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A test of hypothesis is proposed for the comparison of two groups with respect to two binary outcomes. In addition, sample size requirements are determined. The methods are generalized for an arbitrary number of independent binary outcomes.
BACKGROUND: A morphometric study of the rat lung was done to determine the importance, within the precision of a morphometric study, of the sample size in relation to the quality of the image and to propose a method for the quantification of lung collagen fiber. METHODS: Sixty Wistar rats, divided into two age groups consisting of adult and old rats, were used. The left lungs were studied and processed for light microscopy. Methylene blue, resorcin-fuchsin, and Sirius red stainings were performed. The variables were quantified automatically. In the sections stained with methylene blue, the variables alveolar chord, wall thickness, mean linear intercept index, tissue density, and internal alveolar perimeter were quantified, in two series, one with x40 magnification (panoramic image) and the other with x100 magnification. In the sections stained with resorcin-fuchsin, elastic fiber was quantified and the result related with that obtained for the variable tissue density. The results were compared statistically, and those obtained with different magnifications for single variables were related by using the correlation test; the misclassification indices were also calculated. In the sections stained with Sirius red, the surface that was birefringent to polarized light was quantified and related to the collagen fiber; the results were compared statistically. RESULTS: Concerning results obtained for single variables with different magnifications good, correlation indices were obtained (r > or = 0.62) for all but the wall thickness (r = 0.3). The results obtained for the panoramic images were the highest. The misclassification index was lower for the panoramic images. Significant differences (P < 0.5) were not found when comparing the mean birefringent surface in the two groups of animals. CONCLUSIONS: The results obtained lead us to consider that, despite the fact that the quality of the panoramic images is poorer, the results for these images are more accurate, possibly because a greater number of structures was analyzed. The measurement of the birefringent surfaces of the sections stained with Sirius red may be used in the study of lung collagen fiber.
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To remove the influence of spuriously long response times, many investigators compute "restricted means", obtained by throwing out any response time more than 2.0, 2.5, or 3.0 standard deviations from the overall sample average. Because reaction time distributions are skewed, however, the computation of restricted means introduces a bias: the restricted mean underestimates the true average of the population of response times. This problem may be very serious when investigators compare restricted means across conditions with different numbers of observations, because the bias increases with sample size. Simulations show that there is substantial differential bias when comparing conditions with fewer than 10 observations against conditions with more than 20. With strongly skewed distributions and a cutoff of 3.0 standard deviations, differential bias can influence comparisons of conditions with even more observations.
When the measurement of outcome varies within studied subjects and the cost of additional subjects is high, taking more than one measurement for each subject constitutes a useful alternative to increase the power or to reduce the total cost of the study. In this paper, I present sample size formulae for repeated measurements in dichotomous data under different situations. I also discuss optimal sample allocation for repeated measurements.
Seventy-one "negative" randomized control trials were re-examined to determine if the investigators had studied large enough samples to give a high probability (greater than 0.90) of detecting a 25 per cent and 50 per cent therapeutic improvement in the response. Sixty-seven of the trials had a greater than 10 per cent risk of missing a true 25 per cent therapeutic improvement, and with the same risk, 50 of the trials could have missed a 50 per cent improvement. Estimates of 90 per cent confidence intervals for the true improvement in each trial showed that in 57 of these "negative" trials, a potential 25 per cent improvement was possible, and 34 of the trials showed a potential 50 per cent improvement. Many of the therapies labeled as "no different from control" in trials using inadequate samples have not received a fair test. Concern for the probability of missing an important therapeutic improvement because of small sample sizes deserves more attention in the planning of clinical trials.
Cancellous bone screw extraction strengths are determined in four matched anatomical locations in five pairs of unembalmed human distal femora. The results are used to calculate sample size estimates for the experimental detection of differences in screw extraction mechanics. While unmatched designs require prohibitively large numbers of bone specimens, matched designs require between 71.6 and 88.5% fewer, depending on the correlation between matched observations and the homogeneity of sample variances.
We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.
In tests that involve counting or searching for discrete objects, clinical laboratory specimens that are too small produce insensitive and imprecise test results. We found that ten of 57 surveyed New England hospital laboratories examine less than a 50-mg stool sample for parasite eggs; they are, therefore, unlikely to detect infections characterized by low concentrations of eggs in stool. Conversely, all 57 laboratories use the traditional, appropriate sample size of at least 1,000 RBCs for reticulocyte counting. In this report, we discuss theoretical and practical considerations in small sample testing.
When the distribution of the response variable is skewed, the population median may be a more meaningful measure of centrality than the population mean, and when the population distribution of the response variable has heavy tails, the sample median may be a more efficient estimator of centrality than the sample mean. The authors propose a confidence interval for a general linear function of population medians. Linear functions have many important special cases including pairwise comparisons, main effects, interaction effects, simple main effects, curvature, and slope. The confidence interval can be used to test 2-sided directional hypotheses and finite interval hypotheses. Sample size formulas are given for both interval estimation and hypothesis testing problems.
