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PubMed2002

Power and sample sizes for linkage with extreme sampling under an oligogenic model for quantitative traits.

Extreme sampling of sibling pairs has been shown to be efficient in terms of statistical power and sample sizes (in number of sibling pairs needed to genotype) to detect a quantitative trait locus (QTL) when the residual distribution is normal. In the present study, the efficiency of extreme sampling strategies to detect each locus under an oligogenic model is analytically explored with a test statistic based on identical-by-descent (IBD) statuses of independent sibling pairs. In the oligogenic model, the joint effect of oligogenes is the sum of the effects of each locus. Under this model, detecting each single locus will depend, in part, on the allele frequencies and magnitudes of effect of the other loci. Effects of two QTLs with different magnitudes of displacement and acting nonepistatically are considered. Three types of extreme sampling-that is, extreme concordant high (ECH), extreme concordant low (ECL), and extreme discordant (ED)-are primarily considered herein. Among these, ED sampling under the oligogenic model is shown to be most efficient in most situations considered here in terms of allele frequency and mode of inheritance. Differences in results between ECH and ECL sampling are purely arbitrary, brought up mostly by the directions of displacement effects. However, power to detect a locus with the lesser (in magnitude) displacement effect does not necessarily increase with extremity of sampling. Combinations of extreme discordant and extreme concordant sibling pairs are briefly discussed.

Alleles↗
PubMedDate not supplied

Sample size determinations using examples drawn from the NCTR Collaborative Behavioral Teratology Study data.

The Collaborative Behavioral Teratology Study (CBTS) introduced the coefficient of detection (CD) as an estimate of the minimum difference needed to detect a significant difference among groups. The CD was used to provide an index of the sensitivity of the tests used. As originally described, the CD is not suitable for estimates of two or more group minimally significant differences because it is based on a one-group formula. Also, the CD operates at a power of 50% in the one-group case (see preceding paper). These drawbacks leave questions about the sensitivity of the tests used in the CBTS unanswered. Using examples drawn from the CBTS data base, a more standard method of approaching this question has been taken here based on power calculations. Using the means and standard deviations from the vehicle controls, alpha = 0.05, 1-beta = 0.80, and 20, 30 or 40% group mean difference sizes, required samples sizes were determined for all the behavioral measures reported in the CBTS final report for Experiment 1. The results showed that most of the measures can detect 30% group mean differences in a two-group, two-tailed t-test situation with group sizes of less than or equal to 20 litters per group. More complex calculations are required when more than two groups are planned. Multigroup designs require additional assumption about the distribution of group differences and accordingly are more difficult to specify.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2001

Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change.

Consider a study in which 2 groups are followed over time to assess group differences in the average rate of change, rate of acceleration, or higher degree polynomial effect. In designing such a study, one must decide on the duration of the study, frequency of observation, and number of participants. The authors consider how these choices affect statistical power and show that power depends on a standardized effect size, the sample size, and a person-specific reliability coefficient. This reliability, in turn, depends on study duration and frequency. These relations enable researchers to weigh alternative designs with respect to feasibility and power. The authors illustrate the approach using data from published studies of antisocial thinking during adolescence and vocabulary growth during infancy.

Adolescent↗
PubMed1997

Planning significant and meaningful research in exercise science: estimating sample size.

Exercise science researchers are familiar with the use of parametric tests to detect significant differences among treatment groups. However, in planning research a question asked with increasing frequency is, "How many participants are needed to detect real and meaningful differences among groups?" In this paper, we provide an overview of the use of alpha, power, and effect size in planning sample sizes that allow tests of real and meaningful differences among groups. Because effect size is the parameter most often missing, we have located meta-analyses in sport and exercise psychology (n = 26), and motor behavior (n = 6). We provide examples and a discussion of how researchers can use these effect sizes along with common estimates of alpha and power to plan for the sample size needed to detect real and meaningful group differences.

Exercise↗
PubMed2001

On sample size calculation in bioequivalence trials.

Sample size calculation plays an important role in bioequivalence trials. In practice, a bioequivalence study is usually conducted under a crossover design or a parallel design with raw data or log-transformed data. In this paper, we discuss the differences in sample size calculation between a crossover design and a parallel design with raw data or log-transformed data. Formulas for sample size calculation under a crossover design and a parallel design with raw data or log-transformed data are derived. A brief discussion for the relationship among these formulas is given.

