This document discusses methods for incorporating single-arm study data into network meta-analyses (NMAs). Currently, NMAs primarily use data from randomized controlled trials. The document presents two methods for including single-arm evidence: 1) Using single-arm results to create informative priors in Bayesian NMA models, and 2) Creating "virtual comparisons" based on patient characteristics to include single-arm studies directly in the NMA. It provides examples applying these methods in analyses of treatments for cryptococcal meningitis and hepatitis C. The results showed inclusion of single-arm evidence can improve model fit and precision of treatment effect estimates in NMAs.

1. Incorporating data from single-arm
studies into network meta-analyses
Steve Kanters PhD(c), Kristian Thorlund PhD, Edward
Mills PhD, Jeroen Jansen PhD, Nick Bansback PhD
April 14th, 2015
1

2. Network meta-analyses (NMA)
• An expansion of traditional pairwise meta-analyses that
consider multiple treatments at a time
• NMA combine direct and indirect comparisons to make the
most of the available evidence
• The utility of NMA is in providing comparative efficacy for
all therapeutics of a given medical condition
• Presently, NMAs are generally restricted to RCT evidence
• Alternative sources of evidence include comparative
observational studies and single-arm studies
2

3. Potential limitations to RCT
evidence
• A large phase 3 RCT is at the top of the hierarchy of evidence
• In some situations it may be viewed as being lower on a ‘hierarchy of relevance’ than other designs
• Timeliness: A large phase 3 RCT can take years to complete
• the relevance of its findings may be reduced by the time of reporting
• E.g. in oncology, if findings of several uncontrolled trials and observational
studies may have already shown promising results
• Ethics: RCTs will often be needed to confirm treatment effects, but not always
ethical.
• Underpowered: For safety endpoints, observational studies can be much more
relevant because RCTs are likely to be too short for safety outcomes
3

4. When are other sources of
evidence needed?
• For some interventions only single arm trials or observational evidence is
available.
• i.e., to connect the network.
• e.g., rare diseases.
• RCTs tend to be powered for efficacy and in turn are often underpowered
for safety.
• Observational studies can often be larger and longer and hence better inform
safety.
• Observational studies may shed light on efficacy and safety within sub-
populations.
• RCTs dominated by Caucasian participants may not speak to Asian or Black
populations.
• In time-to analyses, single arm phase IV trials may help supplement time-
to information for both efficacy and safety.
4

5. Purpose
• Methods have already been suggested for
combining comparative observational studies to
RCTs
• However uptake has been slow
• The purpose of today’s talk is to discuss how to
integrate single-arm evidence into NMA
• We provide motivational examples , but perhaps the
most convincing is the integration of non-comparative
phase IV trials to safety analyses
5

6. Standard NMA models
6
1
1
AB
22
2
AB
jj
j
AB
1
qjk =
mj
mj +dj
ì
í
ï
îï
k = A
k = B
dj ~ Normal dAB,sd
2
( )

7. Standard model definitions
• θj are the likelihood parameters transformed by
the appropriate link function
• E.g. logit(pj), yj, log(rj)
• μj are the study effects: the part of the observed
outcome attributable to prognostic factors
• δj is the comparative treatment effect that we
seek to solve for
7

8. Adjusted indirect comparison
8

9. ADDING STUDIES OF OTHER
EPIDEMIOLOGICAL DESIGN TO AN RCT NMA
9

10. Single-arm studies (& comparative
observational studies)
• Uncontrolled studies: Impossible to disentangle study effects from
treatment effects. Only observed outcomes.
• However, it can be useful to add these kinds of studies to synthesis
of RCT evidence….
…as long as we acknowledge their limitations with the
analyses methods!
10

11. Combining RCT and to other
designs
How can we incorporate single-arm evidence to
NMA?
1. Use the single-arm evidence to create
informative priors
1. Create a virtual comparison based on patient
characteristics
11

12. Informative priors
• > 65% of NMAs conducted today are conducted using Bayesian
hierarchical models
• The majority of the remaining 35% are restricted to adjusted indirect
comparisons using the Bucher method
• These tend to start with non-informative priors for the model parameters.
Specifically:
• dAB ~ N(0, 0.0001)
• μj ~ N(0, 0.0001)
• If single-arm evidence exists for both treatments A and B, we can use this
evidence to create informative priors on dAB
• For example, if dealing with a dichotomous outcome with linear model for
mean difference dAB ~ N(yB,endo – yA,endo, precendoω), where ω is a correction
weight
• Note that it does not make sense to construct informative priors on μ as this is
study specific rather than treatment specific 12

13. Indirect comparison (NMA)
incorporating single arm trial
A
B
C D
A
B
C C D
A
B
C D
1 2
3
Prediction of comparator arm given
patient characteristics in single arm
trial for D. Creation of ‘virtual’ CD
trial.
Interested in relative treatment
effect of D versus A, B and C. Only
single arm trial for D
Incorporation of ‘virtual’ CD
trial in network 13

