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JACC Vol. 63, No. 4, 2014 February 4, 2014:375–9 Correspondence 377 *HTA Unit, Area Vasta Centro Toscana Regional Health System Via Guimaraes 9-11 59100 Prato Italy E-mail: [email protected] http://dx.doi.org/10.1016/j.jacc.2013.05.106 REFERENCES 1. Brayton KM, Patel VG, Stave C, de Lemos JA, Kumbhani DJ. Sameday discharge after percutaneous coronary intervention: a meta-analysis. J Am Coll Cardiol 2013;62:275–85. 2. Liberati A, D’Amico R. Commentary: the debate on non-inferiority trials: “when meta-analysis alone is not helpful.” Int J Epidemiol 2010; 39:1582–3. 3. Wetterslev J, Thorlund K, Brok J, Gluud C. Estimating required information size by quantifying diversity in a random-effects meta-analysis. BMC Med Res Methodol 2009;9:86. 4. Wetterslev J, Thorlund K, Brok J, Gluud C. Trial sequential analysis may establish when firm evidence is reached in cumulative meta-analysis. J Clin Epidemiol 2008;61:64–75. 5. Messori A, Fadda V, Maratea D, Trippoli S. Omega-3 fatty acid supplements for secondary prevention of cardiovascular disease: from “no proof of effectiveness” to “proof of no effectiveness.” JAMA Intern Med 2013;173:1466–8. Figure 1 Trial Sequential Analysis of 6 RCTs Comparing Same-Day Discharge With Routine Overnight Observation After Percutaneous Coronary Intervention The expected relative risk reduction (RRR) was assumed to be 50% (A) or 33% (B). In the z-curve (blue), individual trials correspond to individual segments; trials are plotted in chronological order (from left to right). The x-axis indicates the cumulative number of patients; the starting point of the z-curve is always at x ¼ 0, that is, inclusion of no trials. C ¼ control arm (routine overnight observation); RCT ¼ randomized controlled studies; T ¼ treatment arm (same-day discharge); red lines are the boundaries for superiority or inferiority. (characterized by zero-event frequency in both arms) was uninformative according to the TSA statistical algorithm. Our results indicate that current information from RCTs does not allow us to draw any firm conclusion about the outcome comparison between the two approaches (i.e., “inconclusive result” of TSA). In fact, while the overall number of patients enrolled in the 6 trials was 2,555, our TSA estimated that the optimal information size would be 10,752 patients (assuming RRR ¼ 50%) or 27,243 patients (assuming RRR ¼ 33%). In summary, the number of patients studied in the RCTs presently available is only one-fourth or one-tenth in comparison with the ideal sample size required to draw a firm conclusion. Therefore, the comparison between the 2 discharge strategies remains open. *Andrea Messori, PharmD Valeria Fadda, PharmD Dario Maratea, PharmD Sabrina Trippoli, PharmD Statistical Uncertainty in 10-Year Framingham Risk of Coronary Heart Disease and Cardiovascular Disease In a recent study, Ford (1) presents an important analysis, with implications for public health prioritization. However, we believe some of the findings should be interpreted with caution. The Framingham Heart Study has contributed immeasurably to our understanding of cardiovascular disease in the United States and internationally, but the published regression equations for 10-year risk of coronary heart disease (CHD) and cardiovascular disease (CVD) were developed for clinical use, and variancecovariance matrices were not reported (2,3). Thus, it is impossible to quantify uncertainty or estimate confidence intervals for any patient’s 10-year risk of CHD or CVD. In other words, while the mean of the risk is known, its variance is unknown. For this reason, the standard errors for the population-level 10-year risk of CHD and CVD that Ford (1) presents in Table 1 in his article are misleading. The same method is used to estimate these standard errors as used for measures such as age, blood pressure, and cholesterol level. The difference between them is that, unlike Framingham risk scores, these characteristics can be measured with certainty (or are assumed to be measured with negligible error and thus are treated as “certain”); thus, their standard errors are appropriate and accurate. On the other hand, the standard errors reported for population-level 10-year risk of CHD and CVD are inappropriate because they capture only betweenperson variability in predicted risk but do not account for the fact 378 JACC Vol. 63, No. 4, 2014 February 4, 2014:375–9 Correspondence that each person’s risk was estimated using a statistical model (within-person variability). Said differently, Ford (1) treats each person’s risk as if it were observed without substantial error, which is true for age, blood pressure, and cholesterol but not the case for Framingham risk functions. Thus, the standard errors Ford reports for 10-year risks of CHD and CVD are systematically underestimated. Ford (1) does not discuss this. Moreover, the method used for evaluating trends does not seem to incorporate uncertainty in risk estimates. What are the implications of this statistical issue for how clinicians, researchers, and policymakers should interpret Ford’s study (1)? The implications may be negligible for readers interested strictly in average population risk and uninterested in trends. However, if the reader is interested in trends, Ford’s results (1) are more difficult to interpret, especially in African Americans, Mexican Americans, women, and individuals whose age falls between 30 and 39 years old or 40 and 49 years