Clinical Trials as Topic↗
PubMed1998

A simple method of sample size calculation for linear and logistic regression.

A sample size calculation for logistic regression involves complicated formulae. This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model. One can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor. This method requires no assumption of low response probability in the logistic model as in a previous publication. One can similarly calculate the sample size for linear regression models. This paper also compares the accuracy of some existing sample-size software for logistic regression with computer power simulations. An example illustrates the methods.

Humans↗
PubMed1989

Determination of sample sizes for epidemiological surveys using cluster sampling technique.

Cluster sampling often provides a convenient and low cost device, in epidemiological surveys. The sample size needed under cluster sampling is generally larger than that in an individual based scheme due to the intra-class correlation existing in a cluster. This intra-class correlation coefficient is usually not known and some assumptions or estimates are essential. The strengths and weaknesses of cluster sampling over other sampling plans are presented and briefly discussed in this paper with particular reference to leprosy control programmes. One particular model of multistage cluster sampling technique is suggested in the evaluation of a District level programme, which includes determining the effectiveness of Multi-Drug Therapy, monitoring efficiency of paramedical workers and estimating the incidence of leprosy.

Catchment Area, Health↗
PubMed1995

Volume-weighted mean nuclear volume and nuclear area in advanced ovarian carcinoma. An investigation of sampling methods, sample size and reproducibility.

The influence of sampling issues on the reproducibility of volume-weighted mean nuclear volume (mean v) and mean nuclear area (MNA) assessments in patients with International Federation of Gynecology and Obstetrics stage III and IV ovarian carcinoma was evaluated. Ten cases representing the whole range of MNA values were selected from a population of 131 cases. The MNA and mean v of the same tumor cell nuclei were determined in one session by switching between the stereologic module and the morphometric module of the video overlay program used. For both MNA and mean v in one series of measurements, tumor nuclei were sampled from the whole tumor area and in a second series from the most poorly differentiated part (the measurement area) in each section, thus giving four series of measurements per case. For all four series, 500 nuclei were point sampled from approximately 100 systematically randomly selected fields of vision, using the automated scanning stage controlled by the morphometry program. These large samples, containing 500 nuclei for each case, were regarded as representative in each case. To investigate the susceptibility of MNA and mean v to variance at lower sampling levels (fields, nuclei), a nested analysis of variance was performed. Then the influence of sample size and sampling method was evaluated by drawing subsets from these 500 nuclei in each case in three different ways (cluster, systematic or random) with four different sample sizes (50, 100, 125, 250). It was shown that for MNA assessed in the measurement area, the variance between patients contributed the most to the total variance.(ABSTRACT TRUNCATED AT 250 WORDS)

Carcinoma↗
PubMed2005

Sample size matters: a guide for surgeons.

Considerations of sample size computations in the medical literature have gained increasing importance over the past decade and are now often mandatory for scientific grant proposals, protocols, and publications. However, many surgeons are ill-prepared to understand the parameters on which the appropriate sample size is based. The present article has several objectives: first, to review the need for sample size considerations; second, to explain the ingredients necessary for sample size computations in simple, nonmathematic language; third, to provide options for reducing the sample size if it seems impracticably large; and fourth, to help avoid some of the more common mistakes encountered when computing sample sizes.

Evidence-Based Medicine↗
PubMed2005

Non-linearity of Parkinson's disease progression: implications for sample size calculations in clinical trials.

BACKGROUND: Estimation of sample size for long-term studies of neuroprotection in Parkinson's disease requires information on expected clinical decline. Values may be obtained by analyzing existing long-term data sets or by prediction models of clinical decline applied to available data from shorter-term trials. The most commonly used measure to track clinical decline is the Unified Parkinson's Disease Rating Scale (UPDRS) but this measure is also affected by symptomatic therapy. Models can help better understand behavior of the UPDRS after initiation of symptomatic therapy when scores will improve and eventually start deteriorating again. PURPOSE: To understand how UPDRS scores progress after initiation of symptomatic therapy and how this progression impacts sample size calculations. METHODS: We developed a non-linear model of UPDRS after introduction of symptomatic therapy. The model is specified as a non-linear mixed effects model and is applied to three different data sets from clinical trials. The model is then used to produce estimates for the change in UPDRS and its associated variance for a period of up to five years of follow-up. The estimates produced by the model serve as the basis for sample-size calculations for different lengths of follow-up (one through five years) and for different values of clinically meaningful change in UPDRS. RESULTS: Despite differences in the short-term benefit of the dopaminergic drugs, after a period of approximately six months UPDRS scores progress linearly at an estimated rate of approximately three points a year. The sample size that is required for a clinical trial where the baseline coincides with initiation of symptomatic therapy is very large. On the other hand, if baseline is set at six months after initiation of symptomatic therapy then the sample size required decreases with length of follow-up. LIMITATIONS: Model specification and estimation is based on a set of simplifying assumptions regarding the progression of individual level UPDRS scores. CONCLUSIONS: Sample size calculations based on these estimates indicate a substantial reduction in sample size if patients are required to be on symptomatic treatment for a period of time before being randomized to a neuroprotective trial.

