Statistical methodology: I. Incorporating the prevalence of disease into the sample size calculation for sensitivity and specificity

Bayesian Sample Size Determination for Prevalence and Diagnostic Test Studies in the Absence of a Gold Standard Test

Planning studies involving diagnostic tests is complicated by the fact that virtually no test provides perfectly accurate results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be taken into account, whether the primary goal of the study is to estimate the prevalence of a disease in a population or to investigate the properties of a new diagnostic test. Previous work on sample size requirements for estimating the prevalence of disease in the case of a single imperfect test showed very large discrepancies in size when compared to methods that assume a perfect test. In this article we extend these methods to include two conditionally independent imperfect tests, and apply several different criteria for Bayesian sample size determination to the design of such studies. We consider both disease prevalence studies and studies designed to estimate the sensitivity and specificity of diagnostic tests. As the problem is typically nonidentifiable, we investigate the limits on the accuracy of parameter estimation as the sample size approaches infinity. Through two examples from infectious diseases, we illustrate the changes in sample sizes that arise when two tests are applied to individuals in a study rather than a single test. Although smaller sample sizes are often found in the two-test situation, they can still be prohibitively large unless accurate information is available about the sensitivities and specificities of the tests being used.

Cardiac troponin i as a predictor of respiratory failure in children hospitalized with respiratory syncytial virus (RSV) infections: a pilot study

This pilot study was performed to assess the use of cardiac troponin I to predict respiratory failure in children admitted to the hospital with respiratory syncytial virus (RSV) infections. We enrolled a prospective convenience sample of children under 5 years of age who were admitted to our university-based, tertiary care children's hospital from December 1, 2000, to February 1, 2002, with RSV infections. A cardiac troponin I was drawn at admission. We assessed the test characteristics for positive cardiac troponin I (defined as >0.3 ng/mL, the manufacturer's upper limit of normal) in correctly identifying children who had respiratory failure as evidenced by the need for endotracheal intubation. Twenty-five children from 9 days to 38 months of age were included. Ten children had a positive cardiac troponin I and 3 of these children had respiratory failure. A positive cardiac troponin I demonstrated a sensitivity of 100%, specificity 68%, positive predictive value of 30%, negative predictive value of 100%, and accuracy of 72%. The area under the receiver operating characteristic curve was 0.939 (95% confidence interval, 0.820-1.0), suggesting a high degree of discriminatory power in selecting children with respiratory failure. A sample size calculation revealed that a follow-up study of 359 patients is needed before the clinical use of cardiac troponin I for this purpose.

An introduction to power and sample size estimation

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

Sample size calculations in studies of test accuracy

Methods for determining sample size for studies of the accuracy of diagnostic tests are reviewed. Several accuracy indices are considered, including sensitivity and specificity, the full and partial area under the receiver operating characteristic curve, the sensitivity at a fixed false positive rate, and the likelihood ratio. Sample size formulae are presented for studies evaluating a single test and studies comparing the accuracy of tests. Four real examples illustrate the concepts involved in sample size determination. Lastly, various study design issues are discussed, such as sampling methods, choices in format for the test results, and the issue of replicated readings.

Intrasound vibration testing in acute ankle injuries

OBJECTIVES

To determine the accuracy of intrasound vibration testing (IVT) in comparison with plain radiography in the diagnosis of acute ankle fractures.

METHODS

A group-sequential, nonrandomized, double-blind, observational study design was used. A convenience sample of patients were studied, aged > or = 10 years, with acute ankle injuries, undergoing ankle radiography, evaluated at a community teaching hospital ED. Excluded were cases involving injuries of > 24 hours' duration, inadequate documentation, protocol violation, or positive IVT on the uninjured ankle. IVT was performed with the intrasound apparatus placed on the anterior and posterior aspects of the medial and lateral malleoli of the uninjured and injured ankles; positive IVT was defined as patient withdrawal secondary to pain.

RESULTS

Of 105 patients enrolled, 8 were excluded; 1 for inadequate documentation, 5 for protocol violation, and 2 for positive IVT of the uninjured ankle. Of the 97 patients analyzed, 13 had fractures identified by radiography, including 9 lateral malleolar, 1 medial malleolar, 1 bimalleolar, and 2 talar fractures. Only 5 of the 13 fractures were detected with IVT (sensitivity = 39%; 95% CI: 14-68%). Seventy of 84 nonfractured ankles had negative IVT (specificity = 83%; 95% CI: 74-91%). Of the 19 with positive IVT, 5 had fractures (positive predictive value of 26%; 95% CI: 9-51%). Of the 78 with negative IVT, 70 had no fracture (negative predictive value of 90%; 95% CI: 81-96%). Overall, 75 of 97 IVTs were correct (77%), most of which were among patients without fractures.