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The general procedure for sample size determination based upon the confidence interval approach is reviewed and presented for both absolute and relative precision stipulations. The relationship between precision and sample size is discussed and methods for sample size determination for clinical trials are presented and illustrated with numerical examples.
Analyses of both the nucleotide and amino acid sequences derived from all 13 mitochondrial protein-encoding genes (12,234 bp) of 19 metazoan species, including that of the lancelet Branchiostoma floridae ("amphioxus"), fail to yield the widely accepted phylogeny for chordates and, within chordates, for vertebrates. Given the breadth and the compelling nature of the data supporting that phylogeny, relationships supported by the mitochondrial sequence comparisons are almost certainly incorrect, despite their being supported by equally weighted parsimony, distance, and maximum-likelihood analyses. The incorrect groupings probably result in part from convergent base-compositional similarities among some of the taxa, similarities that are strong enough to overwhelm the historical signal. Comparisons among very distantly related taxa are likely to be particularly susceptible to such artifacts, because the historical signal is already greatly attenuated. Empirical results underscore the need for approaches to phylogenetic inference that go beyond simple site-by-site comparison of aligned sequences. This study and others indicate that, once a sequence sample of reasonable size has been obtained, accurate phylogenetic estimation may be better served by incorporating knowledge of molecular structures and processes into inference models and by seeking additional higher order characters embedded in those sequences, than by gathering ever larger sequence samples from the same organisms in he hope that the historical signal will eventually prevail.
New SARS-CoV-2 variants arise frequently with different viral properties that can impact the effectiveness of the vaccines. Updating estimates of vaccine effectiveness (VE) in public health surveillance can be limited by the necessity of conducting a distinct study that entails analysis of prospective cohort data or using a test-negative design. We introduce a method for dynamically updating estimates of VE using data that accumulate in real time. Our method uses dynamic case-control sampling to estimate VE against a newly emerging variant relative to a previous variant. Dynamic case-control sampling is a technique that continuously updates VE estimates by comparing individuals infected with a newly emerging variant (defined as "cases") to those infected with a previously circulating variant (defined as "controls"). We use this estimate in combination with information about VE from the previous variant (these estimates are typically available from larger, traditional studies) to infer VE against the emerging variant. We demonstrate the utility of this method on the BA.1 and BA.2 sub-lineages of the Omicron variant. The method produces estimates of VE comparable to those produced using traditional methods, although with increased SE. The increase in error, however, is reasonable given a much smaller sample size than other studies, and error ranges of the estimates could be significantly improved by sequencing a larger proportion of identified cases. Our method, which assumes only a fraction of the new cases are being sequenced, can be applied by health departments using routinely collected data to produce timely, rigorous VE estimates to rapidly identify potential changes in VE.
Dominating the literature on sample size determination are papers concerned with observations collected from independent responses. We discuss in this paper, under the common correlation model for binary responses, the issue of estimating the number of groups when the sampling units are clusters of variable sizes.
Quantitative data on lung structure are essential to set up structure-function models for assessing the functional performance of the lung or to make statistically valid comparisons in experimental morphology, physiology, or pathology. The methods of choice for microscopy-based lung morphometry are those of stereology, the science of quantitative characterization of irregular three-dimensional objects on the basis of measurements made on two-dimensional sections. From a practical perspective, stereology is an assumption-free set of methods of unbiased sampling with geometric probes, based on a solid mathematical foundation. Here, we discuss the pitfalls of lung morphometry and present solutions, from specimen preparation to the sampling scheme in multiple stages, for obtaining unbiased estimates of morphometric parameters such as volumes, surfaces, lengths, and numbers. This is demonstrated on various examples. Stereological methods are accurate, efficient, simple, and transparent; the precision of the estimates depends on the size and distribution of the sample. For obtaining quantitative data on lung structure at all microscopic levels, state-of-the-art stereology is the gold standard.