Antiparkinson Agents↗
PubMed2003

A simple method to estimate sample sizes for safety equivalence studies using inverse sampling.

Safety equivalence studies may be required to demonstrate that a new procedure or process is at least as safe as a previous one. They usually involve low or very low outcome rates that are often not precisely determined, making patient-based sample sizing uncertain. Using a reverse sampling approach, a method is derived from standard equations to estimate the number of events that need to be observed to demonstrate equivalence using the confidence interval approach. For instance, for a one-sided (nonsuperiority) hypothesis, 5% alpha risk, and 80% power, almost 100 events need to be observed in each study arm to demonstrate equivalence within 30%, or 250 events for 20% equivalence. The number of patients to be included can be derived directly from expected event rates.

Confidence Intervals↗
PubMed2005

Adaptive statistical analysis following sample size modification based on interim review of effect size.

In designing a comparative clinical trial, the required sample size is a function of the effect size, the value of which is unknown and at best may be estimated from historical data. Insufficiency in sample size as a result of overestimating the effect size can be destructive to the success of the clinical trial. Sample size re-estimation may need to be properly considered as a part of clinical trial planning. This paper is intended to give the motivations for the sample size re-estimation based partly on the effect size observed at an interim analysis and for a resulting simple adaptive test strategy. The performance of this adaptive design strategy is assessed by comparing it with a fixed maximum sample size design that is properly adjusted in anticipation of the possible sample size adjustment.

Algorithms↗
PubMed2006

Sample sizes of studies on diagnostic accuracy: literature survey.

OBJECTIVES: To determine sample sizes in studies on diagnostic accuracy and the proportion of studies that report calculations of sample size. DESIGN: Literature survey. DATA SOURCES: All issues of eight leading journals published in 2002. METHODS: Sample sizes, number of subgroup analyses, and how often studies reported calculations of sample size were extracted. RESULTS: 43 of 8999 articles were non-screening studies on diagnostic accuracy. The median sample size was 118 (interquartile range 71-350) and the median prevalence of the target condition was 43% (27-61%). The median number of patients with the target condition--needed to calculate a test's sensitivity--was 49 (28-91). The median number of patients without the target condition--needed to determine a test's specificity--was 76 (27-209). Two of the 43 studies (5%) reported a priori calculations of sample size. Twenty articles (47%) reported results for patient subgroups. The number of subgroups ranged from two to 19 (median four). No studies reported that sample size was calculated on the basis of preplanned analyses of subgroups. CONCLUSION: Few studies on diagnostic accuracy report considerations of sample size. The number of participants in most studies on diagnostic accuracy is probably too small to analyse variability of measures of accuracy across patient subgroups.

Confidence Intervals↗
PubMed1999

Sample size estimation for the sorcerer's apprentice. Guide for the uninitiated and intimidated.

OBJECTIVE: To review the importance of and practical application of sample size determination for clinical studies in the primary care setting. QUALITY OF EVIDENCE: A MEDLINE search was performed from January 1966 to January 1998 using the MeSH headings and text words "sample size," "sample estimation," and "study design." Article references, medical statistics texts, and university colleagues were also consulted for recommended resources. Citations that offered a clear and simple approach to sample size estimation were accepted, specifically those related to statistical analyses commonly applied in primary care research. MAIN MESSAGE: The chance of committing an alpha statistical error, or finding that there is a difference between two groups when there really is none, is usually set at 5%. The probability of finding no difference between two groups, when, in actuality, there is a difference, is commonly accepted at 20%, and is called the beta error. The power of a study, usually set at 80% (i.e., 1 minus beta), defines the probability that a true difference will be observed between two groups. Using these parameters, we provide examples for estimating the required sample size for comparing two means (t test), comparing event rates between two groups, calculating an odds ratio or a correlation coefficient, or performing a meta-analysis. Estimation of sample size needed before initiation of a study enables statistical power to be maximized and bias minimized, increasing the validity of the study. CONCLUSION: Sample size estimation can be done by any novice researcher who wishes to maximize the quality of his or her study.

