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PubMed2003

Homogeneity score test for the intraclass version of the kappa statistics and sample-size determination in multiple or stratified studies.

When the intraclass correlation coefficient or the equivalent version of the kappa agreement coefficient have been estimated from several independent studies or from a stratified study, we have the problem of comparing the kappa statistics and combining the information regarding the kappa statistics in a common kappa when the assumption of homogeneity of kappa coefficients holds. In this article, using the likelihood score theory extended to nuisance parameters (Tarone, 1988, Communications in Statistics-Theory and Methods 17(5), 1549-1556) we present an efficient homogeneity test for comparing several independent kappa statistics and, also, give a modified homogeneity score method using a noniterative and consistent estimator as an alternative. We provide the sample size using the modified homogeneity score method and compare it with that using the goodness-of-fit method (GOF) (Donner, Eliasziw, and Klar, 1996, Biometrics 52, 176-183). A simulation study for small and moderate sample sizes showed that the actual level of the homogeneity score test using the maximum likelihood estimators (MLEs) of parameters is satisfactorily close to the nominal and it is smaller than those of the modified homogeneity score and the goodness-of-fit tests. We investigated statistical properties of several noniterative estimators of a common kappa. The estimator (Donner et al., 1996) is essentially efficient and can be used as an alternative to the iterative MLE. An efficient interval estimation of a common kappa using the likelihood score method is presented.

Alcohol Drinking↗
PubMed1992

A comparison of sample size methods for the logrank statistic.

Several methods are available for sample size calculation for clinical trials when survival curves are to be compared using the logrank statistic. We discuss advantages and disadvantages of some of these methods, and present simulation results under exponential, proportional hazards and non-proportional hazard situations.

Clinical Trials as Topic↗
PubMed1992

Sixteen S-squared over D-squared: a relation for crude sample size estimates.

I suggest for memorization an equation for calculating approximate sample size requirements intended only for a specific set of values (80 per cent power for a two-tailed alpha = 0.05 test) which seems to occur often in biopharmaceutical research. After presenting the formula in terms of variance estimate s2 and effect size d, I derive a few alternative forms and then discuss the accuracy of the approximation and other properties as well as examples of its use.

Drug Evaluation↗
PubMed1992

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↗
PubMed1983

Minimum sample size of kidney biopsies for semiquantitative and quantitative evaluation.

The minimum sample size for semiquantitative and quantitative evaluation of interstitial tubular and glomerular parameters is calculated. For the majority of parameters a renal cortex area of 2 mm2 or 7 glomeruli (adults) or 13 glomeruli (children) is sufficient. Larger biopsies or more glomeruli are necessary for the evaluation of the area density of interstitium patent and obsolescent glomeruli as well as the numerical density of obsolescent glomeruli. The most sensitive parameters are those concerning crescents which require biopsies of 11-19 glomeruli in adults and 40 glomeruli in children. In summary, biopsies of usual size (10 mm2) containing about 20 glomeruli are sufficient for qualitative and quantitative evaluation.

Adolescent↗
PubMed2002

Topographic heterogeneity in transdermal transport revealed by high-speed two-photon microscopy: determination of representative skin sample sizes.

A novel application of high-speed two-photon microscopy was utilized to determine the optimum number of skin sites required to accurately determine the changes in transdermal transport properties incurred globally, over a clinically relevant area of skin. In contrast to the four to six skin sites (100 microm by 100 mirom area per site) examined previously, this study accounted for the fluorescent probe distributions at 400 consecutive skin sites, covering a total skin area of 2 mm by 2 mm. The oleic-acid-induced changes in the transdermal transport properties of the model hydrophobic probe, rhodamine B hexyl ester, and of the model hydrophilic probe, sulforhodamine B, for this 400-skin-site study exhibited different dependencies on sample size for each probe. Whereas the examination of six skin sites captures the relative changes in the global transdermal transport properties of the hydrophobic probe, the valid assessment of these changes for the hydrophilic probe requires a significantly larger sample size of at least 24 skin sites.

Biological Transport↗
PubMed2000

Sample size in guidelines trials.

