A Bayesian phase 2 model based adaptive design to optimise antivenom dosing: application to a dose-finding trial for a novel Russell's viper antivenom in Myanmar

doi:10.1101/2020.02.06.936815

RESEARCH ARTICLE

A Bayesian phase 2 model based adaptive

design to optimise antivenom dosing:

Application to a dose-finding trial for a novel

Russell’s viper antivenom in Myanmar

James A. Watson

ID

1,2☯

*, Thomas Lamb

ID

2,3☯

, Jane Holmes

ID

4

, David A. Warrell

ID

2

, Khin

Thida Thwin

5

, Zaw Lynn Aung

5

, Min Zaw Oo

6

, Myat Thet Nwe

ID

3

, Frank Smithuis

2,3

,

Elizabeth A. Ashley

ID

2,3,7

1 Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University,

Bangkok, Thailand, 2 Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine,

University of Oxford, Oxford, United Kingdom, 3 Myanmar-Oxford Clinical Research Unit, Yangon, Myanmar,

4 Centre for Statistics in Medicine, Nuffield Department of Medicine, University of Oxford, Oxford, United

Kingdom, 5 University of Medicine 1, Yangon, Myanmar, 6 University of Medicine 2, Yangon, Myanmar,

7 Lao-Oxford-Mahosot Hospital Wellcome Trust Research Unit, Vientiane, Laos

☯ These authors contributed equally to this work.

* jwatowatson@gmail.com

Abstract

For most antivenoms there is little information from clinical studies to infer the relationship

between dose and efficacy or dose and toxicity. Antivenom dose-finding studies usually

recruit too few patients (e.g. fewer than 20) relative to clinically significant event rates

(e.g. 5%). Model based adaptive dose-finding studies make efficient use of accrued

patient data by using information across dosing levels, and converge rapidly to the con-

textually defined ‘optimal dose’. Adequate sample sizes for adaptive dose-finding trials

can be determined by simulation. We propose a model based, Bayesian phase 2 type,

adaptive clinical trial design for the characterisation of optimal initial antivenom doses in

contexts where both efficacy and toxicity are measured as binary endpoints. This design

is illustrated in the context of dose-finding for Daboia siamensis (Eastern Russell’s viper)

envenoming in Myanmar. The design formalises the optimal initial dose of antivenom as

the dose closest to that giving a pre-specified desired efficacy, but resulting in less than a

pre-specified maximum toxicity. For Daboia siamensis envenoming, efficacy is defined as

the restoration of blood coagulability within six hours, and toxicity is defined as anaphy-

laxis. Comprehensive simulation studies compared the expected behaviour of the model

based design to a simpler rule based design (a modified ‘3+3’ design). The model based

design can identify an optimal dose after fewer patients relative to the rule based design.

Open source code for the simulations is made available in order to determine adequate

sample sizes for future adaptive snakebite trials. Antivenom dose-finding trials would ben-

efit from using standard model based adaptive designs. Dose-finding trials where rare

events (e.g. 5% occurrence) are of clinical importance necessitate larger sample sizes

than current practice. We will apply the model based design to determine a safe and

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OPEN ACCESS

Citation: Watson JA, Lamb T, Holmes J, Warrell

DA, Thwin KT, Aung ZL, et al. (2020) A Bayesian

phase 2 model based adaptive design to optimise

antivenom dosing: Application to a dose-finding

trial for a novel Russell’s viper antivenom in

Myanmar. PLoS Negl Trop Dis 14(11): e0008109.

https://doi.org/10.1371/journal.pntd.0008109

Editor: Ulrich Kuch, Goethe University, GERMANY

Received: February 2, 2020

Accepted: October 10, 2020

Published: November 16, 2020

Peer Review History: PLOS recognizes the

benefits of transparency in the peer review

process; therefore, we enable the publication of

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responses alongside final, published articles. The

editorial history of this article is available here:

https://doi.org/10.1371/journal.pntd.0008109

access article distributed under the terms of the

Creative Commons Attribution License, which

permits unrestricted use, distribution, and

reproduction in any medium, provided the original

author and source are credited.

Data Availability Statement: The results in the

manuscript are from simulated data. All underlying

code can be found at: https://github.com/

jwatowatson/AdaptiveAntivenomDesign.

efficacious dose for a novel lyophilised antivenom to treat Daboia siamensis envenoming

in Myanmar.

Author summary

Snakebite envenoming is one of the most neglected tropical diseases considering its bur-

den of mortality and morbidity. Antivenoms are the only known effective treatment for

snake-bite envenoming but are frequently responsible for high rates of adverse reactions.