Lung-clearance classifications for 238U, 232Th, 230Th, 228Th, 226Ra, 210Pb and 210Po in respirable coal fly ash were estimated for use with the lung clearance model proposed by the ICRP Task Group on Lung Dynamics. Estimates were based on measurements of the dissolution rates for these radionuclides from sized fly-ash samples into simulated lung fluid at 37 degrees C. The estimates were expressed in the classification terms of the model, i.e. D, W and Y, indicating lung clearance half-times of 0-10 days, 11-100 days, and more than 100 days, respectively. Ash from eastern bituminous coal, western bituminous coal and mid-western bituminous coal was examined. Both Class-D and Class-Y components of 238U were found in all samples, whereas all the other radionuclides dissolved very slowly and were classified 100% Class Y. The fraction of 238U in Class D increased with decreasing particle size and increased linearly from 0.02 to 0.17 as the concentration of U in the volatile-metal portion of the samples increased. This relationship suggests that a major fraction of the U in coal fly ash may be shielded from exposure to simulated lung fluid by more-abundant metals deposited on the outer surface of fly ash during coal combustion.
The authors evaluated support in the literature for the hypothesis that ambient air pollution causes childhood cancer. The PubMed database was searched for original articles, which were reviewed for evidence of a relation with the main types of childhood cancer, using criteria including sample size, magnitude and precision of relative risk estimates, presence of a dose-response pattern and potential for bias. The hypothesis has been studied almost entirely with respect to traffic-related air pollution. Since derivation of the hypothesis from 2 case-control studies in Denver, USA, two further case-control studies have provided new positive evidence and 4 case-control and 7 ecological studies mainly negative evidence. The 4 case-control studies providing positive evidence were relatively small and tended to have more methodological limitations than those showing no association. Publication bias is possible. The weight of the epidemiological evidence indicates no increased risk for childhood cancer associated with exposure to traffic-related residential air pollution. Nevertheless, the limited number of studies, the methodological limitations of both positive and negative studies and the absence of consistency in the results obviate a firm conclusion of no effect. In particular, nondifferential misclassification of exposure might have masked true, weak associations.
A general rationale and specific procedures for examining the statistical power characteristics of psychology-of-aging empirical studies are provided. First, 4 basic ingredients of statistical hypothesis testing are reviewed. Then, 2 measures of effect size are introduced (standardized mean differences and the proportion of variation accounted for by the effect of interest), and methods are given for estimating these measures from already-completed studies. Power and sample size formulas, examples, and discussion are provided for common comparison-of-means designs, including independent samples I-factor and factorial analysis of variance (ANOVA) design, analysis of covariance designs, repeated measures (correlated samples) ANOVA designs, and split-plot (combined between- and within-subjects) ANOVA designs. Because of past conceptual differences, special attention is given to the power associated with statistical interactions, and cautions about applying the various procedures are indicated. Illustrative power estimations also are applied to a published study from the literature. It is argued that psychology-of-aging researchers will be both better informed consumers of what they read and more "empowered" with respect to what they research by understanding the important roles played by power and sample size in statistical hypothesis testing.
OBJECTIVE: Examination of the extent to which federal surveys provide the data needed to estimate the coverage/cost impacts of policy alternatives to address the problem of uninsurance. DATA SOURCES/STUDY SETTING: Assessment of the major federal household surveys that regularly provide information on health insurance and access to care based on an examination of each survey instrument and related survey documentation and the methodological literature. STUDY DESIGN: Identification of the data needed to address key policy questions on insurance coverage, assessment of how well existing surveys meet this need, definition of the critical elements of an ideal survey, and examination of the potential for building on existing surveys. DATA COLLECTION/EXTRACTION METHODS: Collection and critical assessment of pertinent survey documentation and methodological studies. PRINCIPAL FINDINGS: While all the federal surveys examined provide valuable information, the information available to guide key policy decisions still has major gaps. Issues include measurement of insurance coverage and critical content gaps, inadequate sample sizes to support precise state and substate estimates, considerable delays between data collection and availability, and concerns about response rates and item nonresponse. Our assessment is that the Current Population Survey (CPS) and the National Health Interview Survey could be most readily modified to address these issues. CONCLUSIONS: The vast resources devoted to health care and the magnitude of the uninsurance problem make it critical that we have a reliable source for tracking health care and coverage at the national and state levels and for major local areas. It is plausible that this could be more cost effectively done by building on existing surveys than by designing and fielding a new one, but further research is needed to make a definitive judgment. At a minimum, the health insurance information collected on the CPS should be revised to address existing measurement problems.
