Sample size estimation: an overview with applications to orthodontic clinical trial designs

Proper sample size estimation is an important part of clinical trial methodology and closely related to the precision and power of the trial's results. Trials with sufficient sample sizes are scientifically and ethically justified and more credible compared with trials with insufficient sizes. Planning clinical trials with inadequate sample sizes might be considered as a waste of time and resources, as well as unethical, since patients might be enrolled in a study in which the expected results will not be trusted and are unlikely to have an impact on clinical practice. Because of the low emphasis of sample size calculation in clinical trials in orthodontics, it is the objective of this article to introduce the orthodontic clinician to the importance and the general principles of sample size calculations for randomized controlled trials to serve as guidance for study designs and as a tool for quality assessment when reviewing published clinical trials in our specialty. Examples of calculations are shown for 2-arm parallel trials applicable to orthodontics. The working examples are analyzed, and the implications of design or inherent complexities in each category are discussed.

Sample size in orthodontic randomized controlled trials: are numbers justified?

Sample size calculations are advocated by the Consolidated Standards of Reporting Trials (CONSORT) group to justify sample sizes in randomized controlled trials (RCTs). This study aimed to analyse the reporting of sample size calculations in trials published as RCTs in orthodontic speciality journals. The performance of sample size calculations was assessed and calculations verified where possible. Related aspects, including number of authors; parallel, split-mouth, or other design; single- or multi-centre study; region of publication; type of data analysis (intention-to-treat or per-protocol basis); and number of participants recruited and lost to follow-up, were considered. Of 139 RCTs identified, complete sample size calculations were reported in 41 studies (29.5 per cent). Parallel designs were typically adopted (n = 113; 81 per cent), with 80 per cent (n = 111) involving two arms and 16 per cent having three arms. Data analysis was conducted on an intention-to-treat (ITT) basis in a small minority of studies (n = 18; 13 per cent). According to the calculations presented, overall, a median of 46 participants were required to demonstrate sufficient power to highlight meaningful differences (typically at a power of 80 per cent). The median number of participants recruited was 60, with a median of 4 participants being lost to follow-up. Our finding indicates good agreement between projected numbers required and those verified (median discrepancy: 5.3 per cent), although only a minority of trials (29.5 per cent) could be examined. Although sample size calculations are often reported in trials published as RCTs in orthodontic speciality journals, presentation is suboptimal and in need of significant improvement.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Iodine-129: Sample preparation, quality control and analyses of pre-nuclear materials and of natural waters from Lower Saxony, Germany

Sample preparation procedures for AMS measurements of 129I and 127I in environmental materials and some methodological aspects of quality assurance are discussed. Measurements from analyses of some pre-nuclear soil and thyroid gland samples and of a systematic investigation of natural waters in Lower Saxony, Germany, are described. Although the up-to-now lowest 129I/127I ratios in soils and thyroid glands were observed, they are still suspect to contamination since they are significantly higher than the pre-nuclear equilibrium ratio in the marine hydrosphere. A survey on all available 129I/127I isotopic ratios in precipitation shows a dramatic increase until the middle of the 1980s and a stabilization since 1987 at high isotopic ratios of about (3.6–8.3)×10−7. In surface waters, ratios of (57–380)×10−10 are measured while shallow ground waters show with ratios of (1.3–200)×10−10 significantly lower values with a much larger spread. The data for 129I in soils and in precipitation are used to estimate pre-nuclear and modern 129I deposition densities.

