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PubMed2001

[Roaming through methodology. XXXIII. Ethics of sample size estimation: less subjects needed for a one-sided than for a two-sided statistical investigation].

In sample size calculations for clinical trials, two-sided statistical testing is the usual starting point. Compared with one-sided testing, this option requires the inclusion of a larger number of study subjects, and a larger number of study events will be needed before a conclusion can be reached. It is therefore ethically relevant to consider in which situations one-sided testing should be the preferred option. One-sided statistical testing is preferable when the research hypothesis is one-sided (is intervention A better and intervention B?), or when only a clearly better result for A compared to B will have clinical consequences (e.g. if A is more cumbersome or more invasive to the patient than B). For the estimation of the number of study subjects needed, one-sided testing should then be assumed. If a new intervention is to be tested by comparison with placebo treatment or with absence of treatment, one-sided testing is an adequate starting point for sample size estimation.

Case-Control Studies↗

PubMed2004

On sample size for sensitivity and specificity in prospective diagnostic accuracy studies.

The design of a study of disease screening tests may be based on hypothesis tests for the sensitivity and specificity of the tests. The case-control study requires knowledge of the disease status of patients at the time of enrollment. This may not be possible in a prospective setting, when the gold standard is obtained subsequent to the initial screening and the number of diseased individuals is random and can not be fixed by design. Several ad hoc procedures for determining the total sample size are commonly used by practitioners, for example, the prevalence inflation method. The properties of these methods are not well understood. We develop a formal method for sample size and power calculations based on the unconditional power properties of the test statistics. The approach provides novel insights into the behaviour of the commonly used methods. We find that the ad hoc prevalence inflation method may serve as a useful approximation to our rigorous framework for sample size determination in the prospective set-up. The design of a large population-based study of mammography for breast cancer screening illustrates the key issues.

Breast Neoplasms↗

PubMed1998

Sample size and power calculations for comparing two independent proportions in a 'negative' trial.

Statistical methods for evaluating the adequacy of sample size and power cater mainly to the testing for treatment difference in a 'positive' trial. In biomedical research, the trial can sometimes be postulated as 'negative' to demonstrate that the different treatment groups are statistically equivalent. Herein we describe a computer program to determine the adequacy of sample size and power for comparing two independent proportions in a 'negative' trial. The program is written in MicroSoft QuickBasic Version 4.5, and its executable file is suitable for use as a stand-alone program on a microcomputer.

Clinical Trials as Topic↗

PubMed2005

Sample size calculation for simulation-based multiple-testing procedures.

In this article, we present a simple method to calculate sample size and power for a simulation-based multiple testing procedure which gives a sharper critical value than the standard Bonferroni method. The method is especially useful when several highly correlated test statistics are involved in a multiple-testing procedure. The formula for sample size calculation will be useful in designing clinical trials with multiple endpoints or correlated outcomes. We illustrate our method with a quality-of-life study for patients with early stage prostate cancer. Our method can also be used for comparing multiple independent groups.

Computer Simulation↗

PubMed2001

Effect of continuous versus dichotomous outcome variables on study power when sample sizes of orthopaedic randomized trials are small.

It is often not feasible to conduct large trials in orthopaedic surgery. Therefore, surgeons must identify strategies to optimize the statistical power of their smaller studies. The aim of this study was to compare study power in randomized trials with continuous versus dichotomous outcome variables. We performed a systematic review of the literature to identify randomized trials in orthopaedic trauma. Of these, we examined only those trials with small sample sizes (50 patients or less). The outcomes in each eligible study were categorized as continuous or dichotomous. Standard power calculations were performed for each study, and comparisons were made between continuous and dichotomous outcome variables. We identified 196 randomized trials in orthopaedic trauma. Of these, 76 trials had a sample size of 50 patients or fewer (29 trials with continuous outcomes, 47 trials with dichotomous outcomes). Studies that reported continuous outcomes had a significantly higher mean power than those that reported dichotomous variables (power 49% vs 38%, p=0.042). Twice as many trials with continuous outcome variables reached acceptable levels of study power (i.e. >80% power) when compared with trials with dichotomous variables (37% vs 18.6%, p=0.04). When orthopaedic surgeons anticipate small sample sizes for their study, they can optimize their study's statistical power by choosing a continuous outcome variable.

