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PubMed1995

Survival estimates and sample size: what can we conclude?

Attempts to understand aging processes often involve life-span measurements from which a survival curve is constructed and model parameters estimated. The parameter estimates are then compared, and conclusions concerning the underlying biological processes are subsequently deduced, based upon the magnitude of the parameter differences. In this article we discuss the role of sample size and sample fluctuation on the parameter estimates and the profound effect that these factors may play in our arrival at meaningful biological conclusions. We then extend this discussion to examine one methodology that can help select sample sizes for specific parametric survival models.

Aging↗
PubMed1985

Sample size determination in case-control studies: the influence of the distribution of exposure.

In the design of case-control studies, the determination of the required number of cases and controls is based on consideration of the strength of the relationship between the disease and exposure to the putative cause, the variability in exposure within the population under study, and the desired size and power of the statistical test. This paper derives sample size equations for studies with a continuous exposure which allow the investigator to specify the strength of the relationship between disease and exposure in terms of relative risk, etiologic fraction or the slope of an exposure response relationship. With these formulations it becomes apparent that the size of the sample increases with decreasing variability in exposure in the population under study, a finding not apparent in the use of conventional methods of sample size determination for continuous data. The ability of a case-control study to detect a significant association between disease and exposure therefore depends critically on the distribution of exposure which exists in the community to be studied. Implications of these findings for studies of diet and cancer are discussed.

Canada↗
PubMed1994

The effect of exposure variance and exposure measurement error on study sample size: implications for the design of epidemiologic studies.

A small variability of exposure in a population, for example small variance in nutrient intake, limits the power of an epidemiologic study. McKeown-Eyssen and Thomas (J Chron Dis 1985; 38:559-568) have shown that by selecting a population with larger exposure variance vs one with smaller variance, the study sample size can be reduced by a factor equal to the ratio of the smaller to larger variance. The authors show that this benefit may be even greater for exposures measured with error. When there is measurement error, the sample size requirements are greatly increased. However, the proportional reduction in sample size from selecting a population with larger variance may be even greater when there is error than when there is not. Under certain assumptions, the validity of the exposure (correlation coefficient of the mismeasured exposure with the true exposure) is enhanced in the population with larger exposure variance, which provides the additional sample size benefit. Simple equations are presented that demonstrate quantitatively the substantial benefit of selecting a population with larger exposure variance when there is moderate or large measurement error. For example, selecting a population with a 30% greater standard deviation of exposure could reduce sample size requirements by 41% when the exposure is perfectly measured, but when the exposure is poorly measured with a validity coefficient of 0.6, the savings could be 56% if a population with 30% greater standard deviation of exposure could be studied. Applications of these results as well as the limitations of the assumptions are discussed.

Bias↗
PubMed2006

Parasite prevalence and sample size: misconceptions and solutions.

Parasite prevalence (the proportion of infected hosts) is a common measure used to describe parasitaemias and to unravel ecological and evolutionary factors that influence host-parasite relationships. Prevalence estimates are often based on small sample sizes because of either low abundance of the hosts or logistical problems associated with their capture or laboratory analysis. Because the accuracy of prevalence estimates is lower with small sample sizes, addressing sample size has been a common problem when dealing with prevalence data. Different methods are currently being applied to overcome this statistical challenge, but far from being different correct ways of solving a same problem, some are clearly wrong, and others need improvement.

Animals↗
PubMed2007

Determination of suitable sample sizes for multi-patient based finite element studies.

Finite element analysis is used extensively to assess joint replacements, but the majority of these are single sample studies. Recent investigations have suggested that such studies are unable to account for natural inter-patient variation in bone geometry and material property distribution. Recent developments in computer tomography based analyses make multiple sample studies possible; the question remains how many femurs are required to perform a study which accounts for such variations. This work investigates the factors that should be considered in answering this question. It explores sample sizing techniques when comparing strain distribution in the intact and implanted femur and when comparing two or more implant designs in a group of femurs. An example analysis of the effect of femoral head resurfacing was undertaken. Two sample sizing calculations were utilised, one based on achieving the desired precision in results, the other based on determining if a significant difference exists between two designs. The analysis shows that reasonable statistical precision can be achieved with a group of femurs. The study was also able to determine a suitable sample size for the analysis of a statistically significant difference between two groups of femurs with varying design parameters. The study concluded that while sample sizing is recommended for an accurate analysis, consideration must be made for the practicality of such a task.

Biomechanical Phenomena↗
PubMed2006

A simple method for assessing sample sizes in microarray experiments.

BACKGROUND: In this short article, we discuss a simple method for assessing sample size requirements in microarray experiments. RESULTS: Our method starts with the output from a permutation-based analysis for a set of pilot data, e.g. from the SAM package. Then for a given hypothesized mean difference and various samples sizes, we estimate the false discovery rate and false negative rate of a list of genes; these are also interpretable as per gene power and type I error. We also discuss application of our method to other kinds of response variables, for example survival outcomes. CONCLUSION: Our method seems to be useful for sample size assessment in microarray experiments.

