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PubMed2000

Re-calculating the sample size in internal pilot study designs with control of the type I error rate.

When designing a clinical trial, there is usually some uncertainty about the variability of the primary outcome variable. This may lead to an unnecessarily high or inadequately low sample size. The internal pilot study approach uses data from patients recruited up to an interim stage to re-estimate the variance and to re-calculate the final sample size accordingly. Previously, simulation studies have shown that this methodology may highly improve the chance to obtain a well-powered trial. However, it also turned out that the type I error rate may be inflated by this procedure. We quantify the maximum excess of the type I error rate for normally distributed outcomes. If strict control of the alpha-level is considered to be an important issue, a method is proposed to achieve this when re-calculating the sample size in internal pilot studies. The characteristics of the power distributions are investigated for various sample size adaptation rules and implications are discussed.

Data Interpretation, Statistical↗
PubMed1983

Recovering the parameters of finite mixtures of normal distributions from a noisy record: an empirical comparison of different estimating procedures.

Three procedures were compared for their ability to estimate the known parameters of mixtures of normal distributions: maximum likelihood estimators (MLE), X2 minimization method and the least-square error procedure. For this purpose a Monte-Carlo study was undertaken to evaluate empirically the performance of the estimators. We chose to investigate their behaviour using closely-positioned mixtures of two or 3 univariate Gaussians. The Monte-Carlo simulations clearly demonstrate the superiority of the MLE and X2 minimum methods. Other reasons why the MLE is to be preferred are discussed. The effect of sample size was also examined. All 3 estimators have also been applied to data derived from different physiological experiments, and the use of the estimators is considered in practical terms. The formulae for all 3 procedures are given in the Appendix.

Animals↗
PubMed2002

An estimator for pairwise relatedness using molecular markers.

I propose a new estimator for jointly estimating two-gene and four-gene coefficients of relatedness between individuals from an outbreeding population with data on codominant genetic markers and compare it, by Monte Carlo simulations, to previous ones in precision and accuracy for different distributions of population allele frequencies, numbers of alleles per locus, actual relationships, sample sizes, and proportions of relatives included in samples. In contrast to several previous estimators, the new estimator is well behaved and applies to any number of alleles per locus and any allele frequency distribution. The estimates for two- and four-gene coefficients of relatedness from the new estimator are unbiased irrespective of the sample size and have sampling variances decreasing consistently with an increasing number of alleles per locus to the minimum asymptotic values determined by the variation in identity-by-descent among loci per se, regardless of the actual relationship. The new estimator is also robust for small sample sizes and for unknown relatives being included in samples for estimating allele frequencies. Compared to previous estimators, the new one is generally advantageous, especially for highly polymorphic loci and/or small sample sizes.

Animals↗
PubMed1993

Design effects for binary regression models fitted to dependent data.

Dependent data, such as arise with cluster sampling, typically yield variances of parameter estimates which are larger than would be provided by a simple random sample of the same size. This variance inflation factor is called the design effect of the estimator. Design effects have been derived for cluster sampling designs using simple estimators such as means and proportions, and also for linear regression coefficient estimators. In this paper, we show that a method to derive design effects for linear regression estimators extends to generalized linear models for binary responses. In particular, some simple expressions for design effects in the linear regression model provide accurate approximations for binary regression models such as those based on the logistic, probit and complementary log-log links. We corroborate our findings with two examples and some simulation studies.

Acquired Immunodeficiency Syndrome↗
PubMed1998

Comparative performance of species richness estimation methods.

In most real-world contexts the sampling effort needed to attain an accurate estimate of total species richness is excessive. Therefore, methods to estimate total species richness from incomplete collections need to be developed and tested. Using real and computer-simulated parasite data sets, the performances of 9 species richness estimation methods were compared. For all data sets, each estimation method was used to calculate the projected species richness at increasing levels of sampling effort. The performance of each method was evaluated by calculating the bias and precision of its estimates against the known total species richness. Performance was evaluated with increasing sampling effort and across different model communities. For the real data sets, the Chao2 and first-order jackknife estimators performed best. For the simulated data sets, the first-order jackknife estimator performed best at low sampling effort but, with increasing sampling effort, the bootstrap estimator outperformed all other estimators. Estimator performance increased with increasing species richness, aggregation level of individuals among samples and overall population size. Overall, the Chao2 and the first-order jackknife estimation methods performed best and should be used to control for the confounding effects of sampling effort in studies of parasite species richness. Potential uses of and practical problems with species richness estimation methods are discussed.