In clinical trials, the statistical concepts of significance and power are used in the determination of sample size for trials. The trialist must provide an estimate of standard deviation and a hypothetical population difference to be detected. This must be modified to deal with the designs encountered in guideline research. These are cluster randomized trials, because the patients of a single doctor or practice form a cluster. The trialist must be able to provide information about the effects of clustering, in the form of an intraclass correlation coefficient.

Family Practice↗
PubMed1988

Sample size for comparison of changes in the presence of right censoring caused by death, withdrawal, and staggered entry.

In estimating and comparing the rates of change of a continuous variable between two groups, the unweighted averages of individual simple least-square estimates from each group are often used. Under the linear random effects model, these statistics are maximum likelihood estimates for the expected rates of change when all individuals have complete observations. However, death and withdrawal often cause observations on the variable of interest to be right censored for some participants, which makes any subsequent measurements impossible (to be referred to as right censoring). In this situation, the unweighted averages are no longer efficient in comparison with the generalized least-square estimates. Relationship between sample size, frequency of measurement, and right censoring are described for the different estimation procedures. Using realistic estimates of the random effect parameters, we illustrate that if there were 8% right censored observations each year due to participants' death or loss to follow-up, the sample size requirements for a proposed 3-year controlled clinical trial of alpha 1-protease inhibitor replacement therapy could be more than doubled if the unweighed rather than the generalized least-square estimates were used.

Clinical Trials as Topic↗
PubMed1998

Visual acuity repeatability in keratoconus: impact on sample size. Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study Group.

PURPOSE: The purpose of this paper is to determine the repeatability of visual acuity measurement in keratoconus and to describe the impact of measurement repeatability on sample size. METHODS: Approximately 10% of a 1209 patient sample in the Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study were selected randomly for a Repeat CLEK Study Visit. Patients were tested at the 15 CLEK Participating Clinics. The test-retest sample consisted of 1 34 keratoconus patients who met the entry criteria of the CLEK Study. High and low contrast Bailey-Lovie visual acuity was measured with the patient's habitual visual correction (entrance visual acuity monocularly and binocularly), and with the best correction monocularly (either the patient's rigid contact lens and over-refraction, or with a CLEK Study trial lens and appropriate over-refraction) at two visits separated by a median of 90 days (range 22 to 268 days). RESULTS: The mean absolute differences between the number of letters correct at the two visits ranged from a low of 3.24 +/- 3.1 for entrance high contrast binocular acuity to a high of 5.48 +/- 5.1 for best corrected low contrast monocular acuity. Intraclass correlation coefficients ranged from 0.757 to 0.853. The visual acuity score was somewhat higher at the Repeat Visit than at the Baseline Visit when the examiners were different between visits. CONCLUSIONS: Given the variable vision reported by keratoconus patients, visual acuity in this sample was very repeatable. Repeatability was slightly poorer when different examiners tested visual acuity at the Baseline and Repeat Visits.

Adolescent↗
PubMed1999

Issues in genomic screening: critical values, sample sizes, and the ability to detect linkage.

The aims of this study were to empirically investigate the ability of affected sib pairs (ASPs) to localize a gene through screening and to explore estimation of lod score critical values through resampling. To do so, we repartitioned 25 replicates of 100 simulated nuclear families into six data sets of sizes 100, 200, 300, 400, 500, and 1,000 and chose at most one mildly ASP per family. Using all marker data, we calculated maximum lod scores across the six-chromosome genome for each set. Then, we determined the cutoff value corresponding to a 5% genome-wide false positive rate using both the method of Lander and Kruglyak [1995] and a simple resampling algorithm that allows greater scan-specific flexibility. For chromosome 1, the ability of the ASPs to detect the region between markers 9 and 10 clearly increases with the sample size, and genome-wide significance is achieved for samples of size 400 or greater. Also, as expected, the critical values based on the less conservative resampling approach are generally slightly smaller than those from theoretical calculations based on the Ornstein-Uhlenbeck diffusion process of Lander and Kruglyak.

Genetic Linkage↗
PubMed2005

Variability and sample size requirements of quality-of-life measures: a randomized study of three major questionnaires.

