Design characteristic of randomised controlled trials for geographic atrophy in age-related macular degeneration: selection of outcomes and sample size calculation

PurposeThe selection of suitable outcomes and sample size calculation are critical factors in the design of a randomised controlled trial (RCT). The goal of this study was to identify the range of outcomes and information on sample size calculation in RCTs on geographic atrophy (GA).MethodsWe carried out a systematic review of age-related macular degeneration (AMD) RCTs. We searched MEDLINE, EMBASE, Scopus, Cochrane Library, www.controlled-trials.com, and www.ClinicalTrials.gov. Two independent reviewers screened records. One reviewer collected data and the second reviewer appraised 10% of collected data. We scanned references lists of selected papers to include other relevant RCTs.ResultsLiterature and registry search identified 3816 abstracts of journal articles and 493 records from trial registries. From a total of 177 RCTs on all types of AMD, 23 RCTs on GA were included. Eighty-one clinical outcomes were identified. Visual acuity (VA) was the most frequently used outcome, presented in 18 out of 23 RCTs and followed by the measures of lesion area. For sample size analysis, 8 GA RCTs were included. None of them provided sufficient Information on sample size calculations.ConclusionsThis systematic review illustrates a lack of standardisation in terms of outcome reporting in GA trials and issues regarding sample size calculation. These limitations significantly hamper attempts to compare outcomes across studies and also perform meta-analyses.

Use of sample size calculation in scientific research in Brazilian Physical Education journals

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

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 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.

Statistical power calculation and sample size determination for environmental studies with data below detection limits

Power calculation and sample size determination are critical in designing environmental monitoring programs. The traditional approach based on comparing the mean values may become statistically inappropriate and even invalid when substantial proportions of the response values are below the detection limits or censored because strong distributional assumptions have to be made on the censored observations when implementing the traditional procedures. In this paper, we propose a quantile methodology that is robust to outliers and can also handle data with a substantial proportion of below-detection-limit observations without the need of imputing the censored values. As a demonstration, we applied the methods to a nutrient monitoring project, which is a part of the Perth Long-Term Ocean Outlet Monitoring Program. In this example, the sample size required by our quantile methodology is, in fact, smaller than that by the traditional t-test, illustrating the merit of our method.

Calculation of sample size for stroke trials assessing functional outcome: comparison of binary and ordinal approaches

Background Many acute stroke trials have given neutral results. Sub-optimal statistical analyses may be failing to detect efficacy. Methods which take account of the ordinal nature of functional outcome data are more efficient. We compare sample size calculations for dichotomous and ordinal outcomes for use in stroke trials. Methods Data from stroke trials studying the effects of interventions known to positively or negatively alter functional outcome – Rankin Scale and Barthel Index – were assessed. Sample size was calculated using comparisons of proportions, means, medians (according to Payne), and ordinal data (according to Whitehead). The sample sizes gained from each method were compared using Friedman 2 way ANOVA. Results Fifty-five comparisons (54 173 patients) of active vs. control treatment were assessed. Estimated sample sizes differed significantly depending on the method of calculation (Po00001). The ordering of the methods showed that the ordinal method of Whitehead and comparison of means produced significantly lower sample sizes than the other methods. The ordinal data method on average reduced sample size by 28% (inter-quartile range 14–53%) compared with the comparison of proportions; however, a 22% increase in sample size was seen with the ordinal method for trials assessing thrombolysis. The comparison of medians method of Payne gave the largest sample sizes. Conclusions Choosing an ordinal rather than binary method of analysis allows most trials to be, on average, smaller by approximately 28% for a given statistical power. Smaller trial sample sizes may help by reducing time to completion, complexity, and financial expense. However, ordinal methods may not be optimal for interventions which both improve functional outcome

Sample size in studies on diagnostic accuracy in ophthalmology:A literature survey

Aim: To assess the sample sizes used in studies on diagnostic accuracy in ophthalmology. Design and sources: A survey literature published in 2005. Methods: The frequency of reporting calculations of sample sizes and the samples' sizes were extracted from the published literature. A manual search of five leading clinical journals in ophthalmology with the highest impact (Investigative Ophthalmology and Visual Science, Ophthalmology, Archives of Ophthalmology, American Journal of Ophthalmology and British Journal of Ophthalmology) was conducted by two independent investigators. Results: A total of 1698 articles were identified, of which 40 studies were on diagnostic accuracy. One study reported that sample size was calculated before initiating the study. Another study reported consideration of sample size without calculation. The mean (SD) sample size of all diagnostic studies was 172.6 (218.9). The median prevalence of the target condition was 50.5%. Conclusion: Only a few studies consider sample size in their methods. Inadequate sample sizes in diagnostic accuracy studies may result in misleading estimates of test accuracy. An improvement over the current standards on the design and reporting of diagnostic studies is warranted.

Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Statnote 8: statistical power and sample size

Statistical software is now commonly available to calculate Power (P') and sample size (N) for most experimental designs. In many circumstances, however, sample size is constrained by lack of time, cost, and in research involving human subjects, the problems of recruiting suitable individuals. In addition, the calculation of N is often based on erroneous assumptions about variability and therefore such estimates are often inaccurate. At best, we would suggest that such calculations provide only a very rough guide of how to proceed in an experiment. Nevertheless, calculation of P' is very useful especially in experiments that have failed to detect a difference which the experimenter thought was present. We would recommend that P' should always be calculated in these circumstances to determine whether the experiment was actually too small to test null hypotheses adequately.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

Optimal image sample size for corneal nerve morphometry

Purpose Arbitrary numbers of corneal confocal microscopy images have been used for analysis of corneal subbasal nerve parameters under the implicit assumption that these are a representative sample of the central corneal nerve plexus. The purpose of this study is to present a technique for quantifying the number of random central corneal images required to achieve an acceptable level of accuracy in the measurement of corneal nerve fiber length and branch density. Methods Every possible combination of 2 to 16 images (where 16 was deemed the true mean) of the central corneal subbasal nerve plexus, not overlapping by more than 20%, were assessed for nerve fiber length and branch density in 20 subjects with type 2 diabetes and varying degrees of functional nerve deficit. Mean ratios were calculated to allow comparisons between and within subjects. Results In assessing nerve branch density, eight randomly chosen images not overlapping by more than 20% produced an average that was within 30% of the true mean 95% of the time. A similar sampling strategy of five images was 13% within the true mean 80% of the time for corneal nerve fiber length. Conclusions The “sample combination analysis” presented here can be used to determine the sample size required for a desired level of accuracy of quantification of corneal subbasal nerve parameters. This technique may have applications in other biological sampling studies.

Sample size considerations and augmentation of computer experiments

Computer Experiments, consisting of a number of runs of a computer model with different inputs, are now common-place in scientific research. Using a simple fire model for illustration some guidelines are given for the size of a computer experiment. A graph is provided relating the error of prediction to the sample size which should be of use when designing computer experiments. Methods for augmenting computer experiments with extra runs are also described and illustrated. The simplest method involves adding one point at a time choosing that point with the maximum prediction variance. Another method that appears to work well is to choose points from a candidate set with maximum determinant of the variance covariance matrix of predictions.