14. Relative advantages of each
method
• Both approaches allow for the integration of
single-arm evidence to NMA
• Informative priors offer a more convenient way to
weight the evidence
• Direct inclusion into the NMA requires a more
contrived reduction of the effective sample size
• Direct inclusion lends itself better to all additional
manipulations of the NMA, such as meta-
regression adjustments
14

15. APPLICATIONS
15

16. Single-arm evidence as prior
Example 1 - Meningitis
• Cryptococcal meningitis is a leading cause of HIV-associated
death and is the most common cause of meningitis in sub-
Saharan Africa
• Multiple guidelines recommend use of Amphotericin B (AmB)
in combination either 5-flucytosine (5FC), where available, or
fluconazole (Azole)
• Despite high level of recommendations:
• No RCTs have shown mortality benefit for addition of Azoles to AmB
• Single, recent RCT has shown mortality benefit for addition of 5FC to
AmB
16

17. Randomized Controlled Trials
( ) 17
Observational studies
Single-arm Studies
Campbell JI, Kanters S, Bennett JE, Thorlund K, et al. Comparative effectiveness of induction
therapy for human immunodeficiency virus-associated cryptococcal meningitis: A network
meta-analysis. Open Forum Infect Dis. 2015;2(1)

18. Example 1 – Meningitis
Methods applied
• Pooled single arm results for each intervention
• Used single-arm based comparative effects as
‘informative priors’ in the Bayesian NMA model
• Estimated expected comparative pairwise efficacy by
taking the difference between single arm results.
• Penalized precision of single arm comparative
estimates by 4
18

19. Amphotericin
+ Azole
Conceptual
control
Rationale for Penalization
Amphotericin
+ 5FC
Conceptual
Indirect
Comparison
19

20. Example 1 – Meningitis
Results
• Heterogeneity in the model was reduced
• By 26%
• Model fit was improved
• DIC 144 vs. 234
• Effect estimates were more precise
• Two comparisons became “statistically significant”
20

21. Example 2 – Hepatitis C
• Sofosbuvir is a recently licensed direct acting antiviral (DAA) for
hepatitis C
• Single arm trials makes up much of the evidence for the two
Sofosbuvir regimens
• Non-RCT evidence is required to connect the network, particularly
when restricted to non-cirrhotic patients
• We analyzed the network by
• Directly including single-arm evidence by using virtual comparisons
• Integrating the single arm data through informative priors
• With informative priors with decreased precision (factor of 4)
• Excluding the single arm-evidence
21

22. Application to Hepatitis C
22
Randomized Controlled Trials
Single-arm Studies( ) 22
Full network
Non-cirrhotic patients only

23. Odds ratios for sustained
virological response
23
Comparison
Versus P2aR
Direct inclusion
of single arm
evidence
Fully informative
priors
Penalized prior
precision (x4)
Conventional
non-informed
P2bR 0.80 (071, 0.91) 0.68 (0.56, 0.80) 0.67 (0.50, 0.87) 0.63 (0.37, 0.95)
BOC+P2bR (SDT) 2.87 (1.86, 4.49) 2.53 (1.51, 4.29) 2.53 (1.43, 4.36) 2.42 (1.02, 5.23)
BOC+P2bR (RGT) 2.36 (1.40, 3.99) 2.08 (1.11, 3.84) 2.09 (1.06, 3.91) 1.99 (0.71, 4.89)
TEL + P2aR (SDT) 2.56 (1.22, 5.41) 1.99 (0.82, 4.74) 1.98 (0.80, 4.79) 1.87 (0.55, 5.63)
TEL + P2aR (RGT) 3.68 (2.12, 6.37) 3.80 (2.02, 7.22) 3.80 (2.02, 7.16) 3.80 (1.53, 9.26)
SIM + P2aR (RGT) 4.95 (3.39, 7.33) 3.77 (2.35, 6.12) 3.75 (2.31, 6.03) 3.73 (2.04, 6.79)
SIM + P2bR (RGT) 3.42 (2.01, 5.90) 2.31 (1.06, 5.16) 2.28 (1.06, 5.08) 2.25 (0.84, 5.82)
SOF + P2aR 9.82 (6.16, 15.9) 9.35 (6.89, 12.7) 8.97 (5.01, 15.8) 6.59 (1.51, 31.1)
SOF + LDV 34.5 (19.0, 67.6) 34.1 (16.7, 69.5) 34.0 (8.1, 138.7) --
P2bR = pegylated interferon alpha-2b; P2aR = pegylated interferon alpha-2a
BOC = boceprevir; TEL = telaprevir; SIM = simeprevir;
SOF = sofosbuvir; LDV = ledipasvir;
(SDT) = standard duration therapy;
(RGT) = response guided therapy

24. TAKE HOME MESSAGES
24

25. Take home messages
• Typically evidence synthesis of only RCT evidence has good
internal validity.
• In some cases adding single-arm evidence can be very
informative, especially when there are a limited number of
RCTs.
• We have to be aware of limitations of observational single-
arm evidence
• Analyses should be done using multiple methods, including those
restricted to RCTs (if possible)
• It comes back to validity vs. precision
25

26. THANK YOU
26