Mortality Benefit of Alirocumab: A Bayesian Perspective

Abstract

Background
The ODYSSEY OUTCOMES (Alirocumab and Cardiovascular Outcomes after Acute Coronary Syndrome) trial demonstrated that alirocumab reduced major cardiovascular events. However, because of the hierarchical testing strategy used for the multiple outcomes examined, the observed reduction in all‐cause mortality was labeled “nominally significant” which has clouded its interpretation.

Methods and Results
We re‐analyzed data from ODYSSEY OUTCOMES using Bayesian methods and generated various prior probabilities by incorporating mortality data from previous similar PCSK 9 (proprotein convertase subtilisin‐kexin type 9) inhibitor trials. We first used data from the ODYSSEY OUTCOMES trial with a non‐informative prior, then sequentially added data from ODYSSEY LONG TERM and the FOURIER trial, giving FOURIER full weight, 50% weight and 10%. The posterior probability of a mortality reduction using only the ODYSSEY OUTCOMES data was hazard ratio 0.85 (95% CI 0.74–0.99) which corresponded to a 98.4% probability of a mortality benefit. When the ODYSSEY LONG TERM data were added to the analysis, the posterior probability was hazard ratio 0.84 (95% CI 0.72–0.97) with a 99.9% probability of mortality reduction, and when the FOURIER data were added to the analysis the posterior probability was hazard ratio 0.94 (95% CI 0.85–1.04) with an 89.1% probability of a mortality reduction. When the FOURIER trial was given only 50% or 10% weight, the probability of a mortality reduction rose 95.4% and 98.7%, respectively. We estimate that the probability of >1% absolute risk reduction ranges from 8% to 24%, while the probability of >0.5% absolute risk reduction ranges from 66% to 89%.

Conclusions
Our analysis demonstrates a high likelihood that alirocumab confers a reduction in all‐cause mortality, despite the equivocal interpretation of the data in the original ODYSSEY OUTCOMES publication.

