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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
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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