Animals↗
PubMed1987

Gender, firm size, industry, and estimates of the value-of-life.

Two national probability samples are used to investigate four empirical questions associated with estimating the value-of-life using coefficients from wage regressions. The four questions pertain to whether wage regression coefficients on fatality rate variables are sensitive to (1) including or excluding women from the sample, (2) definitions of the fatality rate which include estimates of either male only or female only deaths, (3) removing the influence of firm size from the fatality rate or the wage rate, (4) respondents' inaccuracies in reporting their three-digit industry. Problems associated with (3) and (4) are found to be minimal. Problems associated with (1) and (2) also appear to be small if the goal is to estimate the value-of-life for men.

Accidents, Occupational↗
PubMed2006

Comparison of bioenergetic synchronization technique and customary chiropractic care for older adults with chronic musculoskeletal pain.

OBJECTIVE: The aim of the study was to compare the clinical outcomes of 2 approaches to chiropractic care for patients with chronic musculoskeletal pain. Included were the approach most commonly used by doctors of chiropractic (diversified technique spinal manipulation) and a nonmanipulative mind-body approach (Bioenergetic Synchronization Technique). This clinical experiment tested the null hypothesis that there is no clinically or statistically significant difference in effect between the 2 approaches. METHODS: The study was conducted in the research clinic of the Parker College of Chiropractic. Patients were initially recruited by contacting a previously developed pool used for studies related to fall prevention in the elderly. Eighty-one patients (74 females; median age, 66 years) were enrolled and 78 (96%) completed the study. The primary end point was the end of a 3-week nontreatment interval after a 4-week treatment period. An intention-to-treat analysis was used; all patients who completed assessments were included whether or not they were compliant with the treatment protocol. A sample size of 55 per group was estimated to be necessary to detect a clinically significant (6-point) between-group difference in the Pain Disability Index (PDI). The primary outcome, the mean between-group difference between PDI scores at visit 1 and the exit visit, was tested with a 2-tailed t test for independent samples. RESULTS: Mean improvements in the PDI from visit 1 to the exit visit were 6.9 points in the Bioenergetic Synchronization Technique group (n = 40) and 6.4 in the diversified technique group (n = 38); the between-groups difference was not statistically or clinically significant (95% confidence interval, -4.7 to 5.8). CONCLUSIONS: For this particular group of patients, both groups demonstrated similar improvement scores on the PDI; the study's null hypothesis was not rejected.

Adult↗
PubMed2003

Computed tomography and magnetic resonance imaging in staging of uterine cervical carcinoma: a systematic review.

OBJECTIVE: The goal of this article is to systematically review the available evidence on the diagnostic performance of computed tomography (CT) and magnetic resonance imaging (MRI) in staging of cervical carcinoma. METHODS: A comprehensive computer literature search was performed in MEDLINE and EMBASE databases from January 1985 to May 2002. Two reviewers independently scored methodological quality of included studies and extracted relevant data for data analysis. A bivariate random effect approach was used to summarize estimates of sensitivity and specificity values. Covariates were added to this model to study the influence of sample size, publication year, methodological criteria, and MRI techniques on summary estimates. RESULTS: Fifty-seven articles were included. In 49 articles one imaging modality was evaluated (MRI, 38; CT, 11), and in 8 articles, both. Inclusion criteria were: minimum of 10 patients included, histopathology as reference standard, sufficient data presented to construct 2(x) 2 tables. The exclusion criterion was: data reported elsewhere in more detail. Sensitivity estimates for parametrial invasion were 74% (95% C: 68-79%) for MRI and 55% (95% CI: 44-66%) for CT, and for lymph node involvement, 60% (95% CI 52%-68%) and 43% (95% CI: 37-57%), respectively. MRI and CT had comparable specificities for parametrial invasion and lymph node involvement. For bladder invasion and rectum invasion the sensitivities for MRI were respectively 75% (95% CI: 66-83%) and 71% (95% CI: 53-83%), higher compared with CT. The specificity in evaluating bladder invasion for MRI was significantly higher compared with CT: 91% (95% CI: 83-95%) for MRI and 73% (95% CI: 52-87%) for CT. The specificities for rectum invasion were comparable. Differences in patient sample size, publication year, methodological criteria, and MRI techniques had no effect on the summary estimates. CONCLUSIONS: For overall staging of cervical carcinoma, MRI is more accurate than CT.

Female↗
PubMed1999

Test-based exact confidence intervals for the difference of two binomial proportions.

