Research Q and Q. Is there an optimal sample size for research involving human subjects? Is there a rule of thumb that might be used in determining sample size?
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A graphical aid for determining sample size when comparing two independent proportions.
Standard sample size calculations for n, the number of observations per group when comparing two independent proportions, P1 and P2, require the specification of four quantities: P1, one of the two proportions of interest; delta = P2 - P1, the smallest difference which it is important to detect; alpha, the significance level; and beta, the chance of failing to detect a difference as large as delta. In terms of these four quantities, the graphical aid is a series of charts showing isographs of sample size for selected values of n ranging from 35 to 500. The isographs, i.e. curves connecting points of equal sample size, are based on the asymptotic arc sine approximation and are plotted on the grid formed by P1 on the abscissa and delta on the ordinate. Eight separate charts are available for different choices of alpha and beta. These charts are especially useful in situations where the feasible sample size is roughly known, in which case the detectable difference, delta, can be read directly from the graph.
Mathematics↗
[Determination of the sample size and distribution of the ABO and Rh blood groups in Botucatu, Sã Paulo, Brazil (author's transl)].
In the present paper some statistical aspects referred to the distribution of the ABO and Rh blood groups were studied. The sample included 4,037 data, about white and no white persons, of both sexes, living in Botucatu. The results are presented with a calculation of the frequencies of the alleles responsible for the polymorphisms studied, the sample frequencies of the blood groups and their populations confidence-intervals estimates. The possibles interdependences for sex and color with the blood groups were verified by the chi2 test. The principal aim of the present study was to determine the ideal sample size. It was elaborated a table where are given populations sizes, samples sizes and the percentual relations between these values.
ABO Blood-Group System↗
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↗
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↗
On the sample size for studies based upon McNemar's test.
When computing the sample size for studies using McNemar's test, one needs to know the probability of discordance and the odds ratio to be detected. In many studies, the investigator is unable to specify the probability of discordance, but can state, at least approximately, the marginal probabilities of each variable. This information leads to restrictions on the possible values of the cell probabilities and provides a range of admissible values for the off-diagonal cells. We compute the sample size needed in these circumstances and compare them to the results cited by Schlesselman and Connett et al. These sample sizes for the method are quite close to those found in the Monte Carlo study of Connett et al.
Antibodies, Monoclonal↗
Sample size requirements for evaluating a conservative therapy.
Determination of an adequate sample size for a clinical trial has traditionally involved the specification of type I (false positive) and type II (false negative) error rates, and a difference that one wishes to detect. Because newer therapy has generally been more invasive or more toxic, it is conventional for the type I error to be 0.05 in order that new therapy not be accepted as superior unless its advantages are definitively established. Recently, many new trials have been directed toward showing that a more conservative treatment is equivalent in efficacy to a standard intensive therapy. In this paper, we provide formulas which prescribe the sample size necessary to meet certain criteria specified by the investigator for this alternative type of clinical trial. In addition, the percent increase in total sample size is described when more patients are allocated to one treatment than the other.
Biometry↗
Sample size needed for student ratings of instruction.
The number of evaluation forms students are asked to complete is multiplying. To reduce that number, the present study determines the minimum sample size needed for accurate student ratings of instruction. Typical questionnaire items using four- and seven-category ratings scales were studied. Data for four class sizes (40, 60, 100, 140) were sampled in graduated sizes, and a standard error of the mean was computed for each sample size. A permissible error index was computed to estimate the accuracy of ratings obtained from any sample size needed for the four different class sizes. Figures are presented from which minimum sample sizes necessary for accurate student evaluation of instruction can be computed. The figures show that sampling only one-third of classes of 100-140 students is sufficient to obtain accurate evaluations.
Evaluation Studies as Topic↗
Significance testing in mutagen screening: the dependence of statistical power on the control sample size.
The continuous accumulation of control data in multicellular mutagen screening systems prompted us to study the dependence of the statistical power on the size of the control sample (for fixed control values). Two widely used screening systems were chosen: dicentric chromosomes in human lymphocytes and recessive sex-linked lethals in Drosophila melanogaster. The power increases rapidly at first as the control sample size increases, then levels off at a few tens of thousands of control units tested and thereafter remains almost constant up to the historical control. The practical implications from our study are discussed.
Animals↗
Sample size determination under an exponential model in the presence of a confounder and type I censoring.
In controlled clinical trials, random assignment of treatments to individuals is usually used to eliminate the effects of confounding variables. When there is censorship in data, however, confounding effects may not be automatically removed solely by random assignment of treatments to individuals under the exponential model. Therefore, it is important to incorporate the confounding effect into the sample size calculation even after randomization of treatments to individuals. In this paper, the discussion is restricted only to the situation where there are two comparison groups and one single Bernoulli confounding variable. Based on an exponential covariate model, an explicit sample size formula considering the confounding effect has been derived for the design of trials with type I censoring, in which an end time is fixed in advance and all responses occurring after that time are censored. The resulting sample size formula can also be applied to nonrandomized clinical trials. Finally, to provide insight into the influence of different factors on sample size calculation, a discussion on the effects of treatments, the confounder, the length of follow-up times for studied individuals, and the joint distribution of the treatment and the confounder has been included.
Clinical Trials as Topic↗
Sample size determination based on Fisher's Exact Test for use in 2 x 2 comparative trials with low event rates.
A collection of sample size tables are presented for designing comparative trials when the event rates p1 and p2 are low. The tables are based on exact power calculations for Fisher's Exact Test. Both one-sided and two-sided alternative hypotheses are considered. A comparison is made between these sample sizes and those obtained by using popular asymptotic approximations.
