Embed Size (px)
Citation preview
How informative priors can help model heterogeneity
Network meta-analyses in a
sparse evidence bases
April 11, 2016
Background
• Sparse networks are relatively common when dealing with network meta-analyses (NMA) • For example, biologics trials can be very expensive
leading to few trials describing each comparison
• When a network is too sparse it may become infeasible to conduct random-effects (RE) NMA • If conducted, credible intervals can “explode”
• Random effects estimates not significant when the pairwise meta-analysis is
2
Psoriatic arthritis example
• As a motivating example, consider a network of biologics for the treatment of psoriatic arthritis (PsA)
• The principal outcome was the American College of Rheumatology responder criteria (ACR) 20 (20 percent improvement in tender or swollen joint counts as well as 20 percent improvement in three of the other five criteria)
• Also of interest was Psoriasis Area and Severity Index (PASI) 50 (reduction in PASI score of at least 50%)
3
placebo
Etanercept 25mg biw
ACR 20 at 12 weeks – Biologics-naïve
Ustekinumab 90mg
RAPID-PSA
ADEPT Genovese 2007
PSUMMIT1 PSUMMIT2
PSUMMIT1 PSUMMIT2
PSUMMIT1 PSUMMIT2
Mease 2004
GO-REVEAL
GO-REVEAL
GO-REVEAL
Golimumab
100mg
Golimumab
50mg
Ustekinumab 45mg
Adalimumab
40mg
Certolizumab
400 mg
Relative risk of ACR 20 at 12 weeks
5
Placebo 0.29
(0.22, 0.53)
0.40
(0.23, 1.04)
0.29
(0.20, 0.64)
0.26
(0.19, 0.52)
0.26
(0.19, 0.52)
0.49
(0.30, 1.12)
0.51
(0.30, 1.18)
3.41
(1.88, 4.64) ADA40
1.36
(0.63, 3.43)
0.99
(0.52, 2.13)
0.90
(0.48, 1.73)
0.89
(0.49, 1.78)
1.68
(0.78, 3.79)
1.74
(0.82, 3.95)
2.51
(0.96, 4.26)
0.74
(0.29, 1.60) CZP
0.73
(0.27, 1.83)
0.66
(0.25, 1.52)
0.66
(0.25, 1.49)
1.24
(0.43, 3.16)
1.28
(0.45, 3.26)
3.45
(1.56, 5.05)
1.01
(0.47, 1.92)
1.37
(0.55, 3.69) ETN25BIW
0.91
(0.42, 1.84)
0.90
(0.41, 1.81)
1.69
(0.71, 3.87)
1.75
(0.73, 4.18)
3.80
(1.92, 5.29)
1.11
(0.58, 2.08)
1.51
(0.66, 3.95)
1.10
(0.54, 2.38) GOL100
0.99
(0.62, 1.56)
1.87
(0.82, 4.35)
1.93
(0.85, 4.44)
3.84
(1.94, 5.32)
1.12
(0.56, 2.05)
1.52
(0.67, 3.93)
1.11
(0.55, 2.42)
1.01
(0.64, 1.60) GOL50
1.88
(0.85, 4.41)
1.94
(0.86, 4.45)
2.03
(0.89, 3.36)
0.59
(0.26, 1.28)
0.81
(0.32, 2.31)
0.59
(0.26, 1.42)
0.53
(0.23, 1.22)
0.53
(0.23, 1.18) UST45
1.03
(0.54, 1.99)
1.96
(0.85, 3.28)
0.58
(0.25, 1.22)
0.78
(0.31, 2.22)
0.57
(0.24, 1.36)
0.52
(0.23, 1.18)
0.51
(0.22, 1.16)
0.97
(0.50, 1.84) UST90
Pair wise MA RRs: 2.03 (1.15-3.29) and 1.97 (1.12-3.00)
PASI 50 at 12 weeks – Biologics-naïve
placebo Adalimumab
40mg ADEPT SPIRIT-P1
Infliximab 5mg/kg
IMPACT2
GO-REVEAL
GO-REVEAL GO-REVEAL
Golimumab
50mg
Golimumab
100mg
Relative risk of PASI 50 at 12 weeks
7
Placebo 0.18
(0.09, 188.34)
0.15
(0.08, 5362.44)
0.17
(0.09, 17609.73)
0.13
(0.08, 813.65)
5.51
(0.01, 11.14) ADA40
0.85
(0.00, 9871.41)
0.98
(0.00, 38643.48)
0.73
(0.00, 1793.35)
6.84
(0.00, 11.87)
1.18
(0.00, 367.10) GOL100
1.13
(0.00, 2770.24)
0.89
(0.00, 1238.09)
5.75
(0.00, 11.62)
1.02
(0.00, 322.66)
0.89
(0.00, 647.70) GOL50
0.76
(0.00, 1176.73)
7.91
(0.00, 12.32)
1.38
(0.00, 506.41)
1.12
(0.00, 12822.37)
1.32
(0.00, 42370.61) INF5
QUICK REVIEW
8
Bayesian parameter estimation
Pr(|Y) Pr(Y|) x Pr()
“Likelihood”
Suppose we wish to draw inference on , a parameter or set of parameters of interest (e.g., treatment effects), therefore
= parameter of interest
Y represents the observed data
We begin with a “prior” probability distribution for the parameters
• Typically a non-informative prior (blank slate)
• Full Bayesian framework allows for external information to inform our prior belief
“Prior”
Then use the data to determine the likelihood