One can obtain population-based estimates of the penetrance of a measurable mutation from cohort studies, from population-based case-control studies, and from genotyped-proband designs (GPD). In a GPD, we assume that representative individuals (probands) agree to be genotyped, and one then obtains information on the phenotypes of first-degree relatives. We also consider an extension of the GPD in which a relative is genotyped (GPDR design). In this paper, we give methods and tables for determining sample sizes needed to achieve desired precision for penetrance estimates from such studies. We emphasize dichotomous phenotypes, but methods for survival data are also given. In an example based on the BRCA1 gene and parameters given by Claus et al. [(1991) Am J Hum Genet 48:232-242], we find that similar large numbers of families need to be studied using the cohort, case-control, and GPD designs if the allele frequency is known, though the GPDR design requires fewer families, and, if one can study mainly probands with disease, the GPD design also requires fewer families. If the allele frequency is not known, somewhat larger sample sizes are required. Surprisingly, studies with mixtures of families of affected and non-affected probands can sometimes be more efficient than studies based exclusively on affected probands when the allele frequency is unknown. We discuss the feasibility and validity of these designs and point out that GPD and GPDR designs are more susceptible to a bias that results when the tendency for an individual to volunteer to be a proband or to be a subject in a cohort or case-control study depends on the phenotypes of his or her relatives.
Guenther derived a simple formula for the accurate computation of equal sample sizes when the two-sample t-test with pooled variance estimate is used. In the present paper, the Guenther formula is generalized to the case of unequal sample sizes. In addition, the case of unequal variances is considered.
A recently developed model uses the localization of abnormalities on images to improve statistical precision in measuring detection accuracy Az, the area below an observer's receiver operating characteristic (ROC) curve for ratings of sampled normal and abnormal cases. This study evaluated that improvement by investigating how much the standard error of estimated Az decreased when the statistical analysis included localization data. Comparisons of analyses with vs without localizations were made for: 1) the estimates of Az from observers' rating ROC curves for nodular lesions on clinical chest films and liver CT scans; 2) the probability of correct choices between paired samples of normal and abnormal cases (equivalent to Az); and 3) the sampling distributions of Az measured in Monte Carlo simulations of 2,000 independent rating experiments. Localization information considerably improved the precision of Az estimates, particularly when detection accuracy was low (Az approximately 0.60). These data provided roughly the same benefits in estimation precision as would two-to-fourfold increases in the sizes of both 1) the samples of positive and negative cases and 2) the observer samples used to estimate Az means.
We studied the possibility of enzymatic estimation of myocardial infarct size in patients late (between days 2 and 6) after the onset of acute myocardial infarction (AMI), in whom estimation of infarct size was difficult by analysis of time-activity curves of serum creatine kinase (CK) because of the lack of the enzymatic information during the initial 48 hours. Serial determinations of serum enzymes were performed in 32 patients within 6 hours after the onset of AMI and significantly close correlations were observed between cumulative total CK release and the cardiac fraction of lactate dehydrogenase isoenzyme (LDH1) activities from day 2 to day 6 after the onset of AMI (r = 0.863 to 0.870; p less than 0.001). We developed a nomogram to estimate cumulative total CK release by serum LDH1 activities obtained between days 2 and 6 after AMI and evaluated the reliability of the nomogram. Cumulative total CK release obtained from serial serum CK activities correlated closely with total CK release obtained from the nomogram in the second group of patients with AMI (r = 0.923 to 0.946; n = 24; p less than 0.001). Our total CK nomogram requiring few blood samples was useful in late estimation of infarct size in patients who were admitted to the hospital between days 2 and 6 after the onset of AMI.
The accuracy of clinical observations was estimated using Bayesian latent-class models with two or more independent tests. Four veterinarians carried out systematic independent clinical examinations on 155 pigs in three herds. Based on the results of binary recordings of clinical observations on dullness, poor body condition (PBC), skin lesions, lameness, respiratory disease, and diarrhea, a latent disease state for each clinical disease was estimated using Gibbs sampling. The accuracy of the clinical observations differed for the four observers and for different clinical signs. Population parameters were estimated from a Bayesian hierarchical model, and the accuracy of a random observer was calculated. We concluded that the accuracy of the veterinarians in this study substantiated the need to pursue more-precise definitions of the clinical findings and that larger sample sizes would be needed to provide reasonable variance estimates. Finally, we concluded that the uncertainty in the clinical decision-making process (starting with the clinical examination) needs to be represented fully.