Computer Simulation↗
PubMed2005

Sample-size calculations for studies with correlated ordinal outcomes.

Correlated ordinal response data often arise in public health studies. Sample-size (power) calculations are a crucial step in designing such studies to ensure an adequate sample to detect a significant effect. Here we extend Rochon's method of sample-size estimation with a repeated binary response to the ordinal case. The proposed sample-size calculations are based on an analysis with generalized estimating equations (GEE) and inference with the Wald test. Simulation results demonstrate the merit of the proposed power calculations. Analysis of an arthritis clinical trial is used for illustration.

Antirheumatic Agents↗
PubMed2002

[Sample size determination in reference-controlled diagnostic trials].

PURPOSE: A tutorial illustration of a flexible approach to determine the sample size in reference-controlled diagnostic trials. MATERIALS AND METHODS: Assuming the usual setting of a new diagnostic method to be compared with a reference method, the emphasis is on the sensitivity of the new method in comparison with the reference method, using a binary outcome (positive versus negative) for both methods. Based on the confidence interval of the sensitivity, a simple but flexible procedure for determining the sample size is described, which incorporates clinically interpretable information. The procedure is illustrated by the fictitious planning of a trial to assess the diagnostic value of MRI versus arthroscopy as a reference, in the detection of meniscal ruptures. RESULTS: The principal investigator merely has to propose the range for the sensitivity in which the new method is considered equal to the reference method. Furthermore, it must be decided in advance how accurate the study outcome should determine the sensitivity of the new method, i.e., how wide its maximum confidence interval may become. The minimum sample size necessary for the trial can be directly derived from this outlined strategy, which can easily be extended by simultaneous consideration of sensitivity and specificity of the new method being tested. CONCLUSION: The flexible approach to planning by means of the confidence interval of the sensitivity controls the desired confidence of the outcome of the diagnostic trial. It allows a priori evaluation of study budget, study duration, number of study centers and, above all, any ethical limitations. It provides arguments for the investigator to proceed with the comparison and a rationale for the decision to conduct the comparison as mono- or multicentric trial

Arthroscopy↗
PubMed2004

Sample size for gene expression microarray experiments.

MOTIVATION: Microarray experiments often involve hundreds or thousands of genes. In a typical experiment, only a fraction of genes are expected to be differentially expressed; in addition, the measured intensities among different genes may be correlated. Depending on the experimental objectives, sample size calculations can be based on one of the three specified measures: sensitivity, true discovery and accuracy rates. The sample size problem is formulated as: the number of arrays needed in order to achieve the desired fraction of the specified measure at the desired family-wise power at the given type I error and (standardized) effect size. RESULTS: We present a general approach for estimating sample size under independent and equally correlated models using binomial and beta-binomial models, respectively. The sample sizes needed for a two-sample z-test are computed; the computed theoretical numbers agree well with the Monte Carlo simulation results. But, under more general correlation structures, the beta-binomial model can underestimate the needed samples by about 1-5 arrays. CONTACT: jchen@nctr.fda.gov.

Algorithms↗
PubMed1994

Speech sample size and test-retest stability of connected speech measures for adults with aphasia.

The effect of speech sample size on the test-retest stability of two measures of connected speech--words per minute (WPM) and percent of words that are correct information units (Percent CIUs)--was evaluated. A standard set of 10 stimuli was used to elicit connected speech from 20 non-brain-damaged adults and 20 adults with aphasia. Each subject's responses to the 10 stimuli were transcribed and scored for WPM and Percent CIUs. Then each subject's responses to the 10 stimuli were randomly divided to produce smaller speech samples representing his or her responses to 1, 2, 3, 4, 5, and 7 stimuli. The test-retest stability of the WPM and Percent CIUs measures was then evaluated for each of the smaller sample sizes and for the complete 10-stimulus sample. For both groups, the test-retest stability of the two measures increased as sample size increased, with the greatest increases occurring as samples increased in size from those representing 1 stimulus to those representing 4 or 5 stimuli, with smaller increases in stability thereafter. In general, these results suggest that the best balance between high test-retest stability and the time and effort required to transcribe and score speech samples can be achieved with samples representing 4 or 5 stimuli (an average of 300 to 400 words for aphasic subjects), although this will vary across individuals.

Aged↗
PubMed2003

Randomizing patients by family practice: sample size estimation, intracluster correlation and data analysis.

