A Bayesian dose-finding design for drug combination clinical trials based on the logistic model.
Summary (3 min read)
1 Introduction
- For oncologists, the objective of phase I dose-finding studies is to determine the maximum tolerated dose (MTD), defined as the highest dose with a relatively acceptable dose-limiting toxicity (DLT) [1, 2].
- Mandrekar et al. proposed an approach incorporating the toxicity and efficacy of each agent into the identification of an optimal dosing region for the combination by using a continuation ratio model to separate each agent’s toxicity and efficacy curves [8, 9].
- Most of these existing designs rely on complicated statistical models that typically are not familiar to clinicians, which hinder their acceptance and application in practice.
- In addition, the performance of these designs seems comparable and there is no consensus which design should be used [13].
Dose-combination model
- Let there be a two-drug combination used in a phase I dose-finding clinical trial for which the dose-toxicity relationship is monotonic and increases with the dose levels.
- Before two agents can be combined, each of them typically have been thoroughly investigated individually.
- Therefore, there is often rich prior information on pj’s and qk’s and their values can be readily elicited from physicians.
- Using the prior information to define standardized dose has been widely used in dose-finding trial designs, and the most well known example perhaps is the skeleton of the continuous reassessment method (CRM) [21] with a logistic model.
- Research has shown that this approach improves the estimation stability and trial performance [2, 22].
Likelihood and posterior inference
- Under the proposed model, the likelihood is simply a product of the Bernoulli density, given by L(β0, β1, β2, β3|data) ∝ (2) We sample this posterior distribution using Gibbs sampler, which sequentially draws each of the parameters from their full conditional distributions .the authors.the authors.
- Dose finding algorithm and determination of the MTD During the trial conduct, the authors use the dose-finding algorithm proposed by Yin and Yuan [11, 10] to determine dose escalation and deescaltion, and propose a different criterion for MTD selection at the end of the trial.
- Shown in dark gray is the AUC for a toxicity probability greater than 0.4, which is equal to the probability of overdosing.
BCOPULA and BGUMBEL methods
- Yin and Yuan proposed two Bayesian methods that use copula regression for combinations.
- The parameter γ characterizes the drug interactive effect, and α and β the uncertainty of the initial guesses.
- The combination allocation algorithm is the same as that presented in Section 2.1.
- The final MTD is the combination with a toxicity probability closest to the target among the combinations already administered in the trial.
LOGODDS
- By backsolving this equation, an explicit expression for the probability of toxicity is obtained.
- A normal prior centered in 0 and with variance of 100 was chosen for the interaction parameter.
- The rest of the dose allocation process, estimation and MTD determination was the same as their proposed design in order to compare their method involving a simple interaction logistic model with other logistic models.
One-dimensional CRM
- In practice, one-dimensional CRM sometimes is used to conduct dose-combination trials [13].
- Under this method, the authors first preselect a subset of combinations, for which the toxicity probability order is known, and then apply the standard CRM to find the MTD.
- The drawback of such an approach is that the authors only investigate a subset of the whole two-dimensional dose space and may miss the true MTD.
3 Simulations
- The authors simulated 2000 independent replications of phase I trials that evaluate two agents in drug combinations, with five dose levels for Agent 1 and three for Agent 2, giving 15 possible combinations.
- The authors fixed the toxicity target at 0.3 and used an overall sample size of 60.
- The design parameters of all the designs (e.g., working model) have been calibrated via simulation before used for the comparison.
- The authors selected these features in order to employ typical trial set-ups in their simulation study.
- The authors set the length around the targeted interval, δ, at 0.1.
4 Results
- For each scenario, the authors present the correct MTD selection rate, or percentages of correct selection (PCS), in Table 2.
- For these scenarios, all model-based designs gave high PCS, whereas LOGISTIC seemed to perform better than the other methods.
- The addition of the stopping rule for unacceptable toxicity resulted in PCS that were similar to those presented above (Table 5), except in scenario 4 in which the first dose combination, (1, 1), was the MTD.
