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.

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.

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.

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.

Contextualizing local-scale point sample data using global-scale spatial datasets: Lessons learnt from the analysis of large-scale land acquisitions

This paper examines how the geospatial accuracy of samples and sample size influence conclusions from geospatial analyses. It does so using the example of a study investigating the global phenomenon of large-scale land acquisitions and the socio-ecological characteristics of the areas they target. First, we analysed land deal datasets of varying geospatial accuracy and varying sizes and compared the results in terms of land cover, population density, and two indicators for agricultural potential: yield gap and availability of uncultivated land that is suitable for rainfed agriculture. We found that an increase in geospatial accuracy led to a substantial and greater change in conclusions about the land cover types targeted than an increase in sample size, suggesting that using a sample of higher geospatial accuracy does more to improve results than using a larger sample. The same finding emerged for population density, yield gap, and the availability of uncultivated land suitable for rainfed agriculture. Furthermore, the statistical median proved to be more consistent than the mean when comparing the descriptive statistics for datasets of different geospatial accuracy. Second, we analysed effects of geospatial accuracy on estimations regarding the potential for advancing agricultural development in target contexts. Our results show that the target contexts of the majority of land deals in our sample whose geolocation is known with a high level of accuracy contain smaller amounts of suitable, but uncultivated land than regional- and national-scale averages suggest. Consequently, the more target contexts vary within a country, the more detailed the spatial scale of analysis has to be in order to draw meaningful conclusions about the phenomena under investigation. We therefore advise against using national-scale statistics to approximate or characterize phenomena that have a local-scale impact, particularly if key indicators vary widely within a country.

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.

Does land-based exercise reduce pain and disability associated with hip osteoarthritis? A meta-analysis of randomized controlled trials

Objective To determine if clinical guidelines recommending therapeutic exercise for people with hip osteoarthritis (OA) are supported by rigorous scientific evidence. Methods A meta-analysis of randomized controlled trials (RCTs) recruiting people with hip OA and comparing some form of land-based exercise program (as opposed to exercises conducted in the water) with a non-exercise group in terms of hip pain and/or self-reported physical function. Results Thirty-two RCTs were identified, but only five met the inclusion criteria. Only one of the five included RCTs restricted recruitment to people with hip OA, the other four RCTs also recruiting participants with knee OA. The five included studies provided data on 204 and 187 hip OA participants for pain and physical function, respectively. Combining the results of the five included RCTs using a fixed-effects model demonstrated a small treatment effect for pain (standardized mean difference (SMD) −0.38; 95% confidence interval (CI) −0.67 to −0.09). No significant benefit in terms of improved self-reported physical function was detected (SMD −0.02; 95% CI −0.31 to 0.28). Conclusion Currently there is only silver level evidence (one small RCT) supporting the benefit of land-based therapeutic exercise for people with symptomatic hip OA in terms of reduced pain and improved physical function. The limited number and small sample size of the included RCTs restricts the confidence that can be attributed to these results.

Reporting of research quality characteristics of studies published in 6 major clinical dental specialty journals

The objective of this article was to record reporting characteristics related to study quality of research published in major specialty dental journals with the highest impact factor (Journal of Endodontics, Journal of Oral and Maxillofacial Surgery, American Journal of Orthodontics and Dentofacial Orthopedics; Pediatric Dentistry, Journal of Clinical Periodontology, and International Journal of Prosthetic Dentistry). The included articles were classified into the following 3 broad subject categories: (1) cross-sectional (snap-shot), (2) observational, and (3) interventional. Multinomial logistic regression was conducted for effect estimation using the journal as the response and randomization, sample calculation, confounding discussed, multivariate analysis, effect measurement, and confidence intervals as the explanatory variables. The results showed that cross-sectional studies were the dominant design (55%), whereas observational investigations accounted for 13%, and interventions/clinical trials for 32%. Reporting on quality characteristics was low for all variables: random allocation (15%), sample size calculation (7%), confounding issues/possible confounders (38%), effect measurements (16%), and multivariate analysis (21%). Eighty-four percent of the published articles reported a statistically significant main finding and only 13% presented confidence intervals. The Journal of Clinical Periodontology showed the highest probability of including quality characteristics in reporting results among all dental journals.