varied from trial to trial and when it varied between blocks, and the relationship held over more widely varying attentional allocations than had previously been studied. In addition, discriminations were more accurate overall with varied than with blocked attentional allocation, suggesting that the two types of allocation do not merely differ in the degree to which attention is focused. The second experiment examined the effects of attentional allocation and stimulus variance, the latter being manipulated by randomly incrementing or decrementing line lengths. These manipulations had additive effects on total Thurstonian variance, and a version of the sample-size model gave an excellent quantitative fit to the obtained results. Besides supporting the sample-size model, the results of Experiment 2 suggest that criterion variance is at least as large as sensory variance and that criterion but not sensory variance increases with stimulus variance.

Attention↗
PubMed1991

Confidence intervals and sample sizes.

In a recent paper, Beal (1989, Biometrics 45, 969-977) considers the problem of determining the appropriate sample size when inference about a parameter theta is to be made on the basis of a confidence interval (CI). He suggests that the sample size should be chosen so that the probability that the length of the CI is less than a given value, conditional on the interval including the true theta, is greater than a specified level. In this note, in which we concentrate on two-sided intervals, this suggestion is examined, as is the effect of uncertainty in our knowledge of the population variance sigma 2 on estimates of sample size.

Biometry↗
PubMed1994

Sample sizes for usability studies: additional considerations.

Recently, Virzi (1992) presented data that support three claims regarding sample sizes for usability studies: (1) observing four or five participants will allow a usability practitioner to discover 80% of a product's usability problems, (2) observing additional participants will reveal fewer and fewer new usability problems, and (3) more severe usability problems are easier to detect with the first few participants. Results from an independent usability study clearly support the second claim, partially support the first, but fail to support the third. Problem discovery shows diminishing returns as a function of sample size. Observing four to five participants will uncover about 80% of a product's usability problems as long as the average likelihood of problem detection ranges between 0.32 and 0.42, as in Virzi. If the average likelihood of problem detection is lower, then a practitioner will need to observe more than five participants to discover 80% of the problems. Using behavioral categories for problem severity (or impact), these data showed no correlation between problem severity (impact) and rate of discovery. The data provided evidence that the binomial probability formula may provide a good model for predicting problem discovery curves, given an estimate of the average likelihood of problem detection. Finally, data from economic simulations that estimated return on investment (ROI) under a variety of settings showed that only the average likelihood of problem detection strongly influenced the range of sample sizes for maximum ROI.

Equipment Design↗
PubMed2002

Power and sample size determination for noninferiority trials using an exact method.

Noninferiority studies are frequently conducted to justify the development of new drugs and vaccines that have been shown to offer better safety profiles, easier administration, or lower cost while maintaining similar efficacy as compared to the standard treatment. Recently, exact methods have been developed to address the concern that existing asymptotic methods for analyzing and planning noninferiority may fail because of small sample size or because of skewed or sparse data structure. In this paper, we explore the use of exact methods in determining sample size and power for noninferiority studies that focus on the difference of two proportions. The methodology for sample size and power calculations is developed based on an exact unconditional test of noninferiority. We illustrate this exact method using a clinical trial example in childhood nephroblastoma and briefly discuss the optimal sample-size allocation strategy. This exact unconditional method performs very well in various scenarios and compares favorably to its asymptotic counterpart in terms of sensitivity. Therefore, it is a very desirable tool for planning noninferiority trials, especially in situations where asymptotic methods are likely to fail.

Algorithms↗
PubMed2006

Computing asymptotic power and sample size for case-control genetic association studies in the presence of phenotype and/or genotype misclassification errors.

It is well established that phenotype and genotype misclassification errors reduce the power to detect genetic association. Resampling a subset of the data (e.g, double-sampling) of genotype and/or phenotype with a gold standard measurement is one method to address this issue. We derive the non-centrality parameter (NCP) for the recently published Likelihood Ratio Test Allowing for Error (LRTae) in the presence of random phenotype and genotype errors. With the NCP, power and sample size can be analytically determined at any significance level. We verify analytic power with simulations using a 2**k factorial design given high and low settings of: case and control genotype frequencies, phenotype and genotype misclassification probabilities, total sample size, ratio of cases to controls, and proportions of phenotype and/or genotype double-samples. We also perform example applications of our method assuming equal costs for the LRTae method and the standard method that does not use double-sample information (LRTstd) to determine if power gain due to double-sampling a proportion of samples outweighs the reduction in sample size due to additional costs in obtaining double-samples. Our results showed a median difference of at most 0.01 between analytic and simulation power for the factorial design settings, with maximum difference of 0.054. For our cost/benefits analysis calculations, results for genotype errors are that double-sampling appears most beneficial (in terms of power gain) when cost of double-sampling is relatively low, irrespective of the proportion of individuals double-sampled. In the presence of phenotype error, there is always power gain using the LRTae method for the parameter settings considered. We have freely available software that performs power and sample size calculations for the LRTae method and cost/benefits analyses comparing power for LRTae and LRTstd methods assuming equal costs.