Humans↗
PubMed2005

Sample size calculations for a split-cluster, beta-binomial design in the assessment of toxicity.

Mouse embryo assays are recommended to test materials used for in vitro fertilization for toxicity. In such assays, a number of embryos is divided in a control group, which is exposed to a neutral medium, and a test group, which is exposed to a potentially toxic medium. Inferences on toxicity are based on observed differences in successful embryo development between the two groups. However, mouse embryo assays tend to lack power due to small group sizes. This paper focuses on the sample size calculations for one such assay, the Nijmegen mouse embryo assay (NMEA), in order to obtain an efficient and statistically validated design. The NMEA follows a stratified (mouse), randomized (embryo), balanced design (also known as a split-cluster design). We adopted a beta-binomial approach and obtained a closed sample size formula based on an estimator for the within-cluster variance. Our approach assumes that the average success rate of the mice and the variance thereof, which are breed characteristics that can be easily estimated from historical data, are known. To evaluate the performance of the sample size formula, a simulation study was undertaken which suggested that the predicted sample size was quite accurate. We confirmed that incorporating the a priori knowledge and exploiting the intra-cluster correlations enable a smaller sample size. Also, we explored some departures from the beta-binomial assumption. First, departures from the compound beta-binomial distribution to an arbitrary compound binomial distribution lead to the same formulas, as long as some general assumptions hold. Second, our sample size formula compares to the one derived from a linear mixed model for continuous outcomes in case the compound (beta-)binomial estimator is used for the within-cluster variance.

Animals↗
PubMed1990

Power and sample size calculations. A review and computer program.

Methods of sample size and power calculations are reviewed for the most common study designs. The sample size and power equations for these designs are shown to be special cases of two generic formulae for sample size and power calculations. A computer program is available that can be used for studies with dichotomous, continuous, or survival response measures. The alternative hypotheses of interest may be specified either in terms of differing response rates, means, or survival times, or in terms of relative risks or odds ratios. Studies with dichotomous or continuous outcomes may involve either a matched or independent study design. The program can determine the sample size needed to detect a specified alternative hypothesis with the required power, the power with which a specific alternative hypothesis can be detected with a given sample size, or the specific alternative hypotheses that can be detected with a given power and sample size. The program can generate help messages on request that facilitate the use of this software. It writes a log file of all calculated estimates and can produce an output file for plotting power curves. It is written in FORTRAN-77 and is in the public domain.

Case-Control Studies↗
PubMed2005

Effect of dropouts on sample size estimates for test on trends across repeated measurements.

Sample size calculation is an important component at the design stage of clinical trials. We investigate the implications of dropouts for the sample size estimates in testing differences in the rates of changes produced by two treatments in a randomized parallel-groups repeated measurement design. Statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of dropouts correctly. In this article, we examine the impact of dropouts on sample size estimate and compare the power with the approach of Jung and Ahn [Jung, S. H., Ahn, C. (2003). Sample size estimation for GEE method for comparing slopes in repeated measurements data. Stat. Med. 22: 1305-1315] with that suggested by Patel and Rowe [Patel, H., Rowe, E. (1999). Sample size for comparing linear growth curves. J. Biopharm. Stat. 9:339-350] through a simulation study.

Clinical Trials as Topic↗
PubMed2000

Interim analysis and sample size reassessment.

This article deals with sample size reassessment for adaptive two-stage designs based on conditional power arguments utilizing the variability observed at the first stage. Fisher's product test for the p-values from the disjoint samples at the two stages is considered in detail for the comparison of the means of two normal populations. We show that stopping rules allowing for the early acceptance of the null hypothesis that are optimal with respect to the average sample size may lead to a severe decrease of the overall power if the sample size is a priori underestimated. This problem can be overcome by choosing designs with low probabilities of early acceptance or by midtrial adaptations of the early acceptance boundary using the variability observed in the first stage. This modified procedure is negligibly anticonservative and preserves the power.

Animals↗