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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

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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

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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

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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.

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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

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Standard NMA models

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1

AB22

2

ABjj

j

AB1

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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

Adjusted indirect comparison

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ADDING STUDIES OF OTHER EPIDEMIOLOGICAL DESIGN TO AN RCT NMA

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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!

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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

2. Create a virtual comparison based on patient characteristics

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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

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Indirect comparison (NMA) incorporating single arm trial

AB

C DA

B

C C D

AB

C D

1 2

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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

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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

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APPLICATIONS

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Single-arm evidence as priorExample 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

Randomized Controlled Trials

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Observational studies

Single-arm StudiesCampbell 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)

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Example 1 – MeningitisMethods 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

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Amphotericin + Azole

Conceptual control

Rationale for Penalization

Amphotericin + 5FC

Conceptual Indirect

Comparison

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Example 1 – MeningitisResults

• 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”

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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

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Application to Hepatitis C

Randomized Controlled Trials

Single-arm Studies( ) 22

Full network

Non-cirrhotic patients only

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Odds ratios for sustained virological response

P2bR = pegylated interferon alpha-2b; P2aR = pegylated interferon alpha-2aBOC = boceprevir; TEL = telaprevir; SIM = simeprevir; SOF = sofosbuvir; LDV = ledipasvir; (SDT) = standard duration therapy; (RGT) = response guided therapy

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TAKE HOME MESSAGES

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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

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THANK YOU