Simple nomograms to calculate sample size in diagnostic studies

Objectives: To produce an easily understood and accessible tool for use by researchers in diagnostic studies. Diagnostic studies should have sample size calculations performed, but in practice, they are performed infrequently. This may be due to a reluctance on the part of researchers to use mathematical formulae.

Methods: Using a spreadsheet, we derived nomograms for calculating the number of patients required to determine the precision of a test's sensitivity or specificity.

Results: The nomograms could be easily used to determine the sensitivity and specificity of a test.

Conclusions: In addition to being easy to use, the nomogram allows deduction of a missing parameter (number of patients, confidence intervals, prevalence, or sensitivity/specificity) if the other three are known. The nomogram can also be used retrospectively by the reader of published research as a rough estimating tool for sample size calculations.

     

Power and sample size calculation for neuroimaging studies by non-central random field theory

Determining power and sample size in neuroimaging studies is a challenging task because of the massive multiple comparisons among tens of thousands of correlated voxels. To facilitate this task, we propose a power analysis method based on random field theory (RFT) by modeling signal areas within images as non-central random field. With this framework, power can be calculated for specific areas of anticipated signals within the brain while accounting for the 3D nature of signals. This framework can also be extended to visualize local variability in sensitivity as a power map and a sample size map. We validated our non-central RFT framework based on Monte-Carlo simulations. Moreover, we applied our method to a blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) data set with a small sample size in order to demonstrate its use in study planning. From the simulations, we found that our method was able to estimate power quite accurately. In the fMRI data analysis, despite the small sample size, we were able to determine power and the number of subjects required to detect signals.     

Uniform power method for sample size calculation in historical control studies with binary response

Makuch and Simon gave a sample size calculation formula for historical control (HC) studies that assumed that the observed response rate in the control group is the true response rate. We dropped this assumption and computed the expected power and expected sample size to evaluate the performance of the procedure under the omniscient model. When there is uncertainty in the HC response rate but this uncertainty is not considered, Makuch and Simon's method produces a sample size that gives a considerably lower power than that specified. Even the larger sample size obtained from the randomized design formula and applied to the HC setting does not guarantee the advertised power in the HC setting. We developed a new uniform power method to search for the sample size required for the experimental group to yield an exact power without relying on the estimated HC response rate being perfectly correct. The new method produces the correct uniform predictive power for all permissible response rates. The resulting sample size is closer to the sample size needed for the randomized design than Makuch and Simon's method, especially when there is a small difference in response rates or a limited sample size in the HC group. HC design may be a viable option in clinical trials when the patient selection bias and the outcome evaluation bias can be minimized. However, the common perception of the extra sample size savings is largely unjustified without the strong assumption that the observed HC response rate is equal to the true control response rate. Generally speaking, results from HC studies need to be confirmed by studies with concurrent controls and cannot be used for making definitive decisions.     

Aspects of sample size determination and power calculation illustrated on examples from rehabilitation research

Often it is reported in medical studies that an expected effect could not be detected. This may be the case if the sample size had been too small to detect an effect which actually exists. This often is due to the fact that sound sample size estimation had been omitted prior to the study outset. As a result, it is not known how many persons should have been involved in the study to detect this effect if present. On the other hand, if sample size estimation has not been realized, more persons than needed might be included in the study. This is problematic for economic and in particular for ethical reasons. The aim of this paper is to point out the principles of sample size estimation as well as to emphasize its importance not only in general but also in medical rehabilitation research.     

Statistical power and sample size estimation for headache research: an overview and power calculation tools

The present article reviews the concept of statistical power analysis for research designs in headache. First, we present a basic overview of the concepts of statistical hypothesis testing. Then we discuss the elements of power analysis and, where appropriate, we address conventions for power calculations. We offer, for public use, an applied power calculator for two applications that are often encountered in headache research. We intend to help headache researchers design trials with adequate statistical power by offering a conceptual overview and the power calculators. In closing, we briefly address the implications of the present trend toward reporting point estimates of effect sizes with confidence levels.     

Design, statistical analysis and sample size calculation of dose response study of telmisartan and hydrochlorothiazide

Many patients with hypertension take some antihypertensive drugs with complementary mechanisms of action to lower their blood pressure and achieve the therapeutic goals reducing the risk of cardiovascular events. Telmisartan, angiotensin II receptor blocker, and hydrochlorothiazide, diuretic are two antihypertensive drugs that have a well-recognized clinical efficacy. Their combination is expected to be one of the most appropriate therapies for hypertensive patients. However there is no information to show the effective dose combination of two drugs for the Japanese patients with mild to moderate hypertension. Therefore, the prospective, randomized, double-blinded study was planed for showing the dose response surface of two components. The 3 by 3 factorial design was applied for this purpose and the approach for calculating sample size was proposed. This study was registered with ClinicalTrial.gov (NCT00153049).     

The large sample size fallacy

Scand J Caring Sci; 2013; 27; 487–492 The large sample size fallacy Background: Significance in the statistical sense has little to do with significance in the common practical sense. Statistical significance is a necessary but not a sufficient condition for practical significance. Hence, results that are extremely statistically significant may be highly nonsignificant in practice. The degree of practical significance is generally determined by the size of the observed effect, not the p‐value. The results of studies based on large samples are often characterized by extreme statistical significance despite small or even trivial effect sizes. Interpreting such results as significant in practice without further analysis is referred to as the large sample size fallacy in this article. Aim: The aim of this article is to explore the relevance of the large sample size fallacy in contemporary nursing research. Results: Relatively few nursing articles display explicit measures of observed effect sizes or include a qualitative discussion of observed effect sizes. Statistical significance is often treated as an end in itself. Conclusion: Effect sizes should generally be calculated and presented along with p‐values for statistically significant results, and observed effect sizes should be discussed qualitatively through direct and explicit comparisons with the effects in related literature.     