• “How likely parameter values are given the observed data”
• The basis of frequentist statistics
Parameter estimation is based on the posterior distribution
• Bayesian thinking: given my prior knowledge and data likelihood, what is the probability of a parameter estimate being true
“Posterior”
NMA can be conducted in either the frequentist of Bayesian framework
• Majority of NMA are conducted in the Bayesian framework
Arm-based fixed & random effects network meta-analysis model
Random effects
Fixed effects
10
PROBLEM AND SOLUTION
11
Likelihood
Pro
bab
ilit
y
Prior
Posterior
Can result in unrealistically wide 95% credible intervals
0 1 2 3 4
Between-trial variance (2)
Posterior heterogeneity distributions
Informative priors
• If there is too little information to overcome vague, non-informative priors, what are we to do? • Informative priors can be used to integrate scientific knowledge
external to the evidence base
• Turner et al reviewed 14,886 meta-analyses to help inform
the distribution of τ when working with binary data • This information can be used to construct informative priors on
the heterogeneity variance parameter
• How it is done: • Use a log-Normal prior on the heterogeneity variance τ2 with
mean and precision based on decades of scientific work
13
Informative heterogeneity priors
10
15
Changes to the BUGS/JAGS model
• Effectively, this implies changing only two lines to most NMA code • From
• To
• Why a log-Normal distribution? • Best fitting distribution among a variety of
candidates
16
PsA example revisited
17
Placebo 0.18
(0.11, 0.33)
0.14
(0.09, 0.30)
0.17
(0.10, 0.42)
0.12
(0.08, 0.20)
5.60
(2.99, 8.98) ADA40
0.81
(0.43, 1.68)
0.97
(0.49, 2.36)
0.69
(0.38, 1.16)
6.93
(3.39, 10.71)
1.23
(0.60, 2.33) GOL100
1.19
(0.74, 2.25)
0.85
(0.44, 1.40)
5.76
(2.40, 9.58)
1.03
(0.42, 2.05)
0.84
(0.44, 1.36) GOL50
0.71
(0.31, 1.24)
8.18
(4.98, 12.00)
1.46
(0.86, 2.62)
1.17
(0.71, 2.29)
1.41
(0.80, 3.25) INF5
Placebo ADA40 CZP ETN25BIW GOL100 GOL50
UST45 2.03
(1.20, 3.05)
0.59
(0.34, 1.02)
0.81
(0.42, 1.63)
0.59
(0.33, 1.09)
0.54
(0.30, 0.96)
0.53
(0.30, 0.94)
UST90 1.96
(1.12, 2.98)
0.58
(0.32, 0.99)
0.78
(0.40, 1.58)
0.57
(0.31, 1.06)
0.52
(0.28, 0.93)
0.52
(0.28, 0.92)
Relative risk of ACR 20
Relative risk of PASI 50
Application to other data
• Dichotomous data are very popular
• A more recent study has conducted the same exercise for continuous data modeled with a Normal likelihood • It requires that the data first be transformed as
standardized mean differences • And be back-transformed after completing the NMA
• As of yet, there is no such evidence for models based on Poisson or Multinomial likelihoods
18
Placebo
LAMA LABA+LAMA
ICS+LABA+LAMA
LAMA+PDE-4
LABA PDE-4 LABA+PDE-4
ICS+LABA
ICS 3 trials
Pair wise MA RR: 0.84 (0.71-0.97)
Network MA RR: 0.85 (0.66-1.03)
Example - COPD
A B
C
A B
C
Scenario #1 Scenario #2
I2=25%
I2=35% I2=45%
I2=5%
I2=35% I2=65%
How else might this be used?
• Most NMA assumes the degree of heterogeneity is equal in each comparison
k=3
k=4 k=5
k=12
k=12 k=12
• If we relax this assumption, we may have to borrow strength estimation power from somewhere else
Conclusions
• Sparse networks and heterogeneity are two distinct concepts
• Informative priors can be used to ensure the correct model is used (i.e., random-effects) when it is otherwise infeasible
• Use of informative heterogeneity priors are becoming widely endorsed (used within NICE, CADTH, and academic experts)
• There are limitations to the use of informative priors: • It can only be used with Binomial and Normal likelihoods • It can only be used when all treatment comparisons fall
within the same category
21