PURPOSE: To compare the variability and sample size requirements of the global quality-of-life (QOL) scores of the following three major QOL instruments: the Functional Assessment of Cancer Therapy-General (FACT-G), Functional Living Index-Cancer (FLIC), and European Organisation for Research and Treatment of Cancer Core Quality of Life Questionnaire C30 (EORTC QLQ-C30). PATIENTS AND METHODS: Cancer patients were randomly assigned to answer two of the three instruments using an incomplete block design (n = 1,268). The instruments were compared in terms of coefficient of variation, effect size in detecting a difference between patients with different performance status, and correlation coefficient between scores at baseline and follow-up. RESULTS: The FACT-G and FLIC had significantly smaller coefficients of variation than the EORTC QLQ-C30 (both P < .05). The FLIC also had significantly larger correlation coefficients between scores at baseline and follow-up than the EORTC QLQ-C30 (P < .05). The FACT-G and the FLIC had a larger effect size in a cross-sectional and longitudinal setting, respectively, than the EORTC QLQ-C30 in differentiating patients with different performance status (both P < .05). CONCLUSION: In some aspects, the FACT-G and FLIC global QOL scores had smaller variability and larger discriminative ability than the EORTC QLQ-C30. Further research using other criteria to compare the three instruments is recommended.

Female↗
PubMed1992

Sample size considerations in designing studies with intra-oral models.

Especially during recent years, the use of pre-clinical models for predicting the efficacy of fluoride systems has assumed greater importance within the scientific community. Originally utilized primarily to screen experimental fluoride delivery systems, preclinical models are now being considered as predictors of clinical efficacy in lieu of controlled clinical caries trials. Of the various preclinical models presently available, human intra-oral models have the greatest potential for reflecting intended usage conditions and therefore may be the most meaningful models for predicting clinical efficacy. However, only with the proper consideration of numerous critical variables can studies using intra-oral models be appropriately designed to achieve the desired objectives. Clearly, these models must provide relevant information in a manner which reflects clinically established cariostatic activity and be capable of detecting established differences in the amount of cariostatic activity, i.e., dose-response effects. Three sources of variation must be considered before an appropriate study design and sample size can be chosen. Based on fluoride uptake data from an intra-oral model with proximally-located enamel specimens, estimates of variation among subjects, within subjects, and among specimens within subjects were obtained. Multiple specimens per panelist do not affect the first two sources of variation. Thus, the number of panelists, and not the number of specimens, is of primary importance when pre-test data are used to choose the appropriate study design and calculate the required sample size.

Adult↗
PubMed2004

Surgical mortality as an indicator of hospital quality: the problem with small sample size.

CONTEXT: Surgical mortality rates are increasingly used to measure hospital quality. It is not clear, however, how many hospitals have sufficient caseloads to reliably identify quality problems. OBJECTIVE: To determine whether the 7 operations for which mortality has been advocated as a quality indicator by the Agency for Healthcare Research and Quality (coronary artery bypass graft [CABG] surgery, repair of abdominal aortic aneurysm, pancreatic resection, esophageal resection, pediatric heart surgery, craniotomy, hip replacement) are performed frequently enough to reliably identify hospitals with increased mortality rates. DESIGN AND SETTING: The US national average mortality rates and hospital caseloads of the 7 operations were determined using the 2000 Nationwide Inpatient Sample (NIS), and sample size calculations were performed to determine the minimum caseload necessary to reliably detect increased mortality rates in poorly performing hospitals. A 3-year hospital caseload was used for the baseline analysis, and poor performance was defined as a mortality rate double the national average. MAIN OUTCOME MEASURE: Proportion of hospitals in the United States that performed more than the minimum caseload for each operation. RESULTS: The national average mortality rates for the 7 procedures examined ranged from 0.3% for hip replacement to 10.7% for craniotomy. Minimum hospital caseloads necessary to detect a doubling of the mortality rate were 64 cases for craniotomy, 77 for esophageal resection, 86 for pancreatic resection, 138 for pediatric heart surgery, 195 for repair of abdominal aortic aneurysm, 219 for CABG surgery, and 2668 for hip replacement. For only 1 operation did the majority of hospitals exceed the minimum caseload, with 90% of hospitals performing CABG surgery having a caseload of 219 or higher. For the remaining operations, only a small proportion of hospitals met the minimum caseload: craniotomy (33%), pediatric heart surgery (25%), repair of abdominal aortic aneurysm (8%), pancreatic resection (2%), esophageal resection (1%), and hip replacement (<1%). CONCLUSION: Except for CABG surgery, the operations for which surgical mortality has been advocated as a quality indicator are not performed frequently enough to judge hospital quality.