BACKGROUND: Carotid intima-media thickness (CIMT) measurements are currently widely used in randomized controlled trials (RCTs) to study the efficacy of interventions. In designing a RCT with CIMT as a primary outcome, several ultrasound options may be considered. We discuss the various options and provide a pooled estimate of CIMT progression. In addition, we quantify the effect of these choices on the sample size for a RCT. SUMMARY OF COMMENT: To estimate the average CIMT progression rate, we performed a pooled analysis using CIMT progression rates of control groups from published RCTs. The pros and cons of the following ultrasound options are discussed: which arterial segments may be studied; whether near and far wall CIMT measurements should be performed; whether a single image (1 angle of interrogation) or multiple images (more angles of interrogation) should be used; whether a manual or an automated edge detection reading system should be used; and whether images should be read in a random fashion or in batches. The pooled analysis showed an annual rate of change in mean common CIMT of 0.0147 mm (95% CI, 0.0122 to 0.0173) and in mean maximum CIMT of 0.0176 mm (95% CI, 0.0149 to 0.0203). CONCLUSIONS: Given the current evidence together with our experience with recently developed ultrasound protocols, we favor the use of mean maximum CIMT rather than mean common CIMT as the primary outcome measure in RCTs designed to evaluate the efficacy of pharmacological and nonpharmacological interventions in carotid artery atherosclerosis.
The most cost-effective method to measure the morbidity managed and treatments provided in general practice is from records of a cluster of consultations (encounters) from each general practitioner (GP) in a random sample. A cluster sampling method is proposed for future surveys for analysis of encounter-based general practice data. The sample sizes needed to measure the most common problems managed and drugs prescribed were estimated using ratio-estimator models for cluster sample surveys. Morbidity and treatment rates were estimated from the Australian Morbidity and Treatment Survey in General Practice 1990-1991 (AMTS). The 20 most common problems in the AMTS were managed at estimated rates of 1.5 to 9.5 per 100 encounters. The 20 most common drugs were prescribed at estimated rates of 0.7 to 3.6 per 100 problems. These rates were used to determine precision as a percentage of each true value for future surveys, that is, as relative precision. If we want to be 95 per cent confident that these rates will be within 5 per cent of each true rate, sample sizes of 552 to 5675 GPs are needed. If we fix the sample size at 1000 GPs, relative precision lies within 12 per cent of these rates. If the sample size is increased to 1500 GPs, relative precision improves only marginally. The differences in sample size for each of the most frequent morbidity and treatment data are largely due to their variable distributions and relatively infrequent occurrence in general practice. A sample size of 1000 GPs will enable measurement of the most common morbidity and treatments at 95 per cent confidence.
Previous controlled reliability studies of cup to disc (C/D) ratio estimations may have been biased by lack of criteria for cup determination, small sample size; and/or large interval grouping of collected data. In our study four examiners independently estimated the C/D ratios of 40 patients by direct ophthalmoscopy using a contour criterion for cup determination. Results indicated that 75% of the estimate pairs differed by 0.10 or less. Fewer than 14% of the estimate pairs differed by 0.2 or greater. The results of the study suggest that when examiners use a specified criterion of contour cupping, interexaminer assessment of the C/D ratio estimation is clinically and statistically reliable.
A national health objective for the year 2000 is to implement periodic analysis and publication of each state's progress toward the objectives for each racial/ethnic group that constitutes at least 10% of the state's population (objective 22.5a). In Michigan (1990 population: 9.3 million), blacks represent approximately 12% of the adult population*; prevalence estimates for risk factors for the black population derived from the Behavioral Risk Factor Surveillance System (BRFSS) have varied in consistency because of the limitations of small sample sizes. To improve the precision of risk factor prevalence estimates for blacks in Michigan and to improve measurement of the state's progress toward the national year 2000 objectives for blacks, in 1993, the Michigan Department of Public Health (MDPH) aggregated annual state BRFSS data for 1989-1991. This report summarizes the findings of this analysis and compares them with an analysis of annual state BRFSS data for 1987-1991.