Full text

Mortality Benefit of Alirocumab: A Bayesian Perspective
Christopher Labos, MDCM, MSc; James M. Brophy, MD, PhD; Allan Sniderman, MD; George Thanassoulis, MD, MSc
Background-—The ODYSSEY OUTCOMES (Alirocumab and Cardiovascular Outcomes after Acute Coronary Syndrome) trial
demonstrated that alirocumab reduced major cardiovascular events. However, because of the hierarchical testing strategy used for
the multiple outcomes examined, the observed reduction in all-cause mortality was labeled “nominally significant”which has
clouded its interpretation.
Methods and Results-—We re-analyzed data from ODYSSEY OUTCOMES using Bayesian methods and generated various prior
probabilities by incorporating mortality data from previous similar PCSK9 (proprotein convertase subtilisin–kexin type 9) inhibitor
trials. We first used data from the ODYSSEY OUTCOMES trial with a non-informative prior, then sequentially added data from
ODYSSEY LONG TERM and the FOURIER trial, giving FOURIER full weight, 50% weight and 10%. The posterior probability of a
mortality reduction using only the ODYSSEY OUTCOMES data was hazard ratio 0.85 (95% CI 0.74–0.99) which corresponded to a
98.4% probability of a mortality benefit. When the ODYSSEY LONG TERM data were added to the analysis, the posterior probability
was hazard ratio 0.84 (95% CI 0.72–0.97) with a 99.9% probability of mortality reduction, and when the FOURIER data were added
to the analysis the posterior probability was hazard ratio 0.94 (95% CI 0.85–1.04) with an 89.1% probability of a mortality
reduction. When the FOURIER trial was given only 50% or 10% weight, the probability of a mortality reduction rose 95.4% and
98.7%, respectively. We estimate that the probability of >1% absolute risk reduction ranges from 8% to 24%, while the probability of
>0.5% absolute risk reduction ranges from 66% to 89%.
Conclusions-—Our analysis demonstrates a high likelihood that alirocumab confers a reduction in all-cause mortality, despite the
equivocal interpretation of the data in the original ODYSSEY OUTCOMES publication. (J Am Heart Assoc. 2019;8:e013170. DOI:
10.1161/JAHA.119.013170.)
Key Words: Bayesian •cholesterol •mortality •PCSK9
The publication of the ODYSSEY OUTCOMES (Alirocumab
and Cardiovascular Outcomes after Acute Coronary
Syndrome) trial
1
demonstrated that the PCSK9 (proprotein
convertase subtilisin–kexin type 9) inhibitor (PCSK9i) alirocu-
mab reduced major cardiovascular events. However, because
of the hierarchical testing strategy used for the multiple
outcomes examined, the observed reduction in all-cause
mortality was labeled “nominally significant”which has
clouded its interpretation.
Bayesian analysis allows direct estimation of the probability
of a given outcome and is not encumbered by concerns about
null hypothesis testing (eg, type 1 errors). By updating prior data
(ie, prior probability) with current results (ie, likelihood), Bayesian
methods naturally and intrinsically permit synthesis of all
available evidence allowing more precise and potentially less
biased effect estimates (ie, posterior probability).
2
Importantly,
the posterior probability allows clinicians to directly determine
not only the probability of any mortality benefit, but also the
probability that this exceeds any clinically interesting difference,
for example a 0.5% or 1% absolute mortality difference.
Methods
To cover the range of varying prior probabilities, we generated
various prior probabilities using mortality data from previous
similar PCSK9i trials. We first used data from the ODYSSEY
OUTCOMES trial with a non-informative before generate a
posterior probability and the probability of a mortality reduc-
tion. Non-informative priors provide little a priori information
and consequently a Bayesian posterior probability using a non-
informative prior will yield a result that is numerically similar to
the frequentist analysis, ie, the published result from the
ODYSSEY OUTCOMES trial. However, with Bayesian statistics
one can determine the actual probability of the result being true,
whereas with frequentist statistics one can only establish, if the
From the McGill University Health Center, Montreal, Canada.
Correspondence to: Christopher Labos, MDCM, MSc, Preventive and
Genomic Cardiology, McGill University Health Center, 1001 Decarie Blvd,
D5-5120 Montreal, QC H4A 3J1, E-mail: christopher.labos@mail.mcgill.ca
Received May 2, 2019; accepted July 25, 2019.
ª2019 The Authors. Published on behalf of the American Heart Association,
Inc., by Wiley. This is an open access article under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs License, which permits use
and distribution in any medium, provided the original work is properly cited,
the use is non-commercial and no modifications or adaptations are made.
DOI: 10.1161/JAHA.119.013170 Journal of the American Heart Association 1
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hypothesis being tested were false, what would be the
probability of observing the data obtained.
For ODYSSEY OUTCOMES we generated a normal distri-
bution centered on the log-transformed point estimate
published in the trial, namely the hazard ratio 0.85 (95% CI
0.78–0.93). The non-informative prior in this case was a
normal distribution with a wide variance of 1 000 000. Using
the properties of conjugate priors, these 2 distributions were
combined into the posterior distribution.