Cluster Analysis↗

PubMed1986

Sample size determination in clinical trials with time-dependent rates of losses and noncompliance.

Sample size determination is an important part of planning for clinical trials. During the course of a typical clinical trial, people are lost because of competing risks, noncompliance, and the like. Event rates available to the trial designers usually do not take these losses into consideration so that adjustment of these rates is necessary for sample size calculation. This article presents a method of adjusting such rates in the presence of time-dependent rates of losses, noncompliance, and the like. Lag in the effectiveness of medication is also considered.

Clinical Trials as Topic↗

PubMed2005

Sample size calculation for clinical trials using magnetic resonance imaging for the quantitative assessment of carotid atherosclerosis.

PURPOSE: To provide sample size calculation for the quantitative assessment of carotid atherosclerotic plaque using non-invasive magnetic resonance imaging in multi-center clinical trials. METHODS. As part of a broader double-blind randomized trial of an experimental pharmaceutical agent, 20 asymptomatic placebo-control subjects were recruited from 5 clinical sites for a multi-center study. Subjects had 4 scans in 13 weeks on GE 1.5 T scanners, using TOF, T1-/PD-/T2- and contrast-enhanced Tl-weighted images. Measurement variability was assessed by comparing quantitative data from the index carotid artery over the four time points. The wall/outer wall (W/OW) ratio was calculated as wall volume divided by outer wall volume. The percent lipid-rich/necrotic core (%LR/NC) and calcification (%Ca) were measured as a proportion of the vessel wall. For %LR/NC and %Ca, only those subjects that exhibited LR/NC or Ca components were used in the analysis. RESULTS: Measurement error was 5.8% for wall volume, 3.2% for W/OW ratio, 11.1% for %LR/NC volume and 18.6% for %Ca volume. Power analysis based on these values shows that a study with 14 participants in each group could detect a 5% change in W/OW ratio, 10% change in wall volume, and 20% change in %LR/NC volume (power = 80%, p < .05). The calculated measurement errors presume any true biological changes were negligible over the 3 months that subjects received placebo. CONCLUSION: In vivo MRI is capable of quantifying plaque volume and plaque composition, such as %lipid-rich/necrotic core and %calcification, in the clinical setting of a multi-center trial with low inter-scan variability. This study provides the basis for sample size calculation of future MRI trials.

Aged↗

PubMed1998

Sample size review in a head injury trial with ordered categorical responses.

Between 1993 and 1996, a total of 452 patients were entered into a randomized trial evaluating eliprodil (a non-competitive NMDA receptor antagonist) in patients suffering from severe head injury. The primary efficacy analysis concerned the Glasgow Outcome Score (GOS), six months after randomization. This outcome was classified into three ordered categories: good recovery; moderate disability, and the worst category made up by combining severe disability, vegetative state and dead. A sample size calculation was performed prior to the commencement of the study, using a formula which depends on the anticipated proportions of patients in the three different outcome categories, the proportional odds assumption and on the relationship between outcome and prognostic factors such as Glasgow Coma Score at entry. Owing to uncertainty about the influence of prognostic factors, and about the proportion of patients in the three GOS categories, a blinded sample size review was planned. This review was performed on the basis of the first 93 patients to respond, and this led to an increase in the sample size from 400 to 450. In this paper the pre-trial simulations showing that the type I error rate would be influenced and the power would be preserved will be presented, and the implementation of the procedure will be described.

Craniocerebral Trauma↗

PubMed2004

The impact of sample size and marker selection on the study of haplotype structures.

Several studies of haplotype structures in the human genome in various populations have found that the human chromosomes are structured such that each chromosome can be divided into many blocks, within which there is limited haplotype diversity. In addition, only a few genetic markers in a putative block are needed to capture most of the diversity within a block. There has been no systematic empirical study of the effects of sample size and marker set on the identified block structures and representative marker sets, however. The purpose of this study was to conduct a detailed empirical study to examine such impacts. Towards this goal, we have analysed three representative autosomal regions from a large genome-wide study of haplotypes with samples consisting of African-Americans and samples consisting of Japanese and Chinese individuals. For both populations, we have found that the sample size and marker set have significant impact on the number of blocks and the total number of representative markers identified. The marker set in particular has very strong impacts, and our results indicate that the marker density in the original datasets may not be adequate to allow a meaningful characterisation of haplotype structures. In general, we conclude that we need a relatively large sample size and a very dense marker panel in the study of haplotype structures in human populations.