4.1 Sensitivity analysis
- The authors conducted a sensitivity analysis in order to study the performance of their design using different prior distributions and parameters values.
- According to Table 5, the authors can see that the PCS for all scenarios were very similar under these different prior distributions.
4.2 Time-to-event outcome
- In practice, a longer follow-up time may be required to assess the toxicity outcome.
- Before combination assignment, the likelihood is defined as L(β0, β1, β2, β3|data) =.
- The authors simulated the time-to-toxicity outcomes using an exponential distribution such that the toxicity probabilities at the end of follow-up matched those given in Table 1.
- Table 6 shows the results of the extended LOGISTIC for all 15 scenarios.
- The authors observe that the performance of the design decreases only slightly by 2%, and the PCS for all scenarios are still very high.
5 Discussion
- The authors have proposed a statistical method for clinical trial designs that evaluate various dose combinations for two agents.
- One benefit of their method compared with the other proposed designs is that it is also efficient when the MTDs are not necessarily located on the same diagonal.
- When combining several agents, designs developed for single-agent dose-finding trials cannot be applied to combination studies.
- This approach performs well if the target dose combinations happen to be included in the subset.
- These files are freely available upon request.
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Additional excerpts
...In scenarios with non-flat dose-toxicity surfaces we observed a decline in performance of percent selection consistent with the findings by [16] when working with copula regression models....
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13 citations
12 citations
Cites background from "A Bayesian dose-finding design for ..."
...Model based designs for estimating one or more than one MTD or have been proposed by many authors in the last decade (Thall et al., 2003; Wang and Ivanova, 2008; Yuan and Yin, 2008; Yin and Yuan, 2009a; 2009b; Braun and Wang, 2010; Wages et al., 2011a; 2011b; Shi and Yin, 2013; Tighiouart et al., 2014; Riviere et al., 2014; Mander and Sweeting, 2015; Tighiouart et al., 2016)....
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...…by many authors in the last decade (Thall et al., 2003; Wang and Ivanova, 2008; Yuan and Yin, 2008; Yin and Yuan, 2009a; 2009b; Braun and Wang, 2010; Wages et al., 2011a; 2011b; Shi and Yin, 2013; Tighiouart et al., 2014; Riviere et al., 2014; Mander and Sweeting, 2015; Tighiouart et al., 2016)....
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10 citations
References
1,402 citations
"A Bayesian dose-finding design for ..." refers methods in this paper
...In practice, one-dimensional CRM sometimes is used to conduct dose-combination trials [13]....
[...]
...We also compared the performance of this multidimensional designs with a one-dimensional CRM, CRM anti-diag, as described previously....
[...]
...As the CRM focused on only a subset of doses, it had more patients per dose to find the target doses than the multidimensional designs, given the same total number of patients....
[...]
...Under this method, we first preselect a subset of combinations, for which the toxicity probability order is known, and then apply the standard CRM to find the MTD....
[...]
...Using the prior information to define standardized dose has been widely used in dose-finding trial designs, and the most well-known example perhaps is the skeleton of the continuous reassessment method (CRM) [21] with a logistic model....
[...]
816 citations
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...Therefore, as suggested by other authors [10,16,20,26,27], we implement an algorithm-based start-up phase in order to gather enough information to estimate the j,k ....
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"A Bayesian dose-finding design for ..." refers methods in this paper
...These full conditional distributions do not have closed forms, and we use the adaptive rejection Metropolis sampling (ARMS) method [23] to sample them....
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...Our start-up phase shares the spirit of accelerated titration design [28] and can be described as follows: Treat the first cohort of patients at the lowest dose combination ....
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464 citations
"A Bayesian dose-finding design for ..." refers methods in this paper
...Following the Time-to-event Continual Reassesment Method (TITE-CRM) [30], we considered a weighted dose–toxicity relationship OwF ....
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...Following the Time-to-event Continual Reassesment Method (TITE-CRM) [30], we considered a weighted dose–toxicity relationship O wF ....
[...]