In proportional hazards survival studies, power depends on the observed number of deaths, d*. For a given choice of survival, loss, and patient entry distributions, sample sizes can be determined by equating d* to the expected number of deaths. Approximating the survival and loss distributions with piecewise exponential distributions, and patient entry with a piecewise linear distribution, significantly reduces the computational overhead, and the expected number of deaths can be evaluated routinely. The merits of this approach are illustrated by a clinical trial of chemotherapy for large bowel cancer.
The coefficient of detection (CD) is said to represent the minimal difference statistically detectable with a t-test at some preselected alpha. Although the CD does not explicitly take statistical power into consideration, it is mathematically and empirically demonstrable that the CD operates at approximately 50% power. The CD, as reported in the Collaborative Behavioral Teratology Study (CBTS), also applies only to hypotheses about the difference between one sample mean and a selected standard value, and, consequently, does not apply to a situation where a difference between two sample means is considered. Therefore, the low one-sample CDs reported in the CBTS cannot be used to approximate sample sizes for purposes of meeting the requirement by the Environmental Protection Agency that a 20% difference between two sample means (e.g., control vs. experimental groups) should be detected with a power of 80% (or 90%) at a 5% certainty level.
Formulas are derived for determination of the number of patients needed in a prospective comparison of survival curves, when the control group patients have already been followed for some period. Although an explicit formula for the required sample size is not available, the computing is straightforward, and tables of examples are presented. Situations are described when one might need to allocate some new patients to the control group, rather than exclusively to the experimental group.
The extraction of mRNA from cartilage samples is complicated by the presence of proteoglycans and the low cellular density of the tissue. We required a method that would enable mRNA to be extracted from small biopsy-sized samples of cartilage. The method had to produce consistent results and sufficient RNA for Northern and PCR analysis. Methods of total RNA extraction, previously shown to be effective for cartilage, were compared with a new technique in which an oligo (dT) conjugated to biotin hybridises to the mRNA. The hybrids are captured with covalently coupled streptavidin paramagnetic particles. Samples of growth plate cartilage, including those specifically from the upper (proliferative and transitional) and lower (fully hypertrophic) zones, were collected and some were frozen at -70 degrees C. Samples for extraction by the paramagnetic method weighed approximately 80 mg and approximately 12 micrograms of mRNA was extracted from fresh tissue samples. The yield from similar frozen samples of the same weight was about a seventh of that from the fresh tissues. 5 micrograms of the mRNA from each sample was run on a gel, and a Northern blot was prepared and probed with a [32P]-labelled antisense RNA probe to type II collagen cDNA. A distinct band of type II collagen mRNA was detected (5.3 Kb) in the samples from the upper (proliferative and transitional) zone. The traditional methods of extracting RNA from cartilage required far greater quantities of tissue and the RNA produced was frequently degraded. The results obtained using the paramagnetic bead method precluded further trials with modification of the traditional methods of mRNA extraction.(ABSTRACT TRUNCATED AT 250 WORDS)
Models of O3 distribution in two mountain ranges, the Carpathians in Central Europe and the Sierra Nevada in California were constructed using ArcGIS Geostatistical Analyst extension (ESRI, Redlands, CA) using kriging and cokriging methods. The adequacy of the spatially interpolated ozone (O3) concentrations and sample size requirements for ozone passive samplers was also examined. In case of the Carpathian Mountains, only a general surface of O3 distribution could be obtained, partially due to a weak correlation between O3 concentration and elevation, and partially due to small numbers of unevenly distributed sample sites. In the Sierra Nevada Mountains, the O3 monitoring network was much denser and more evenly distributed, and additional climatologic information was available. As a result the estimated surfaces were more precise and reliable than those created for the Carpathians. The final maps of O3 concentrations for Sierra Nevada were derived from cokriging algorithm based on two secondary variables--elevation and maximum temperature as well as the determined geographic trend. Evenly distributed and sufficient numbers of sample points are a key factor for model accuracy and reliability.
Fifty cytologically malignant, five suspicious, and 27 cytologically benign serous effusions were assessed morphometrically for differences in mean and outlying nuclear and cytoplasmic variables. Significant differences were found between benign and malignant specimens for all nuclear morphometric variables measured, the most significant being largest nuclear area and diameter. No significant differences were found for cytoplasmic size variables. Although measurement of outlying values in serous effusions enhanced the difference between benign and malignant cell populations, it was of insufficient sensitivity or specificity to be of clinical diagnostic use. Increasing the sample size improved test performance but would be tedious to perform manually.