BACKGROUND: Cluster randomized controlled trials increasingly are used to evaluate health interventions where patients are nested within larger clusters such as practices, hospitals or communities. Patients within a cluster may be similar to each other relative to patients in other clusters on key variables; therefore, sample size calculations and analyses of results require special statistical methods. OBJECTIVE: The purpose of this study was to illustrate the calculations used for sample size estimation and data analysis and to provide estimates of the intraclass correlation coefficients (ICCs) for several variables using data from the Seniors Medication Assessment Research Trial (SMART), a community-based trial of pharmacists consulting to family physicians to optimize the drug therapy of older patients. METHODS: The study was a paired cluster randomized trial, where the family physician's practice was the cluster. The sample size calculation was based on a hypothesized reduction of 15% in mean daily units of medication in the intervention group compared with the control group, using an alpha of 0.05 (one-tailed) with 80% power, and an ICC from pilot data of 0.08. ICCs were estimated from the data for several variables. The analyses comparing the two groups used a random effects model for a meta-analysis over pairs. RESULTS: The design effect due to clustering was 2.12, resulting in an inflation in sample size from 340 patients required using individual randomization, to 720 patients using randomization of practices, with 15 patients from each of 48 practices. ICCs for medication use, health care utilization and general health were <0.1; however, the ICC for mean systolic blood pressure over the trial period was 0.199. CONCLUSIONS: Compared with individual randomization, cluster randomization may substantially increase the sample size required to maintain adequate statistical power. The differences in ICCs among potential outcome variables reinforce the need for valid estimates to ensure proper study design.

Aged↗
PubMedDate not supplied

Sample size and power.

This paper sets forth the basic concepts of the calculation of sample size and power in clinical research. It provides the reader with a basic understanding of the relationship between sample size and power and the components within the research, such as the variability of the measure being used as the primary outcome. The paper also discusses a number of general issues related to sample size and power, such as the importance of the difference between clinical and statistical significance, how one approaches trials attempting to establish the equivalence of clinical interventions, and the critical need for appropriate consultation.

Clinical Trials as Topic↗
PubMed2001

Sample size calculations for the two-sample problem using the multiplicative intensity model.

In this paper we propose formulae for calculating the expected number of events or, alternatively, the required trial duration, for clinical trials involving two treatment groups in which patients may potentially experience multiple events and the data will be analysed using a multiplicative intensity (MI) model. We use a partial likelihood-based approach and examine in detail two MI models: one that includes a binary treatment variable as the only covariate and a three-state Markov process model in which a binary time-varying covariate is added to the previous model. For the simpler model, our formula coincides with those derived by Cook using full likelihood methods. We present applications of the derived formulae to chronic granulomatous disease and breast cancer data sets.

Antineoplastic Combined Chemotherapy Protocols↗
PubMed2004

Sample size estimation: a glimpse beyond simple formulas.

Small increments in the complexity of clinical studies can readily take sample size estimation and statistical power analysis beyond the capabilities of simple mathematic formulas. In this article, the method of simulation is presented as a general technique with which sample size may be calculated for complex study designs. Applications of simulation for determining sample size requirements in studies involving correlated data and comparisons of receiver operating characteristic curves are discussed.

Clinical Trials as Topic↗
PubMed1983

Statistical analysis and sample-size determinations for mutagenicity experiments with binomial responses.

Two statistical analyses are studied for their applicability to mutagenicity experiments that produce binomial responses from a control group and a single treated group. Attention is focused on experiments with (1) group sample sizes greater than 500 and (2) a probability less than .05 for a binary observation from any experimental unit being "positive." In addition, it is assumed that historical control data will not be included in the statistical analysis. The first analysis is a conditional binomial test, which has been tabulated extensively by Kastenbaum and Bowman [1970], while the second is based on a standard normal approximation to the distribution of the difference between two sample proportions. A formula is presented for each analysis that relates the associated probability of detecting a mutagen to the mutant frequencies and sample sizes of the two groups. Based on extensive numerical results, the conclusion is drawn that the normal test is the preferred analysis for experiments in which the ratio of the two sample sizes is between 0.80 and 1.25. On the further assumption that an experiment is to be conducted with equal experimental group sample sizes, recommendations are offered for values of this common sample size needed to achieve a specified power, ie, a degree of assurance of detecting a postulated level of mutagenic effect.

Animals↗
PubMed2003

Sample size determination. Influencing factors and calculation strategies for survey research.

The paper reviews both the influencing factors and calculation strategies of sample size determination for survey research. It indicate the factors that affect the sample size determination procedure and explains how. It also provides calculation methods (including formulas) that can be applied directly and easily to estimate the sample size needed in most popular situations.

Sample Size↗
PubMed2002

Calculating the SNP-effective sample size from an alignment.

MOTIVATION: The number of Single Nucleotide Polymorphisms (SNPs) detectable in an alignment is a function of the length and the number of the aligned sequences. The latter is called sample size. However, a typical alignment, for instance obtained as a BLAST-search result of a query sequence against an EST database, does not evenly cover the query sequence. Therefore, it is usually not clear what the actual sample size is. RESULTS: We present a method to calculate the effective sample size, called n(eff), for a given BLAST alignment. This method takes into account that multiple coverage contributes only logarithmically to the SNP yield of a given sequence stretch. We show that the effective sample size n(eff) is usually much smaller than would be expected for a given amount of coverage and illustrate this with two typical examples.

Algorithms↗