Black or African American↗

PubMed1999

Sample size for comparing linear growth curves.

Assuming a linear growth curve model under a suitable link function, we compute the sample size for comparing two treatment groups when the repeated measurements marginally follow exponential family distributions. From the treatment profiles of the chosen link function, we compute the common intercept beta0 and the regression slopes beta1 and beta2 to define delta = beta1 - beta2, the difference to be detected, under a specified alternative hypothesis. The dispersion matrices of the generalized estimating equations estimators are obtained under the null and alternative hypotheses using a suitable working correlation matrix. We compute the sample size assuming that delta is asymptotically normal. Details are worked out for repeated measures designs with binary and count data along with numerical examples.

Female↗

PubMed1992

Sample size requirements for clinical trials of isolated systolic hypertension.

1. This study investigated components of blood pressure variability in elderly subjects with isolated systolic hypertension (ISH) using both ambulatory blood pressure monitoring (ABPM) and casual clinic blood pressure measurement. These were then used to determine sample size requirements for clinical trials of different designs. 2. Eleven elderly subjects not receiving antihypertensive medication were seen on four occasions at weekly intervals. On each occasion blood pressure was measured in the clinic and then for 24 h using a non-invasive ABPM device. Nested analysis of variance was used to calculate the 'between subject' and 'between subject within occasion' components of blood pressure variability. 3. Increasing the number of readings or occasions where measurement was performed in a parallel group trial only reduced the variability substantially when the number of subjects involved was less than 50. Use of a cross-over design substantially reduced the sample size required. 4. ABPM appears most useful as a strategy for reducing sample size in parallel group trials in ISH involving small numbers of subjects measured on one occasion.

Aged↗

PubMed2002

The effect of sample size and disease prevalence on supervised machine learning of narrative data.

This paper examines the independent effects of outcome prevalence and training sample sizes on inductive learning performance. We trained 3 inductive learning algorithms (MC4, IB, and Naïve-Bayes) on 60 simulated datasets of parsed radiology text reports labeled with 6 disease states. Data sets were constructed to define positive outcome states at 4 prevalence rates (1, 5, 10, 25, and 50%) in training set sizes of 200 and 2,000 cases. We found that the effect of outcome prevalence is significant when outcome classes drop below 10% of cases. The effect appeared independent of sample size, induction algorithm used, or class label. Work is needed to identify methods of improving classifier performance when output classes are rare.

Algorithms↗

PubMed2004

Sample size for testing and estimating the difference between two paired and unpaired proportions: a 'two-step' procedure combining power and the probability of obtaining a precise estimate.

Clinical trials and scientific research studies are currently planned calculating sample sizes to fulfill power requirements, but the simultaneous need to obtain a satisfactorily precise effect estimate is not widely recognized. I have devised a 'two-step' iterative procedure for comparing two binomial parameters for two paired and unpaired proportions (the most frequent situations in scientific research), which takes into account power and the probability of obtaining a predetermined precision of the effect estimate. The first step provides the sample size for the power of the statistical test, the expected width of its corresponding confidence interval, and the probability of obtaining, under the alternative hypothesis, confidence intervals whose width is less than that expected. The second step iteratively increases this sample size until the probability of obtaining such confidence intervals exceeds a required threshold.

Clinical Trials as Topic↗

PubMed1992

Sample size for a phylogenetic inference.

The objective of this work is to describe sample-size calculations for the inference of a nonzero central branch length in an unrooted four-species phylogeny. Attention is restricted to independent binary characters, such as might be obtained from an alignment of the purine-pyrimidine sequences of a nucleic acid molecule. A statistical test based on a multinomial model for character-state configurations is described. The importance of including invariable sites in models for sequence change is demonstrated, and their effect on sample size is quantified. The methods are applied to a four-species alignment of small-subunit rRNA sequences derived from two archaebacteria, a eubacteria and a eukaryote. We conclude that the information in these sequences is not sufficient to resolve the branching order of this tree. Estimates of the number of aligned nucleotide positions required to provide a reasonably powerful test are given.