Clinical development of antivenoms rarely follows the iterative phases of clinical develop-

ment applied to other drugs. Dosing is typically based on pre-clinical testing. Here we

propose a Bayesian model based adaptive design for phase 2 clinical trials aiming to deter-

mine the optimal dose of antivenom needed for treatment of snakebite envenoming. Opti-

mality is defined using safety and efficacy thresholds contextual to the study. This design

can be applied to all antivenoms which have binary efficacy and toxicity endpoints. Our

design formally specifies a desired efficacy and a maximum tolerated toxicity. We use sim-

ulation studies to characterise adequate sample sizes to determine an approximately opti-

mal dose under different scenarios. The simulation studies highlight the advantages of a

model based design over simpler rule based alternatives. This design will be used to deter-

mine an effective and safe dose of the new lyophilised viper antivenom currently in use to

treat Russell’s viper envenoming in Myanmar.

Introduction

Snake-bite envenoming (SBE) was re-categorized as a priority neglected tropical disease by the

World Health Organization (WHO) in 2017 [1, 2]. Worldwide, there are as many as 2.7 mil-

lion people affected by SBE resulting in an estimated 81,000 to 138,000 deaths per year [3–5],

the burden of which disproportionately affects the poorest communities [5–7]. Antivenom is

considered to be one of the most cost effective health interventions [8]. Despite this, due to

challenges in manufacture, reliance on cold chain for transport and storage, and the geograph-

ically remote location of most envenomed patients, many patients do not receive the anti-

venom they require in a timely manner [9]. The 2019 WHO strategy for a globally coordinated

response to SBE highlighted the need to prioritise clinical research into the safety and efficacy

of antivenoms [2].

An integral part of the antivenom clinical research pipeline is pre-clinical assessment

including the use of animal models. Pre-clinical assessment includes characterising the neutra-

lisation of venom induced lethality and reversal of specific toxic effects of the venom, and anti-

venomics [10, 11]. Additional quantitative clinical assessment of antivenom pharmacokinetic

properties (e.g. elimination half-life and volume of distribution) and pharmacodynamic prop-

erties (e.g. correction of coagulopathy, nephrotoxicity and haemodynamic instability) allows

for the rational design of dosing strategies [12]. This is rarely done for antivenoms. Comple-

mentary to pharmacological consideration, dose optimisation can be done via phase 2 clinical

trials. Ideally this is performed using adaptive design principles [13]. Adaptive designs are

needed because it is rarely possible to pre-specify a suitably small set of doses that satisfy rea-

sonable expectations for acceptable safety and efficacy. Many antivenoms will have narrow

therapeutic windows and cannot be ethically administered to healthy volunteers, therefore

dose optimisation trials need to simultaneously assess efficacy and toxicity.

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Adaptive design for antivenom dose optimisation

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Funding: The MORU Tropical Health Network is

funded by the Wellcome Trust. TL is on a

fellowship funded by the Hamish Ogston

Foundation. The funders had no role in study

design, data collection and analysis, decision to

publish, or preparation of the manuscript.

Competing interests: The authors have declared

that no competing interests exist.

Adaptive designs for dose-finding trials are of two main types. First, rule based designs

which do not make any parametric assumptions regarding the relationship between the dose

and the outcome of interest (e.g. efficacy or toxicity). A rule based design usually only assumes

that there is a monotone increasing relationship between the dose and the outcome, i.e. the

probability of the outcome increases with higher doses. The ‘3+3’ design is the best known rule

based adaptive design [14]. The standard formulation of the ‘3+3’ design proceeds by recruit-

ing successive cohorts of 3 subjects. Dose escalation for a subsequent cohort of 3 subjects

occurs if no toxicity is observed amongst the previous 3; an additional 3 are given the same

dose if toxicity is observed in only 1 out of 3; dose de-escalation occurs if toxicity is observed

in 2 or more out of the previous 3. Rule based designs do not use information accrued across

dosing levels, and therefore they have limited ability to rapidly identify the desired optimal

dose with high confidence [15]. The alternative is a model based design, which requires deter-

mining a parametric relationship (model) between the dose and the outcome, termed a dose-

response model [16]. The continual reassessment method [17] was the first proposed model

based design for dose-finding. Data from sequentially enrolled patients are used to continually

update the parameters of the dose-response model. Each enrolled patient is then assigned the

expected optimal dose under the estimated dose-response model. The original rule based

designs [14] and model based designs [17] for dose-finding were published around the same

time. Although model based designs are more efficient, more flexible and have better operating

characteristics [18], rule-based designs have been the dominant choice. For example, fewer

than 1 in 10 trials in oncology—where dose-finding is critical—have used a model based

approach [19, 20], mostly due to perceived difficulty of implementation and lack of under-

standing of the methods [21].