Journal Article↗
PubMed2006

Approximate sample size calculations with microarray data: an illustration.

We outline a method of sample size calculation in microarray experiments on the basis of pilot data and illustrate its practical application with both simulated and real data. The method was shown to be consistent (as the number of 'probed genes' tends to infinity) under general conditions in an earlier, more 'theoretical' companion paper. Its implementation requires the values of test statistics, the sample size with which the statistics are computed, and the knowledge of their distribution under the null hypothesis.

Animals↗
PubMed1999

A random coefficient degradation model with random sample size.

In testing product reliability, there is often a critical cutoff level that determines whether a specimen is classified as "failed." One consequence is that the number of degradation data collected varies from specimen to specimen. The information of random sample size should be included in the model, and our study shows that it can be influential in estimating model parameters. Two-stage least squares (LS) and maximum modified likelihood (MML) estimation, which both assume fixed sample sizes, are commonly used for estimating parameters in the repeated measurements models typically applied to degradation data. However, the LS estimate is not consistent in the case of random sample sizes. This article derives the likelihood for the random sample size model and suggests using maximum likelihood (ML) for parameter estimation. Our simulation studies show that ML estimates have smaller biases and variances compared to the LS and MML estimates. All estimation methods can be greatly improved if the number of specimens increases from 5 to 10. A data set from a semiconductor application is used to illustrate our methods.

Computer Simulation↗
PubMed2002

Sample size calculation for a historically controlled clinical trial with adjustment for covariates.

We present a Bayesian approach to determining the optimal sample size for a historically controlled clinical trial. This work is motivated by a trial of a new coronary stent that uses a retrospective control group formed from seven trials of coronary stents currently marketed in the United States. In studies involving nonrandomized control groups, hierarchical regression, propensity score methods, or other sophisticated models are typically required to account for heterogeneity among groups which, if ignored could bias the results. Sample size calculations for historically controlled trials of medical devices are often based on formulae derived for randomized trials and fail to account for estimation of model parameters, correlation of observations, and uncertainty in the distribution of covariates of the patients recruited in the new trial. We propose methodology based on stochastic optimization that overcomes these deficiencies. The methodology is demonstrated using an objective function based on the power of the trial from a Bayesian approach. Analytic approximations based on a covariate-free analysis that convey features of the power function are developed. Our principle conclusions are that exact sample size calculations can be substantially different from current approximations, and stochastic optimization provides a convenient method of computation.

Bayes Theorem↗
PubMed1989

Sample size determination for confidence intervals on the population mean and on the difference between two population means.

Sample size determination is usually based on the premise that a hypothesis test is to be used. A confidence interval can sometimes serve better than a hypothesis test. In this paper a method is presented for sample size determination based on the premise that a confidence interval for a simple mean, or for the difference between two means, with normally distributed data is to be used. For this purpose, a concept of power relevant to confidence intervals is given. Some useful tables giving required sample size using this method are also presented.

Biometry↗
PubMed2004

Sample size calculator for cluster randomized trials.

Cluster randomized trials, where individuals are randomized in groups are increasingly being used in healthcare evaluation. The adoption of a clustered design has implications for design, conduct and analysis of studies. In particular, standard sample sizes have to be inflated for cluster designs, as outcomes for individuals within clusters may be correlated; inflation can be achieved either by increasing the cluster size or by increasing the number of clusters in the study. A sample size calculator is presented for calculating appropriate sample sizes for cluster trials, whilst allowing the implications of both methods of inflation to be considered.

Algorithms↗
PubMed1999

Estimating the sample size for a t-test using an internal pilot.

If the sample size for a t-test is calculated on the basis of a prior estimate of the variance then the power of the test at the treatment difference of interest is not robust to misspecification of the variance. We propose a t-test for a two-treatment comparison based on Stein's two-stage test which involves the use of an internal pilot to estimate variance and thus the final sample size required. We evaluate our procedure's performance and show that it controls the type I and II error rates more closely than existing methods for the same problem. We also propose a rule for choosing the size of the internal pilot, and show that this is reasonable in terms of the efficiency of the procedure.

Clinical Trials, Phase II as Topic↗
PubMed1980

On approximate sample sizes for comparing two independent proportions with the use of Yates' correction.

An investigator wishes to compare two independent proportions, based on perhaps unequal sample sizes, by means of the chi squared test with the Yates' correction. A simple approximation is given to the sample size(s) required for the Yates-corrected chi squared test to have specified power; it is then compared with other approximations and with the exact sample size for the equal sample case. In that case the proposed approximation is quite similar to the approximate formula recently put forward by Casagrande, Pike and Smith (1978, Biometrics 34, 483-486).

Probability↗