Archaea↗

PubMed1993

Power and sample size calculations for exact conditional tests with ordered categorical data.

We develop an algorithm for computing sample sizes, equal or unequal, for categorical data. We illustrate its use in the two-sample setting using the Wilcoxon rank-sum statistic, but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well. The sample size determinations can be based on either exact power or on a very precise Monte Carlo estimate of it. To reduce the computations further, power can be computed as a function of asymptotic critical values when the number of categories is not too small. For the Wilcoxon statistic we show that this approximation works well if there are more than five response categories.

Humans↗

PubMed2002

Sample-size redetermination for repeated measures studies.

Clinical trialists recently have shown interest in two-stage procedures for updating the sample-size calculation at an interim point in a trial. Because many clinical trials involve repeated measures designs, it is desirable to have available practical two-stage procedures for such designs. Shih and Gould (1995, Statistics in Medicine 14, 2239-2248) discuss sample-size redetermination for repeated measures studies but under a highly simplified setup. We develop two-stage procedures under the general mixed linear model, allowing for dropouts and missed visits. We present a range of procedures and compare their Type I error and power by simulation. We find that, in general, the achieved power is brought considerably closer to the required level without inflating the Type I error rate. We also derive an inflation factor that ensures the power requirement is more closely met.

Analysis of Variance↗

PubMed1983

Sample size and duration for cohort studies of survival time with covariables.

The determination of sample size and duration for cohort studies with covariables is considered. An exponential model, using the form due to Feigl and Zelen (1965, Biometrics 21, 826-838) for the hazard with covariates and asymptotic normality of the maximum likelihood estimators of the parameters, is assumed. Emphasis is on applications involving two parameters, namely an underlying hazard and the coefficient of a single concomitant variable. The results of George and Desu (1974, Journal of Chronic Diseases 27, 15-24) are reproduced and extended to take account of censoring. An example with more than two dose groups is presented. For situations where the sample size is fixed and Type I error is specified, extension of the follow-up time is considered for the purpose of achieving the desired Type II error, given a null hypothesis and specific alternative hypothesis. Generalizations to situations with other forms for the hazard rate and multiple covariables are indicated.

Clinical Trials as Topic↗

PubMed1995

Optimal experimental design and sample size for the statistical evaluation of data from somatic mutation and recombination tests (SMART) in Drosophila.

In genetic toxicology it is important to know whether chemicals should be regarded as clearly hazardous or whether they can be considered sufficiently safe, which latter would be the case from the genotoxicologist's view if their genotoxic effects are nil or at least significantly below a predefined minimal effect level. A previously presented statistical decision procedure which allows one to make precisely this distinction is now extended to the question of how optimal experimental sample size can be determined in advance for genotoxicity experiments using the somatic mutation and recombination tests (SMART) of Drosophila. Optimally, the statistical tests should have high power to minimise the chance for statistically inconclusive results. Based on the normal test, the statistical principles are explained, and in an application to the wing spot assay, it is shown how the practitioner can proceed to optimise sample size to achieve numerically satisfactory conditions for statistical testing. The somatic genotoxicity assays of Drosophila are in principle based on somatic spots (mutant clones) that are recovered in variable numbers on individual flies. The underlying frequency distributions are expected to be of the Poisson type. However, some care seems indicated with respect to this latter assumption, because pooling of data over individuals, sexes, and experiments, for sample, can (but need not) lead to data which are overdispersed, i.e., the data may show more variability than theoretically expected. It is an undesired effect of overdispersion that in comparisons of pooled totals it can lead to statistical testing which is too liberal, because overall it yields too many seemingly significant results. If individual variability considered alone is not in contradiction with Poisson expectation, however, experimental planning can help to minimise the undesired effects of overdispersion on statistical testing of pooled totals. The rule for the practice is to avoid disproportionate sampling. It is recalled that for optimal power in statistical testing, it is preferable to use equal total numbers of flies in the control and treated series. Statistical tests which are based on Poisson expectations are too liberal if there is overdispersion in the data due to excess individual variability. In this case we propose to use the U test as a non-parametric two-sample test and to adjust the estimated optimal sample size according to (i) the overdispersion observed in a large historical control and (ii) the relative efficiency of the U test in comparison to the t test and related parametric tests.

Animals↗