Clinical Trials as Topic↗
Quality over quantity: biopsy-anchored CT radiogenomics models outperform all-lesion training in a multi-tumour cohort despite a smaller sample size.
OBJECTIVE: Radiogenomics aims to non-invasively predict tumour genotypes from imaging, but most studies assume molecular homogeneity by assigning a single biopsy-derived label to all lesions within a patient. This approach risks substantial label noise given well-documented interlesional heterogeneity. We investigated whether anchoring training to biopsy-confirmed lesions improves radiogenomic model performance and generalisability. MATERIALS AND METHODS: We retrospectively analysed 1646 patients (11473 segmented lesions) with contrast-enhanced CT and EGFR mutation status from next-generation sequencing at the Netherlands Cancer Institute, alongside an external NSCLC radiogenomics cohort (n = 158). All visible lesions were segmented, and the exact biopsy site was matched to its segmentation. Radiomic features were extracted, and machine learning models were trained with three lesion selection strategies: all lesions, non-biopsied lesions only, and biopsy-confirmed lesions only. To disentangle label quality from sample size, we created size-matched variants (one lesion per patient) for all-lesion and non-biopsied strategies. RESULTS: All models achieved significant discrimination of EGFR status on internal validation (AUC = 0.62-0.68). However, performance of the all-lesion and non-biopsied models declined on external validation (AUC = 0.55-0.63), while the biopsy-anchored model maintained stable performance (AUC = 0.62), despite having only 1/10th of the training sample size. When training sets were size-matched, the biopsy-anchored approach significantly outperformed a model trained on all available lesions on external validation (p = 0.037). CONCLUSIONS: Radiogenomic models trained on biopsy-confirmed lesions outperform conventional all-lesion strategies in external validation, despite using an order of magnitude fewer samples. Prioritising lesion-level label fidelity can mitigate heterogeneity-driven noise, enhancing robustness and clinical translation of imaging-based genomic prediction. KEY POINTS: Question Does assigning biopsy-derived molecular labels to all lesions introduce heterogeneity-driven label noise that reduces the generalisability of radiogenomic models? Findings Models trained exclusively on biopsy-confirmed lesions demonstrated superior external generalisability compared with all-lesion approaches, despite being trained on substantially fewer samples. Clinical relevance Biopsy-anchored radiogenomics improves the reliability of non-invasive mutation prediction by accounting for tumour heterogeneity, potentially supporting clinical decision-making when tissue sampling is limited or molecular results are discordant across lesions.
Humans↗
Effect of changing the bioequivalence range from (0.80, 1.20) to (0.80, 1.25) on the power and sample size.
International harmonization of guidelines for bioequivalence assessment has led to a wide acceptance of the multiplicative model for the extent and rate characteristics AUC and Cmax and--in consistency with this--of the bioequivalence range (0.80, 1.25). The effect of this change from (0.80, 1.20) on the power of the two one-sided test procedure and the sample sizes based thereon is investigated as a function of the within-subject coefficient of variation (CV) and the ratio mu T/mu R of expected medians for test and reference. The relative reduction in sample size is practically zero for mu T/mu R < or = 0.9 and then gradually increases as mu T/mu R approaches 1.2. At mu T/mu R = 1, the reduction is up to 20%. For a fixed ratio mu T/mu R this reduction increases with the coefficient of variation, reaching a plateau at a CV of about 25%.
Models, Statistical↗
Sample size calculations for the log rank test: a Gompertz model approach.
Sample size calculations for clinical trials dealing with survivorship are often based on an exponential model. This model is inappropriate when a non-zero proportion of the population is expected to have indefinite survival. In such cases the Gompertz model offers a reasonable alternative. A method for calculating the required accrual time for a clinical trial in which the treatment arms have Gompertz survival distributions satisfying the proportion hazards assumption is developed. A computer program to perform this method is given, as well as an iterative method that can be used when a computer is not available.
Clinical Trials as Topic↗
Sample size for a dose-response study.
This paper deals with a method of sample size allocation for a dose-response study assuming a logistic model for the dose-response curve. The method is based on the precision with which one wishes to estimate the dose that would produce the efficacy resulting in a clinically important difference from a placebo. An example is given to illustrate the methodology. The main development of the paper is for a binary response and is suitably modified for a continuous variable.
Dose-Response Relationship, Drug↗
Cost considerations and sample size requirements in cohort and case-control studies.
Three methods for incorporating cost considerations into sample size determination for cohort and case-control studies are considered. It is found that when the costs of obtaining exposed and nonexposed subjects or of obtaining case and control subjects differ, an improvement in design can be achieved.
Costs and Cost Analysis↗
Nomograms for obtaining a necessary, minimum sample size. I. When distribution of data is normal.
Four different nomograms were devised to obtain a necessary, minimum sample size at a 95% confidence rate when data were distributed normally. They corresponded to four different cases, the population of which was either infinite or finite and the permitted error of which was either mu--m or mu--m/s, where mu was population mean, m sample mean and s sample standard deviation. They could also be used for obtaining the confidence limits of the population mean from the data after having carried out a work.
Sampling Studies↗
Nomograms for obtaining a necessary, minimum sample size. II. When distribution of proportions from binomial data is approximately normal.
Two different nomograms corresponding to finite and infinite populations were devised to obtain a necessary, minimum sample size at a 95% confidence rate when the distribution of sample proportions calculated from binomial data was approximately normal. They could also be used for obtaining the 95% confidence limits of the population proportion from a sample proportion after having carried out a work.
Ecology↗