This paper outlines a model based, Bayesian adaptive design for phase 2 studies with the

objective of optimising antivenom dosing. The structure of the design was motivated by the

need to determine the optimal dosing for a novel antivenom developed to treat Russell’s viper

envenoming in Myanmar. Following a recent 4-year collaborative initiative between institu-

tions in Myanmar and Australia entitled the Myanmar Snakebite project, antivenom produc-

tion facilities improved, resulting in the production of a new monospecific lyophilised F(ab)2

antivenom (Viper antivenom BPI) [22]. This new lyophilised antivenom has replaced the for-

mer liquid antivenom and is now distributed countrywide. The lyophilised antivenom has the

potential to greatly improve access to antivenom as the electrification rate in Myanmar is one

of the lowest in Asia (70% in 2017 [23]). The current dosing strategy is based on unpublished

results of pre-clinical testing and stratified into two doses according to absence or presence of

clinical features of severity at presentation (80 mL and 160 mL, respectively). No clinical trial

data or post marketing data have been published to support the efficacy or toxicity of these rec-

ommended doses.

This situation in Myanmar mirrors the development of many antivenoms worldwide [2, 24,

25] and highlights the need for high quality dose-optimisation studies. There is a need to stan-

dardise the methodology of clinical trials of antivenom whilst maintaining patient safety with

robust patient monitoring built into study design. This calls for dose-finding phase 2 trials that

can rapidly identify optimal dosing strategies, while minimising harm to patients. There are

two concurrent considerations when optimising antivenom dosing. First, the efficacy of the

dose, defined in the context of Russell’s viper envenoming as the restoration of blood coagula-

tion within 6 hours. Second, the dose-related toxicity, defined in this context as the occurrence

of an anaphylactic reaction within 180 minutes post antivenom administration. Envenoming

from different snakes will require different definitions of efficacy and toxicity. In the context

of Russell’s viper envenoming in Myanmar, the choice of these two binary clinical end-points

was pragmatic due to their clinical significance, resource availability and replication of current

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Adaptive design for antivenom dose optimisation

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clinical practice. The model based design estimates dose-response curves for both the efficacy

outcome and the toxicity outcome, and thus derives a contextually defined ‘optimal dose’. The

particularities of the design reported here were tailor-made for the dose-finding trial in Daboia

siamensis envenoming but the design generalises to any systemic envenoming with clinically

relevant endpoints whereby the efficacy and toxicity outcomes are both binary, e.g. [24, 26,

27]. We compared the in silico performance of this design against that of a tailor-made rule

based design (modified ‘3+3’ design or cumulative cohort design) under multiple simulation

scenarios. The full simulation code written in R is open access and can easily be adapted to dif-

ferent antivenoms.

Methods

Model based adaptive design for dose-finding

In this section we give an overview of how doses are adaptively chosen during the trial and

describe the necessary parameters for the adaptive assignment of doses to patients sequentially

enrolled. First it is necessary to choose a randomisation ratio between the standard of care dos-

ing arm and the adaptive dosing arm. This value can be set to 0 (i.e. all patients are assigned to

the adaptive arm). Values greater than 0 result in a fixed proportion of patients assigned to the

standard of care dose. This allows for a direct comparison (model free) between outcomes

under the standard of care dose and outcomes under the dose to which the adaptive algorithm

converges after a sufficient number of patients are enrolled. It also allows for a model free esti-

mate of the efficacy and safety of the standard of care dose. The randomisation ratio is fixed

throughout the trial.

In the adaptive arm, the adaptive dose assignment will depend on (i) the parametric dose-

response models of toxicity and efficacy; (ii) the prior distribution over the model parameters;

(iii) the toxicity and efficacy data observed for the antivenom in patients treated thus far; and

(iv) the maximum tolerated toxicity and target efficacy (see below). The dose-efficacy and

dose-toxicity models are updated using data from both the standard of care arm and the adap-

tive arm throughout the trial.

Patients are enrolled in successive cohorts of a pre-specified size N

cohort

 1. The choice of

the value of N

cohort

is pragmatic as it determines how often it is necessary to update the model.

Randomisation is performed at the individual level. We assume that the toxicity and efficacy

outcomes for all previously enrolled cohorts of patients are known when a new cohort of

patients is enrolled. At the start of the trial there is a “burn-in” period (a pre-specified number

of patients). During this burn-in period, patients randomised to the adaptive arm are given the

starting dose for the adaptive arm, which is the optimal dose under the prior distribution over

the model parameters. After burn-in, patients randomised to the adaptive arm are given the

posterior predicted optimal dose under the model (the distribution over model parameters is

updated using all accrued data). If the model predicted dose is more than any previously

trialled dose plus the maximum dose increment δ

v

, then patients are given the maximum

allowed dose (the greatest previously assigned dose plus δ

v

).