Variability of carotid artery measurements on 3-Tesla MRI and its impact on sample size calculation for clinical research

Carotid MRI measurements are increasingly being employed in research studies for atherosclerosis imaging. The majority of carotid imaging studies use 1.5 T MRI. Our objective was to investigate intra-observer and inter-observer variability in carotid measurements using high resolution 3 T MRI. We performed 3 T carotid MRI on 10 patients (age 56 ± 8 years, 7 male) with atherosclerosis risk factors and ultrasound intima-media thickness ≥0.6 mm. A total of 20 transverse images of both right and left carotid arteries were acquired using T2 weighted black-blood sequence. The lumen and outer wall of the common carotid and internal carotid arteries were manually traced; vessel wall area, vessel wall volume, and average wall thickness measurements were then assessed for intra-observer and inter-observer variability. Pearson and intraclass correlations were used in these assessments, along with Bland-Altman plots. For inter-observer variability, Pearson correlations ranged from 0.936 to 0.996 and intraclass correlations from 0.927 to 0.991. For intra-observer variability, Pearson correlations ranged from 0.934 to 0.954 and intraclass correlations from 0.831 to 0.948. Calculations showed that inter-observer variability and other sources of error would inflate sample size requirements for a clinical trial by no more than 7.9%, indicating that 3 T MRI is nearly optimal in this respect. In patients with subclinical atherosclerosis, 3 T carotid MRI measurements are highly reproducible and have important implications for clinical trial design.     

Bayesian sample size determination under hypothesis tests

We develop a Bayesian approach for calculating sample sizes for clinical trials under the framework of hypothesis tests. We extend the work of Weiss (The Statistician 1997; 46: 185-191) to include composite distributions for the treatment effect and the variance of the data within the null and alternative hypotheses. We select sample sizes using the Bayes factor and the averaged type I error and type II error defined by Weiss (The Statistician 1997; 46: 185-191). Our approach allows the uncertainty inherent in eliciting prior information for both the treatment effect and the variance and permits informative prior information for unknown quantities through the hypothesis specification. We illustrate our method through a real data example from a clinical trial for treatment of multiple sclerosis and from the cerclage trial for preterm birth prevention in high-risk women.     

Statistics review 4: sample size calculations

The present review introduces the notion of statistical power and the hazard of under-powered studies. The problem of how to calculate an ideal sample size is also discussed within the context of factors that affect power, and specific methods for the calculation of sample size are presented for two common scenarios, along with extensions to the simplest case.     

Estimating sample size in critical care clinical trials

Estimating the required sample size for a study is necessary during the design phase to ensure that it will have maximal efficiency to answer the primary question of interest. Clinicians require a basic understanding of the principles underlying sample size calculation to interpret and apply research findings. This article reviews the critical components of sample size calculation, including the selection of a primary outcome, specification of the acceptable types I and II error rates, identification of the minimal clinically important difference, and estimation of the error associated with measuring the primary outcome. The relationship among confidence intervals, precision, and study power is also discussed.     

Economics in sample size determination for clinical trials

In the design of clinical trials, sample size determinationis usually undertaken by statisticians and clinicians. It israre for health economists to be involved in this aspect oftrial design. However, there are a number of outcome changesthat are of ‘economic significance’, and it is importantfor trial designers and funders to be aware of these beforeplanning, funding and mounting a trial. In this paper we demonstratethrough the use of three examples (prevention of osteoporosis,management of infertility, and endometriosis) how economicscan be used to influence the size of a clinical trial. Trialsthat are too small or too large waste research resources; healtheconomics can lead to more efficient trial designs.     

护理研究中量性研究的样本量估计

护理研究中没有绝对的样本量标准,不同的研究方法、目的、要求和资料决定了样本量~([1]).若样本含量过小,所得的指标不稳定、检验效能太低、结论缺乏充分依据,就难以获得正确的研究结果;若样本含量过大,会增加临床研究的困难,难以严格控制条件,就会造成不必要的人力、物力、时间和经济上的浪费.     

Considerations in determining sample size for pilot studies

There is little published guidance concerning how large a pilot study should be. General guidelines, for example using 10% of the sample required for a full study, may be inadequate for aims such as assessment of the adequacy of instrumentation or providing statistical estimates for a larger study. This article illustrates how confidence intervals constructed around a desired or anticipated value can help determine the sample size needed. Samples ranging in size from 10 to 40 per group are evaluated for their adequacy in providing estimates precise enough to meet a variety of possible aims. General sample size guidelines by type of aim are offered.     

An introduction to power and sample size estimation

The importance of power and sample size estimation for study design and analysis.     

Practical midcourse sample size modification in clinical trials

Power calculations are very important in the planning of a well-designed clinical trial. Sometimes there is limited information available before the trial, making it highly desirable to adjust the sample size after seeing actual trial data. Indeed, there has been a recent proliferation of papers promising great flexibility in midcourse correction of sample size and other design features, such as choice of primary endpoint. We point out the difficulty in accurately estimating the treatment effect midway through a trial, and we encourage the use of a simple, conservative approach whereby sample size can be increased but not decreased from what was originally planned. We show how to compute the p value and confidence interval for this two-stage procedure. If the original sample size is maintained, analysis of the data is the same as for a fixed sample procedure.