Confidence intervals are often provided to estimate a treatment difference. When the sample size is small, as is typical in early phases of clinical trials, confidence intervals based on large sample approximations may not be reliable. In this report, we propose test-based methods of constructing exact confidence intervals for the difference in two binomial proportions. These exact confidence intervals are obtained from the unconditional distribution of two binomial responses, and they guarantee the level of coverage. We compare the performance of these confidence intervals to ones based on the observed difference alone. We show that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.

Biometry↗
PubMed1990

Density, location, and sampling of Sarcoptes scabiei (Acari: Sarcoptidae) on experimentally infested pigs.

Forty-eight weaned pigs were inoculated with 0 (controls), 100 (low dose), and 1,000 (high dose) itch mites, Sarcoptes scabiei (De Geer), and allowed to develop infestations for up to 10 wk. Pigs were slaughtered in sequence during the experiment to sample hides and count mites through potassium hydroxide digestion. Incipient crusted lesions occurred in ears of 4 of 16 low-dose pigs and 7 of 16 high-dose pigs, averaged less than 3 cm2 in area, and contained 86% of all females and 87% of all other mite stages found on those pigs. Crusts aside, faces had the highest mite densities among six body regions in both infested groups. Overall, high-dose pigs had higher mite populations (269 compared with 39 mites on low-dose pigs), although values were not significantly different (P = 0.13). Mite populations did not grow significantly during the 10 wk, but variance increased among pigs in each dose group. A hide-sampling plan derived from these data indicates whole-body populations could be estimated by censusing only the crusts, if present. If absent, sampling mites from the face and dorsum should provide acceptable estimates of whole-body totals of females and other stages. A sample size of 13 hides from a herd will yield an estimate of mean whole-body total with a 90% CI less than or equal to 50% of the estimated mean.

Analysis of Variance↗
PubMed2005

Body mass index in elementary school children, metropolitan area food prices and food outlet density.

OBJECTIVE: The aim of this study was to examine the association between food prices and food outlet density and changes in the body mass index (BMI) among elementary school children in the USA. METHODS: The Early Childhood Longitudinal Study followed a nationally representative sample of kindergarten children over 4 years. We merged individual-level data to (a) metropolitan data on food prices and (b) per capita number of restaurants, grocery stores and convenience stores in the child's home and school zip code. The dependent variables were BMI changes over 1 and 3 years. We analysed mean changes with least-squares regression, and median changes and 85th percentile changes with quantile regression. We controlled for baseline BMI, age, real family income and sociodemographic characteristics. RESULTS: Lower real prices for vegetables and fruits were found to predict a significantly lower gain in BMI between kindergarten and third grade; half of that effect was found between kindergarten and first grade. Lower meat prices had the opposite effect, although this effect was generally smaller in magnitude and was insignificant for BMI gain over 3 years. Differences across subgroups were not statistically significant due to smaller sample sizes in subgroup analyses, but the estimated effects were meaningfully larger for children in poverty, children already at risk for overweight or overweight in kindergarten, and Asian and Hispanic children. There were no significant effects for dairy or fast-food prices, nor for outlet density, once we had controlled for individual characteristics and random intercepts to adjust standard errors for the sampling design. DISCUSSION: The geographic variation in fruit and vegetable prices is large enough to explain a meaningful amount of the differential gain in BMI among elementary school children across metropolitan areas. However, as consumption information was not available, we cannot confirm that this is the actual pathway. We found no effects of food outlet density at the neighbourhood level, possibly because availability is not an issue in metropolitan areas.

Body Mass Index↗
PubMed1999

Analysis of binary outcomes in longitudinal studies using weighted estimating equations and discrete-time survival methods: prevalence and incidence of smoking in an adolescent cohort.

Longitudinal studies are increasingly popular in epidemiology. In this tutorial we provide a detailed review of methods used by us in the analysis of a longitudinal (multiwave or panel) study of adolescent health, focusing on smoking behaviour. This example is explored in detail with the principal aim of providing an introduction to the analysis of longitudinal binary data, at a level suited to statisticians familiar with logistic regression and survival analysis but not necessarily experienced in longitudinal analysis or estimating equation methods. We describe recent advances in statistical methodology that can play a practical role in applications and are available with standard software. Our approach emphasizes the importance of stating clear research questions, and for binary outcomes we suggest these are best organized around the key epidemiological concepts of prevalence and incidence. For prevalence questions, we show how unbiased estimating equations and information-sandwich variance estimates may be used to produce a valid and robust analysis, as long as sample size is reasonably large. We also show how the estimating equation approach readily extends to accommodate adjustments for missing data and complex survey design. A detailed discussion of gender-related differences over time in our smoking outcome is used to emphasize the need for great care in separating longitudinal from cross-sectional information. We show how incidence questions may be addressed using a discrete-time version of the proportional hazards regression model. This approach has the advantages of providing estimates of relative risks, being feasible with standard software, and also allowing robust information-sandwich variance estimates.