For a given distribution over the model parameters, we define the optimal dose as follows.

We first define a maximum tolerated toxicity (MTT), and a target efficacy level (TEL). The

mean posterior predicted dose that has average toxicity equal to the MTT is denoted the maxi-

mum tolerated dose (MTD); and the mean posterior predicted dose that has average efficacy

equal to the TEL is denoted the target efficacious dose (TED). The optimal dose is then defined

as: V



= min(MTD, TED).

Additional parameters in the trial could include a minimum dose (the adaptively chosen

dose cannot go below this dose); a maximum dose (the adaptively chosen dose cannot go

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Adaptive design for antivenom dose optimisation

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above this dose). If a minimum or a maximum dose are defined then these should be put into

context with respect to the starting dose, the maximum dose increment or decrement and the

total sample size. The purpose of a burn-in period for the adaptive arm is to reduce stochasti-

city at the start of the trial, especially in the context of weakly informative prior distributions

over the model parameters. For example, a burn-in of 20 patients would imply that the adap-

tive arm would only be updated after the first 20 patients had been enrolled (irrespective of

how they were randomised).

In addition, it is possible to specify stopping rules for the trial. For example, randomisation

to the control arm (standard of care dose) could be stopped once sufficient evidence of its infe-

riority has been accrued (either too low and thus inferior efficacy, or too high and thus inferior

due to excess toxicity) in comparison to the current adaptive dose. We would recommend the

use of a non-parametric test (e.g. Fisher’s exact test), with appropriate adjustment for multiple

testing.

It may be the case that the antivenom used in the trial is from multiple batches. Batch varia-

tion can be an important contributor to variability in both toxicity and efficacy. It is straight-

forward to add a batch variation term in the adaptive models of efficacy and toxicity. This is an

advantage of a model based design over a rule based design.

Parametric models of toxicity and efficacy. The model based adaptive design necessi-

tates determining parametric dose-response relationships for both the dose-related toxicity

and the dose-related efficacy. We model both the efficacy and toxicity outcomes as Bernoulli

random variables with dose-dependent parameters estimated under a generalised linear

model. For the efficacy outcome we use the probit link function, and for the toxicity outcome

we use the logistic link function.

The use of the probit link for the efficacy dose-response is motivated by a mechanistic

understanding of how the antivenom acts. Assuming (i) there is a fixed linear relationship

between the volume of venom in the body (which is unknown) and the dose of antivenom

needed to neutralise all the circulating venom, and (ii) that the total mass of venom injected is

approximately normally distributed, then the efficacy dose-response curve follows a normal

cumulative distribution with mean μ and standard deviation σ (i.e. probit link with parameters

μ, σ). The parameter μ corresponds to an efficacious dose of antivenom in 50% of patients. The

value of μ + 1.64σ corresponds to an efficacious dose of antivenom in approximately 95% of

patients. Weakly informative and interpretable priors can be set for both these parameters.

We choose to model the dose-toxicity relationship using a logistic function, where the dose

is modelled on the logarithmic scale (base 2 for visual purposes, this does not impact the statis-

tical inference). This is equivalent to fitting a Bayesian logistic regression model to the toxicity

outcomes. Additional details of the Bayesian adaptive design are given in S1 Text.

A modified ‘3+3’ rule based design

In order to illustrate the advantages and disadvantages of model based adaptive designs, we

compared the in silico performance of our model based adaptive design with that of a modified

‘3+3’ rule based design. As in our model based design, patients are recruited in cohorts of size

N

cohort

. This is set to 3 in the classic ‘3+3’ design, but in our case is a trial design parameter.

The rule based design does not make parametric assumptions about the relationship between

the dose and the outcomes. For each dose v trialled, a dose-dependent frequentist estimate of

toxicity,

^

y

tox

v

, and a dose-dependent frequentist estimate of efficacy,

^

y

eff

v

, are calculated. Based

on these estimates, the dose is subsequently increased, decreased, or remains the same for the

next N

cohort

patients, according to a pre-specified set of rules and trial design parameters (the

MTT and the TEL). Our rule based design is a type of cumulative cohort design [28] as it uses

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Adaptive design for antivenom dose optimisation

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A Bayesian phase 2 model based adaptive design to optimise antivenom dosing: application to a dose-finding trial for a novel Russell's viper antivenom in Myanmar

Summary (2 min read)

Introduction

Methods

Simulation study

Results

Discussion

Author Contributions

Figures (3)

Citations

References

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