Role of hepatitis C virus genotype 3 in liver fibrosis progression - a systematic review and meta-analysis

The progression of liver fibrosis in chronic hepatitis C has long been considered to be independent from viral genotypes. However, recent studies suggest an association between Hepatitis C virus (HCV) genotype 3 and accelerated liver disease progression. We completed a systematic review and meta-analysis of studies evaluating the association between HCV genotypes and fibrosis progression. PubMed, Embase and ISI Web of Knowledge databases were searched for cohort, cross-sectional and case-control studies on treatment-naïve HCV-infected adults in which liver fibrosis progression rate (FPR) was assessed by the ratio of fibrosis stage in one single biopsy to the duration of infection (single-biopsy studies) or from the change in fibrosis stage between two biopsies (paired biopsies studies). A random effect model was used to derive FPR among different HCV genotypes. Eight single-biopsy studies (3182 patients, mean/median duration of infection ranging from 9 to 21 years) and eight paired biopsies studies (mean interval between biopsies 2-12 years) met the selection criteria. The odds ratio for the association of genotype 3 with accelerated fibrosis progression was 1.52 (95% CI 1.12-2.07, P = 0.007) in single-biopsy studies and 1.37 (95% CI 0.87-2.17, P = 0.17) in paired biopsy studies. In conclusion, viral genotype 3 was associated with faster fibrosis progression in single-biopsy studies. This observation may have important consequences on the clinical management of genotype 3-infected patients. The association was not significant in paired biopsies studies, although the latter may be limited by important indication bias, short observation time and small sample size.

Effective population size of an indigenous Swiss cattle breed estimated from linkage disequilibrium

Effective population size is an important parameter for the assessment of genetic diversity within a livestock population and its development over time. If pedigree information is not available, linkage disequilibrium (LD) analysis might offer an alternative perspective for the estimation of effective population size. In this study, 128 individuals of the Swiss Eringer breed were genotyped using the Illumina BovineSNP50 beadchip. We set bin size at 50 kb for LD analysis, assuming that LD for proximal single nucleotide polymorphism (SNP)-pairs reflects distant breeding history while LD from distal SNP-pairs would reflect near history. Recombination rates varied among different regions of the genome. The use of physical distances as an approximation of genetic distances (e.g. setting 1 Mb = 0.01 Morgan) led to an upward bias in LD-based estimates of effective population size for generations beyond 50, while estimates for recent history were unaffected. Correction for restricted sample size did not substantially affect these results. LD-based actual effective population size was estimated in the range of 87-149, whereas pedigree-based effective population size resulted in 321 individuals. For conservation purposes, requiring knowledge of recent history (<50 generations), approximation assuming constant recombination rate seemed adequate.

Are sample sizes clear and justified in RCTs published in dental journals?

Sample size calculations are advocated by the CONSORT group to justify sample sizes in randomized controlled trials (RCTs). The aim of this study was primarily to evaluate the reporting of sample size calculations, to establish the accuracy of these calculations in dental RCTs and to explore potential predictors associated with adequate reporting. Electronic searching was undertaken in eight leading specific and general dental journals. Replication of sample size calculations was undertaken where possible. Assumed variances or odds for control and intervention groups were also compared against those observed. The relationship between parameters including journal type, number of authors, trial design, involvement of methodologist, single-/multi-center study and region and year of publication, and the accuracy of sample size reporting was assessed using univariable and multivariable logistic regression. Of 413 RCTs identified, sufficient information to allow replication of sample size calculations was provided in only 121 studies (29.3%). Recalculations demonstrated an overall median overestimation of sample size of 15.2% after provisions for losses to follow-up. There was evidence that journal, methodologist involvement (OR = 1.97, CI: 1.10, 3.53), multi-center settings (OR = 1.86, CI: 1.01, 3.43) and time since publication (OR = 1.24, CI: 1.12, 1.38) were significant predictors of adequate description of sample size assumptions. Among journals JCP had the highest odds of adequately reporting sufficient data to permit sample size recalculation, followed by AJODO and JDR, with 61% (OR = 0.39, CI: 0.19, 0.80) and 66% (OR = 0.34, CI: 0.15, 0.75) lower odds, respectively. Both assumed variances and odds were found to underestimate the observed values. Presentation of sample size calculations in the dental literature is suboptimal; incorrect assumptions may have a bearing on the power of RCTs.

