The estimation of sample size in experiments. I. Using comparisons of averages.
Explore the source record for details and available documents.
SEARCH · Search PubMed
Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
The prevalence of vitamin A deficiency among two to ten years old children in a rural area of Mali was assessed by ophthalmic examination, determination of plasma retinol levels and impression cytology with transfer tests. A Public Health problem of vitamin A deficiency was identified in this rural area by: the prevalence of nightblindness significantly (p < 0.001) above the cut-off (1%) defined by the World Health Organization (WHO); the prevalence of corneal scarring significantly (p < 0.001) above the WHO's cut-off (0.05%); the percentage of subjects with plasma retinol levels below 0.35 mumol/l (10 micrograms/dl) significantly (p < 0.001) higher than the WHO's threshold (5%); and 52.8 +/- 8.2% children with "Abnormal" impression cytology as determined by the impression cytology test (IC). This preliminary survey confirmed widespread vitamin A deficiency in Mali. The minimum sample size required for a study using the impression cytology test to determinate a Public Health problem in a population was calculated for different situations. Ophthalmic examination indicated a very high rate of active trachoma (29.6 +/- 7.0%), and a relationship between active trachoma and impression cytology results was identified.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
OBJECTIVES: Interest has been growing in the use of the theory of planned behaviour (TBP) in health services research. The sample sizes range from less than 50 to more than 750 in published TPB studies without sample size calculations. We estimate the sample size for a multi-stage random survey of prescribing intention and actual prescribing for asthma in British general practice. To our knowledge, this is the first systematic attempt to determine sample size for a TPB survey. METHODS: We use two different approaches: reported values of regression models' goodness-of-fit (the lambda method) and zero-order correlations (the variance inflation factor or VIF method). Intra-cluster correlation coefficient (ICC) is estimated and a socioeconomic variable is used for stratification. We perform sensitivity analysis to estimate the effects of our decisions on final sample size. RESULTS: The VIF method is more sensitive to the requirements of a TPB study. Given a correlation of .25 between intention and behaviour, and of .4 between intention and perceived behavioural control, the proposed sample size is 148. We estimate the ICC for asthma prescribing to be around 0.07. If 10 general practitioners were sampled per cluster, the sample size would be 242. CONCLUSIONS: It is feasible to perform sophisticated sample size calculations for a TPB study. The VIF is the appropriate method. Our approach can be used with adjustments in other settings and for other regression models.
The power of a clinical trial is partly dependent upon its sample size. With continuous data, the sample size needed to attain a desired power is a function of the within-group standard deviation. An estimate of this standard deviation can be obtained during the trial itself based upon interim data; the estimate is then used to re-estimate the sample size. Gould and Shih proposed a method, based on the EM algorithm, which they claim produces a maximum likelihood estimate of the within-group standard deviation while preserving the blind, and that the estimate is quite satisfactory. However, others have claimed that the method can produce non-unique and/or severe underestimates of the true within-group standard deviation. Here the method is thoroughly examined to resolve the conflicting claims and, via simulation, to assess its validity and the properties of its estimates. The results show that the apparent non-uniqueness of the method's estimate is due to an apparently innocuous alteration that Gould and Shih made to the EM algorithm. When this alteration is removed, the method is valid in that it produces the maximum likelihood estimate of the within-group standard deviation (and also of the within-group means). However, the estimate is negatively biased and has a large standard deviation. The simulations show that with a standardized difference of 1 or less, which is typical in most clinical trials, the standard deviation from the combined samples ignoring the groups is a better estimator, despite its obvious positive bias.
Sample size calculations are important and difficult in clinical trails because they depend on the nuisance parameter and treatment effect. Recently, much attention has been focused on two-stage methods whereby the first stage constitutes an internal pilot study used to estimate parameters and revise the final sample size. This paper reviews two-stage methods based on estimation of nuisance parameters in either a continuous or dichotomous outcome setting.
In clinical trials where the variances of the response variables are unknown, in accurate estimates of these can affect the type II error rate considerably. More accurate estimates of the variances may be obtained by taking a look at the data available part way through the trial and re-calculating the required sample size based on these new estimates. The main impetus for sample size re-estimation came from a two-stage procedure developed by Stein in 1945 and the literature is now replete with variations on this approach. In this paper, existing sample size re-estimation methods for both fixed sample and sequential clinical trial models will be reviewed. These will then be extended for use in group-sequential response-adaptive designs. In particular, a test for a recently developed group-sequential response-adaptive design, which compares two treatments with immediate normally distributed responses and unknown variances, is presented based on a modified version of Stein's test. The principal modifications involve updating the required sample size at each interim analysis and calculating the test statistic based on the current estimates of the variances. Hence, all the available information is used at each stage. Simulation is used to assess to what extent the updating of the required sample size at each interim analysis in the new test helps to attain the nominal error rates. The test is compared to modified versions of a simple test and a Stein-type group sequential t-test studied in the recent literature. These tests calculate the required sample sizes based on less accurate estimates of the variances. The type I error rate is close to the nominal value and the power is more accurately maintained in the new test.