Subsequent steps followed the same pattern. We sequen-
tially added data from ODYSSEY LONG TERM
3
and the
FOURIER trial,
4
which used evolocumab, giving FOURIER full
weight, a 50% and then a 10% weight. Using partial weights
allows for a statistical compromise: the prior data from
FOURIER are not given full weight when applied to the current
trial (since this trial used a different molecule) nor is it
dismissed entirely.
5
This weighting was achieved by multiply-
ing the variance of the data distribution. For example,
doubling the variance provides a 50% weight.
We were able to calculate the absolute risk reduction by
using the number of deaths in each of the treatment and
controls arms reported trials. By generating a beta distribution
using these data, we used the same sequential Bayesian
process described above. We started with a beta (1,1)
non-informative prior which was added to the ODYSSEY
OUTCOMES data, and then sequentially added data from
ODYSSEY LONG TERM and the FOURIER trial at full, 50%, and
10% weighting.
Using the beta distributions in this way allowed us to
calculate the probability of a 1% and 0.5% mortality reduction
on the absolute scale, equivalent to a number needed to treat
of 1 in 100 or 1 in 200, respectively.
Results
In the ODYSSEY OUTCOMES trial, all-cause mortality was
3.5% for alirocumab versus 4.1% for placebo. The probability
of a mortality reduction using only the ODYSSEY OUTCOMES
data was 98.4% and rises to >99% when data from the
ODYSSEY LONG TERM were sequentially added to the
analysis. The probability of >1% absolute risk reduction
ranged from 8% to 24%, while the probability of >0.5%
absolute risk reduction ranged from 66% to 89% (Table).
Discussion
This Bayesian analysis demonstrates a high likelihood that
alirocumab confers a reduction in all-cause mortality, despite
the equivocal interpretation of the data in the original
ODYSSEY OUTCOMES publication.
1
When considering the
data from both molecules on the market, the probability of a
mortality reduction with PCSK9 inhibition is high. Although
there remains considerable uncertainty for >1% absolute
mortality difference in mortality, the probability of >0.5%
mortality difference (number needed to treat, 1 in 200) is high
and potentially clinically relevant. Further research will be
needed to determine the economic relevance of these benefits.
An advantage of Bayesian analysis is that it allows us to
incorporate data from multiple trials and use different priors
and weights to simulate how different clinicians might weigh
the data. For example, some clinicians, citing the similar
mechanism of action between alirocumab and evolocumab,
would give the FOURIER data more weight, whereas others
may give them less weight since they are similar but distinct
molecules. This difference in opinion can be formally
expressed in a Bayesian analysis, as performed here, and
represents an advantage of such an approach. It is also
consistent with how individuals naturally incorporate new
information, using the totality of the available evidence.
Bayesian analysis also allows us to directly estimate the
probability that alirocumab reduces all-cause mortality with-
out concern for multiple testing and type 1 error. Therefore,
Bayesian analysis overcomes the potential confusion caused
by the hierarchical testing strategy used in the ODYSSEY
OUTCOMES trials to limit type 1 error (ie, false positives),
which involves testing multiple end points in a predetermined
Table. Posterior Probability of Mortality Benefit Given 4 Different Prior Probabilities
Source of Data
Mortality Data
Posterior Probability
Probability Mortality
Treatment <Control
Probability
Mortality
Reduction >1%
Probability
Mortality
Reduction >0.5%Treatment Arm Control Arm
ODYSSEY outcomes 334/9462 392/9462 HR 0.85 (95% CrI 0.74–0.99) 98.4% 8% 66%
+ODYSSEY LONG TERM 8/1542 10/778 HR 0.84 (95% CrI 0.72–0.97) 99.2% 24% 89%
+FOURIER 444/13 784 426/13 780 HR 0.94 (95% CrI 0.85–1.04) 89.1% <0.1% 8.2%
+FOURIER (50%
weight of trial)
HR 0.91 (95% CrI 0.81–1.02) 95.4% 0.01% 38%
+FOURIER (10%
weight of trial)
HR 0.85 (95% CrI 0.74–0.98) 98.7% 11% 81%
HR indicates hazard ratio; CrI, Credible Interval.
DOI: 10.1161/JAHA.119.013170 Journal of the American Heart Association 2
Mortality Benefit of Alirocumab Labos et al
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sequence and stopping when the first non-significant result
appeared. In our opinion, this non-standard approach, which
may not adequately control for type 1 error, is prone to
misinterpretation.
In summary, we demonstrate that although Bayesian
analysis requires additional inputs (ie, prior data) and different
assumptions than frequentist methods, it also provides addi-
tional clarity to the interpretation of the ODYSSEY OUTCOMES
mortality data and avoids some of the interpretation problems
that can arise with frequent analysis. Our Bayesian estimates of
the probability that alirocumab reduces total mortality provide
an answer to one of the more important clinical questions that
concerns the majority of practitioners and payers.
Disclosures
Dr Thanassoulis has received personal fees as part of advisory
boards and speaker bureaus for Sanofi/Regeneron, Amgen,
Boehringer-Ingelheim, and Servier and has received research
grants from Servier and Ionis. The remaining authors have no
disclosures to report.
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