Small study effects in meta-analyses of osteoarthritis trials: meta-epidemiological study

Objective To examine the presence and extent of small study effects in clinical osteoarthritis research. Design Meta-epidemiological study. Data sources 13 meta-analyses including 153 randomised trials (41 605 patients) that compared therapeutic interventions with placebo or non-intervention control in patients with osteoarthritis of the hip or knee and used patients’ reported pain as an outcome. Methods We compared estimated benefits of treatment between large trials (at least 100 patients per arm) and small trials, explored funnel plots supplemented with lines of predicted effects and contours of significance, and used three approaches to estimate treatment effects: meta-analyses including all trials irrespective of sample size, meta-analyses restricted to large trials, and treatment effects predicted for large trials. Results On average, treatment effects were more beneficial in small than in large trials (difference in effect sizes −0.21, 95% confidence interval −0.34 to −0.08, P=0.001). Depending on criteria used, six to eight funnel plots indicated small study effects. In six of 13 meta-analyses, the overall pooled estimate suggested a clinically relevant, significant benefit of treatment, whereas analyses restricted to large trials and predicted effects in large trials yielded smaller non-significant estimates. Conclusions Small study effects can often distort results of meta-analyses. The influence of small trials on estimated treatment effects should be routinely assessed.

Sample sizes of studies on diagnostic accuracy: literature survey

OBJECTIVES: To determine sample sizes in studies on diagnostic accuracy and the proportion of studies that report calculations of sample size. DESIGN: Literature survey. DATA SOURCES: All issues of eight leading journals published in 2002. METHODS: Sample sizes, number of subgroup analyses, and how often studies reported calculations of sample size were extracted. RESULTS: 43 of 8999 articles were non-screening studies on diagnostic accuracy. The median sample size was 118 (interquartile range 71-350) and the median prevalence of the target condition was 43% (27-61%). The median number of patients with the target condition--needed to calculate a test's sensitivity--was 49 (28-91). The median number of patients without the target condition--needed to determine a test's specificity--was 76 (27-209). Two of the 43 studies (5%) reported a priori calculations of sample size. Twenty articles (47%) reported results for patient subgroups. The number of subgroups ranged from two to 19 (median four). No studies reported that sample size was calculated on the basis of preplanned analyses of subgroups. CONCLUSION: Few studies on diagnostic accuracy report considerations of sample size. The number of participants in most studies on diagnostic accuracy is probably too small to analyse variability of measures of accuracy across patient subgroups.

Magnetic resonance imaging features of orbital inflammation with intracranial extension in four dogs

This retrospective study describes the clinical and magnetic resonance (MR) imaging features of chronic orbital inflammation with intracranial extension in four dogs (two Dachshunds, one Labrador, one Swiss Mountain). Intracranial extension was observed through the optic canal (n=1), the orbital fissure (n=4), and the alar canal (n=1). On T1-weighted images structures within the affected skull foramina could not be clearly differentiated, but were all collectively isointense to hypointense compared with the contralateral, unaffected side, or compared with gray matter. On T2-, short tau inversion recovery (STIR)-, or fluid-attenuated inversion recovery (FLAIR)-weighted images structures within the affected skull foramina appeared hyperintense compared with gray matter, and extended with increased signal into the rostral cranial fossa (n=1) and middle cranial fossa (n=4). Contrast enhancement at the level of the affected skul foramina as well as at the skull base in continuity with the orbital fissure was observed in all patients. Brain edema or definite meningeal enhancement could not be observed, but a close anatomic relationship of the abnormal tissue to the cavernous sinus was seen in two patients. Diagnosis was confirmed in three dogs (one cytology, two biopsy, one necropsy) and was presumptive in one based on clinical improvement after treatment. This study is limited by its small sample size, but provides evidence for a potential risk of intracranial extension of chronic orbital inflammation. This condition can be identified best by abnormal signal increase at the orbital fissure on transverse T2-weighted images, on dorsal STIR images, or on postcontrast transverse or dorsal images.