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

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

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

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.

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

6. Standard NMA models

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

8. Adjusted indirect comparison8

9. Adding Studies of other epidemiological design to an RCT NMA

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!

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

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, )
μj ~ N(0, )
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

13. Indirect comparison (NMA) incorporating single arm trial1 A B C D A B C D 2
Interested in relative treatment effect of D versus A, B and C. Only single arm trial for D
Prediction of comparator arm given patient characteristics in single arm trial for D. Creation of ‘virtual’ CD trial. 3 A B C D
Incorporation of ‘virtual’ CD trial in network

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

15. Applications

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

17. ( ) Observational studies Randomized Controlled Trials
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)
( )
Single-arm Studies

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

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

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”

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

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

23. Odds ratios for sustained virological response
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

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

26. Thank You