Adolescent↗
PubMed1989

Meta-analysis of research on the effect of clinical pharmacokinetics services on therapeutic drug monitoring.

A meta-analysis of 27 published and unpublished studies of the impact of clinical pharmacokinetics services on patients' serum drug concentrations, the appropriate collection of blood samples, and the appropriate use of assay results was conducted. An individual study's effect size (ES) was determined by subtracting probits or by calculating the Bayesian estimate of pi derived from the percentages observed in the experimental and control groups. Weights based on an individual study's sample size were used to estimate the overall ES. Patients monitored by clinical pharmacokinetics services were significantly more likely to have serum drug concentrations within an acceptable therapeutic range than were patients who were not monitored. When each of the monitoring parameters was investigated individually, monitored patients were more likely to have therapeutic peak (ES = 0.51, 95% confidence interval = -0.34 to 1.36) and trough (ES = 1.15, 95% CI = -0.37 to 2.68) serum drug concentrations, to be within therapeutic range (ES = 0.91, 95% CI = 0.19 to 1.63), and to have fewer toxic peak (ES = 0.06, 95% CI = -0.53 to 0.65) and trough (ES = 0.96, 95% CI = 0.12 to 1.82) serum drug concentrations. Clinical pharmacokinetics services were also more likely to have collected blood samples appropriately (ES = 0.87, 95% CI = -0.25 to 2.00) and to have used assay results appropriately (ES = 1.21, 95% CI = -0.46 to 2.88). Clinical pharmacokinetics services appeared to have a significant influence on the proportion of patients with desirable serum drug concentrations.(ABSTRACT TRUNCATED AT 250 WORDS)

Drug Information Services↗
PubMed1995

Profile of hepatitis C virus and the possible modes of transmission of the virus in the Gizan area of Saudi Arabia: a community-based study.

The seroprevalence of antibody to hepatitis C virus (anti-HCV) and the possible modes of transmission of HCV were investigated in Gizan, southern Saudi Arabia. The sample size chosen to give an adequate estimate of the seroprevalence, about 1500, was based on the assumption that 5% of the population in Gizan were anti-HCV-positive. Sera from 1482 subjects (705 males, 777 females; aged > or = 10 years) were initially screened for anti-HCV using a commercial, ubiquitin-based enzyme immunoassay. Repeatedly reactive sera were confirmed positive using second-generation immunoassays. Serum samples were also tested by ELISA for hepatitis B surface antigen (HbsAg) and antibodies to this antigen and to the hepatitis B core antigen. Of the subjects tested, 27 (1.8%) were anti-HCV-positive. Exposure to HCV was generally similar in both sexes, age-prevalence curves for anti-HCV peaking in males aged > 49 years (6.2%) and in females aged 40-49 years (5.0%). In the youngest subjects, those aged 10-19 years, the HbsAg carrier rate was significantly higher in males (10.4%) than in females (3.6%). Exposure to the hepatitis B virus was similar in both sexes (31.0% in males v. 28.6% in females). Some 7.4% and 14.8% of the 27 anti-HCV-positive cases had histories of schistosomiasis and blood transfusion, respectively. The corresponding values for the 1455 anti-HCV-negative cases investigated, 1.1% for schistosomiasis and 3.5% for blood transfusion, were much lower. The spouses and other family members of eight anti-HCV-positive index cases were investigated but none was anti-HCV-positive.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗
PubMedDate not supplied

Evaluation of the number of laser-Doppler measurements in assessing regional diaphragmatic microcirculation.