old. Each of these groups have p values at the borderline of significance, at the 5% or 10% level in some of Ford’s (1) analyses. Would incorporation of the uncertainty in 10-year risks of CHD and CVD have affected whether these or other comparisons demonstrated a trend? With the information we have, we cannot tell. Methods such as bootstrap analysis (4) and the Taylor seriesbased delta method (5) have been used to capture uncertainty and approximate variance when a closed form estimate is intractable, particularly in decision analysis and cost-effectiveness analysis (6). With adequate information, these methods could be applied to analyses like Ford’s (1). In their absence, we believe it is important for readers to recognize that analytics incorporating Framingham CHD or CVD risk scores do not reflect the withinperson uncertainty in risk. *Joseph A. Ladapo, MD, PhD Keith S. Goldfeld, DrPH *New York University School of Medicine Department of Population Health 550 First Avenue, VZ30 6th Floor, 614 New York, New York 10016 E-mail: [email protected] http://dx.doi.org/10.1016/j.jacc.2013.07.108 REFERENCES 1. Ford ES. Trends in predicted 10-year risk of coronary heart disease and cardiovascular disease among U.S. adults from 1999 to 2010. J Am Coll Cardiol 2013;61:2249–52. 2. D’Agostino RB Sr, Vasan RS, Pencina MJ, et al. General cardiovascular risk profile for use in primary care: the Framingham Heart Study. Circulation 2008;117:743–53. 3. Wilson PW, D’Agostino RB, Levy D, Belanger AM, Silbershatz H, Kannel WB. Prediction of coronary heart disease using risk factor categories. Circulation 1998;97:1837–47. 4. Briggs AH, Wonderling DE, Mooney CZ. Pulling cost-effectiveness analysis up by its bootstraps: a non-parametric approach to confidence interval estimation. Health Econ 1997;6:327–40. 5. Briggs AH, Mooney CZ, Wonderling DE. Constructing confidence intervals for cost-effectiveness ratios: an evaluation of parametric and non-parametric techniques using Monte Carlo simulation. Stat Med 1999;18:3245–62. 6. Ladapo JA, Shaffer JA, Fang Y, Ye S, Davidson KW. Cost-effectiveness of enhanced depression care after acute coronary syndrome: results from the Coronary Psychosocial Evaluation Studies randomized controlled trial. Arch Intern Med 2012;172:1682–4. Positron Emission Tomography/ Computed Tomography for Diagnosis of Prosthetic Valve Endocarditis Suggestions to Increase Diagnostic Accuracy A very interesting article was recently published on the role of 18 F-labeled fluorodeoxyglucose positron emission tomography/ computed tomography ([18F]FDG-PET/CT) for diagnosis of prosthetic valve endocarditis (PVE) (1). Although [18F]FDGPET/CT alone could not actually be considered the “magic” modality capable of diagnosing any PVE episodes, in light of the results of the present study, it could certainly be considered one more weapon in the diagnostic arsenal for PVE detection. In particular, some remarks and considerations could be suggested to increase the diagnostic accuracy of [18F]FDG -PET/CT: in this difficult clinical and diagnostic setting, the preparation of the patient and the image acquisition protocol have fundamental roles. Beyond the factors already cited by the authors, such as a diet rich in fat and very low in carbohydrate to minimize myocardial [18F]FDG uptake and the opportunity to perform [18F]FDGPET/CT before the start of antibiotic therapy (metabolic changes occur very early and precede morphological ones), other factors could be crucial in diagnosing PVE and should be addressed: acquisition time after [18F]FDG injection, timing of prosthetic valve positioning, and blood glucose levels in the cardiac setting. All the studies conducted so far have adopted the “standard” PET/CT protocol used for oncological purposes, consisting of imaging acquisition performed 1 h after [18F]FDG injection. Because valve infective foci can be very small around the spatial resolution of PET systems (4 to 5 mm) and because cardiac uptake is still present despite adequate dietary preparation, low blood glucose levels and delayed imaging could improve sensitivity (2). Hyperglycemia is widely known to be able to lower the sensitivity of [18F]FDG-PET/CT because [18F]FDG is a glucose analog and its uptake in malignant and inflammatory cells is affected by the blood glucose level acting as a competitor. Consequently, the usefulness of [18F]FDG-PET/CT in patients with hyperglycemia could be limited (3,4); for example, a glucose level of 1.8 g/l could be different in terms of [18F]FDG uptake interference from 0.8 g/l, especially in relation to the small dimensions of the area of interest. Despite the suggestion by Rabkin et al. (5) that high blood glucose levels did not significantly affect the detectability rate of infectious and inflammatory processes (although endocarditis was not considered) and had no statistically significant impact on the number of false-negative studies, we must consider the synergistic effects among blood glucose levels, dimensions of the structure or lesions to be studied, and the “cardiac setting.” In fact, another element affecting the accuracy and impairing detectability is the constant movement of the entire heart, the entire mediastinum, and the entire thorax, causing motion artifacts and a “smearing effect.” The solutions to, or at least ways to reduce, these problems could be the use of ß-blockade and cardiac gating to attenuate cardiac motion and artifacts (6). Moreover, it could be reasonably hypothesized that higher