Aortic Aneurysm, Abdominal↗
PubMed2005

Split-plot microarray experiments: issues of design, power and sample size.

This article focuses on microarray experiments with two or more factors in which treatment combinations of the factors corresponding to the samples paired together onto arrays are not completely random. A main effect of one (or more) factor(s) is confounded with arrays (the experimental blocks). This is called a split-plot microarray experiment. We utilise an analysis of variance (ANOVA) model to assess differentially expressed genes for between-array and within-array comparisons that are generic under a split-plot microarray experiment. Instead of standard t- or F-test statistics that rely on mean square errors of the ANOVA model, we use a robust method, referred to as 'a pooled percentile estimator', to identify genes that are differentially expressed across different treatment conditions. We illustrate the design and analysis of split-plot microarray experiments based on a case application described by Jin et al. A brief discussion of power and sample size for split-plot microarray experiments is also presented.

Analysis of Variance↗
PubMed1987

Sample size determination in clinical trials with an emphasis on exponentially distributed responses.

Sample size determination in clinical trials (and other similar studies) depends on a number of factors including the distribution of patient survival (remission) times, available estimates of the requisite parameters of the distribution under the null and alternative hypotheses, sizes of the Type I and Type II errors, and the length of the clinical trial, which in turn determines whether there are many, few, or no censored observations with regard to patient survival (remission). A further consideration is the patient recruitment period, which is assumed to begin simultaneously with the clinical trial but whose length is less than the length of the clinical trial. The purpose of this article is to explore the optimum lengths of the clinical trial and the recruitment period on the basis of minimizing the expected cost of the trial. A specified cost function, patient entry distribution, and exponential survival distribution are all assumed, primarily for illustrative purposes.

Biometry↗
PubMed1982

Needle muscle biopsy: techniques to increase sample sizes, and complications.

Muscle biopsy samples of the vastus lateralis (444) using Bergström needles were obtained under local anesthesia from 43 normal athletes and 17 patients with suspected muscle disease. Five biopsy techniques were used and sample weights were compared. Biopsy during isometric muscle contraction was the most effective technique, yielding a mean sample weight 3.2 times that obtained by simple needle insertion, the least effective method (p less than 0.001). Use of a 5mm rather than 4mm diameter needle raised the mean (+/- 1 SD) sample weight to 35mg (+/- 7.3) from 13.7mg (+/- 5.2) (p less than 0.001), and total yields of 150-200mg were easily obtained by resampling. No difficulties were encountered in the biochemical, histochemical, or immunofluroescent evaluations of these samples. Several subjects were assessed for complications at various times following biopsy. Mild to moderate symptoms, signs, and investigative findings were noted in some subjects within the first few days. Only one person reported subsequent persistent symptoms at the biopsy site-a mild "awareness" during athletic exertion. The higher-yield techniques were generally safe, well tolerated, and provided samples of sufficient size and quality for multiple simultaneous studies. Needle biopsy appears to warrant increased use in physiatric research and clinical practice.

Adolescent↗
PubMed2001

Modification of the sample size and the schedule of interim analyses in survival trials based on data inspections.

A method is presented which allows us to adapt the sample size as well as the number and time points of interim analyses to the treatment difference observed at an interim look during the course of a clinical trial with censored survival time as the endpoint. The method allows the inclusion of data inspections during the course of the trial and redesign of the trial on the basis of the observed treatment difference without affecting the type I error risk. Formulae for recalculating the required number of events and the number of further patients to be randomized as a function of the observed hazard rates and the detectable hazard ratio are given.

Carcinoma, Non-Small-Cell Lung↗
PubMed2000

Sample size determination in clinical research: 2.

In the second of this two-part series, comparative study design is considered and, using examples, power calculation is explained. The information required for calculating sample size for comparative studies is highlighted.

Data Interpretation, Statistical↗