As regional diaphragmatic microvascular blood flow varies widely, the aim in this study was to estimate the number of repeated measurements, obtained by Laser-Doppler flowmetry (LDF), required to achieve a standard level of precision. In 40 urethane-anesthetized Sprague-Dawley rats, computer-aided LDF scanning coupled with a microscope generated diaphragmatic blood flow (Qdi) ranging between 94 and 944 mV with the frequency histogram displaying non-Gaussian distributions. A sampling technique was used to assess the number of measuring sites required for valid estimates of the regional diaphragmatic microvascular flow. From a total of 1,000 Qdi values, random samples of sizes between 5 and 100 were repeatedly drawn to estimate the variability of median flow. Our data shows that the 95th percentile decreased gradually, from a +30% error at n = 5 down to +20% at n = 15-20, remained between +20 and +15% up to n = 35, and reached +10% at n = 50. Moreover, by expressing the precision level of measurements as the length of a 95% confidence interval (beta), a linear relationship between beta values obtained either by the sampling method or repeated measures analysis of variance can be shown (r = 0.902, p < 0.001); beta values by either method were within +/-20% error of the mean values at sample sizes above n = 15. It is therefore recommended that for microscope-guided LDF scanning in the assessment of the distribution of diaphragmatic microvascular blood flow, at least 15 repeated measurements should be done to reach an acceptable standard level of precision. However, facing with clinical situations where 'blind' LDF scanning inevitably includes measurements over large vessels, the minimal sample sizes required to represent tissue perfusion demand further exploration.

Analysis of Variance↗
PubMed1998

Transvaginal versus transperineal ultrasonography: a blinded comparison in the assessment of cervical length at midgestation.

OBJECTIVE: The study's objective was to determine the correlation and agreement between transperineal ultrasonography and transvaginal ultrasonography in the assessment of cervical length in gravid patients. STUDY DESIGN: After a pilot, unblinded series of transperineal and transvaginal cervical length measurements in 200 gravid patients, 206 study patients between 14 and 34 weeks' gestation with intact membranes and cervical dilatation of < or = 2 cm underwent transperineal and transvaginal cervical length assessment under a blinded, 2-sonographer protocol. The Pearson correlation coefficient, Lin concordance coefficient, and Bland-Altman plot were used. Acceptable concordance was defined as > 0.82, with an acceptable correlation of > 0.9 and an acceptable difference between the means of < 3 mm. The power of the study to detect this degree of concordance was estimated to be 95% at this sample size. RESULTS: Paired ultrasonographic measurements were obtained for all 206 study patients. Transperineal mean cervical length was 35 +/- 8.6 mm. Transvaginal mean cervical length was 35.9 +/- 8.8 mm. The Pearson correlation coefficient was 0.959, and the Lin concordance coefficient was 0.955, with a 95% confidence lower bound of 0.949. Close agreement between transperineal and transvaginal measurements was observed across the full range of cervical lengths (1-5 cm). The estimated difference between the paired means was 1 mm. The 95% tolerance interval for any given paired observation (Transperineal length - Transvaginal length) was -5.7 to +4 mm. CONCLUSIONS: Cervical length measured by transperineal ultrasonography demonstrates close correlation and agreement with transvaginal measurements. With sonographer experience and optimal technique, approximately 95% of transperineal cervical length observations can be expected to be within 5 mm of a given paired transvaginal measurement. Transperineal ultrasonography may be a preferred method of cervical length assessment for situations in which vaginal placement of instruments should be minimized.

Cervix Uteri↗
PubMed1978

The use of regression constants in estimating tooth size in a Negro population.

A study of a sample of 105 Negro children and adolescents, residents of Connecticut, was undertaken to determine the degree of correlation between mandibular tooth size and the size of the canines and premolars. The correlation between the total mesiodistal width of the mandibular permanent incisors and that of the maxillary or mandibular canine and first and second premolars was found to be 0.63 and 0.71, respectively. Further, regression constants were determined in an attempt to estimate the buccal segments from the mandibular incisors.

Adolescent↗
PubMed2004

Heterozygote excess in small populations and the heterozygote-excess effective population size.

It has been proposed that effective size could be estimated in small dioecious population by considering the heterozygote excess observed at neutral markers. When the number of breeders is small, allelic frequencies in males and females will slightly differ due to binomial sampling error. However, this excess of heterozygotes is not generated by dioecy but by the absence of individuals produced through selfing. Consequently, the approach can also be applied to self-incompatible monoecious species. Some inaccuracies in earlier equations expressing effective size as function of the heterozygote excess are also corrected in this paper. The approach is then extended to subdivided populations, where time of sampling becomes crucial. When adults are sampled, the effective size of the entire population can be estimated, whereas when juveniles are sampled, the average effective number of breeders per subpopulations can be estimated. The main limitation of the heterozygote excess method is that it will only perform satisfactorily for populations with a small number of reproducing individuals. While this situation is unlikely to happen frequently at the scale of the entire population, structured populations with small subpopulations are likely to be common. The estimation of the average number of breeders per subpopulations is thus expected to be applicable to many natural populations. The approach is straightforward to compute and independent of equilibrium assumptions. Applications to simulated data suggest the estimation of the number of breeders to be robust to mutation and migration rates, and to specificities of the mating system.

Biological Evolution↗