A method of sample size determination for estimation of probabilities based on a test variable is presented. Applications to estimation of sensitivity and specificity of medical tests are the focus of this research, although the methods can be applied to other areas of study such as engineering reliability. Examples are given for determining sample sizes required for the classification of patients with cutaneous lupus erythematosus based on the incidence of several markers. In this example, the test variable is the number of markers present. The methodology employs a weighted average of model-based and non-model-based estimates of the probability with the weights determined by the closeness to or the confidence in the given model. Formulas and charts required for determining sample size are provided for test variables that can be modeled by the binomial, Poisson, or normal distributions, i.e., for the most commonly encountered distributions for counting events (binomial and Poisson) and for measurements (normal). However, the methods given can be applied to any distribution, including multivariate. Especially when relatively small probabilities (the rare events) are being estimated, the techniques provided assistance in safeguarding against undersampling brought on by unwarranted confidence in a test variable distribution and against oversampling required for high accuracy in non-model-based probability estimators.
Magnitude differences in scores on a measure of quality of life that correspond to differences in function or clinical course are called clinically important differences (CIDs). Anchor-based and distribution-based methods were used to provide ranges of CIDs for five targeted scale scores of the Functional Assessment of Cancer Therapy-Anemia (FACT-An) questionnaire. Three samples of cancer patients were used: Sample 1 included 50 patients participating in a validation study of the FACT-An; Sample 2 included 131 patients participating in a longitudinal study of chemotherapy-induced fatigue; sample 3 included 2,402 patients enrolled in a community-based clinical trial evaluating the effectiveness and safety of a treatment for anemia. Three clinical indicators (hemoglobin level; performance status; response to treatment) were used to determine anchor-based differences. One-half of the standard deviation and 1 standard error of measurement were used as distribution-based criteria. Analyses supported the following whole number estimates of a minimal CID for these five targeted scores: Fatigue Scale = 3.0; FACT-G total score = 4.0; FACT-An total score = 7.0; Trial Outcome Index-Fatigue = 5.0; and Trial Outcome Index-Anemia = 6.0. These estimates provide a basis for sample size estimation when planning for a clinical trial or other longitudinal study, when the purpose is to ensure detection of meaningful change over time. They can also be used in conjunction with more traditional clinical markers to assist investigators in determining treatment efficacy.
We derive formulae for estimating sample size and power for detecting the effect of an unrestricted covariate on survival time. These are useful in designing survival studies with different patterns of recruitment and follow-up when survival time is exponentially distributed. We use the asymptotic covariance matrix, conditional expectation and Taylor's expansion techniques to develop these formulae. Computer simulations indicate that the asymptotic approximations used in developing the formulae are good over a range of parameter values and different patterns of recruitment and follow-up that are relevant to survival studies.
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.
The consequence of reducing sample size on the accuracy and precision of estimates of citrus rust mite, Phyllocoptruta oleivora (Ashmead), densities on oranges was investigated. The sample unit was a 1-cm2 surface area on fruit. Sampling plans consisting of 360, 300, 200, 160, 80, 48, 36, or 20 samples per 4 ha were evaluated through computer simulations by using real count data from 32 data sets of 600 sample units per 4 ha. The original and reduced sampling plans were hierarchical with different numbers of sample areas per 4 ha, trees per area, fruit per tree, and samples per fruit. Individual estimates (n=100 simulations per data set) using each plan were sometimes considerably below or above target densities. In an original set of count data with a mean of six mites per cm2, simulations of 36 samples per 4 ha produced individual estimates ranging from one to 16 mites per cm2, whereas 80 samples per 4 ha produced estimates ranging from two to 10 mites per cm2. The plans consisting of 36 or more samples were projected to provide precision levels of 0.25 (SEM/mean) or better at densities of five or more mites per cm2 based on log-data, a projection that needs to be verified under real-grove situations. Each plan consistently provided mite detection in these sampling simulations except those consisting of 20 or 36 samples, which sometimes failed to detect mites when the target density was less than five mites per cm2. The study provided insight into the probable precision, accuracy and detection thresholds for eight candidate sampling plans varying from relatively low to high resource input.