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Despite of an extensive statistical literature showing that discretizing continuous variables in substantial loss of information, categorization of continuous variables has been a common practice in clinical research and in cancer dose finding phase I clinical trials. The objective of this study is to quantify the loss of information incurred by using a discrete set of doses to estimate the maximum tolerated dose MTD in phase I trials, instead of a continuous dose support.

Escalation With Overdose Control and Continuous Reassessment Method were used because they are model-based des where dose can be specified either as continuous or as a set of discrete levels. Five equally spaced sets of doses with different interval lengths and three sample sizes with sixteen scenarios were evaluated to compare the operating characteristics between continuous and discrete dose des by Monte Carlo simulation. Loss of information was quantified by safety and efficiency measures.

We conclude that if there is insufficient knowledge about the true MTD value, as commonly happens in phase I clinical trials, a continuous dose scheme minimizes information loss. If one is required to implement a de using discrete doses, then a scheme with 9 to 11 doses may yield similar to the continuous dose scheme.

This is an open access article distributed under the terms of the Creative Commons Attributionwhich permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All relevant data are within the paper and its Supporting Information files. There was no additional external funding received for this study. The funders had no role in study de, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist. Measurements of continuous variables are made in all fields of medicine. In medical research such continuous variables are often converted into categorical variables by grouping values into two or more in order to have easier interpretations.

Cox [ 1 ] presented the first optimization criterion for discretizing a continuous variable showing the minimum loss of information as a function of the of. Since then, several authors [ 2 — 7 ] have pursued methodologies to provide optimal criteria of discretization for continuous variables based on test statistics. On the other hand, extensive statistical literature [ 8 — 14 ] has advised against categorization due the loss of power and precision of the estimated quantities.

This debate has been ignored for cancer phase I clinical trials. Phase I trials are the first step of translation of a new drug from laboratory research to clinical practice. The compromise underlying the de of cancer phase I clinical trials is that reaching the MTD as fast as possible while at the same time avoiding unacceptable toxic events.

Following the up-and-down approach, a large collection of methods estimates the MTD of a new agent using a pre-specified set of doses. However, Hu et al. Even though intravenous drugs are still more prevalent than oral drugs [ 2223 ], clinical trials using continuous dose [ 2425 ] are less often performed since clinicians are used to the up-and-down approach. In this work, a Monte Carlo simulation study to compare the operating characteristics of continuous and discrete dose using model-based des is presented.

The loss of information is evaluated using the statistical measures bias and mean squared error as well as specific measures for phase I clinical trials to quantify safety and efficacy of the trial. Other authors e. This article is organized as follows. In the next section, the EWOC de is briefly introduced. Then, a simulation study is described and its are presented with discussion.

Let X min and X max denote the minimum and maximum dose levels available for use in the trial. Note that the dose given to the first cohort of patients is not necessarily equal to X min but there must be strong evidence that it is a safe dose. Tighouart et al. Uniform distributions will be used for both parameters for simplicity. The choice of the next dose based on the posterior information depends on the de.

Notice that there are many versions of CRM i.

Following Babb et al. The feasibility bound could vary during the trial as discussed by Tighiouart and Rogatko [ 32 ]. As the trial progresses, uncertainty about the MTD declines and the likelihood of selecting a dose level ificantly above the MTD become ificantly smaller. There are several suggestions for the choice of the feasibility boundary. Originally Babb et al. Babb and Rogatko [ 33 ] suggested an increasing feasibility boundary until 0. Wheeler et al.

Both des were applied for continuous dose and discrete dose. Considering the discrete dose, five equally spaced sets with different interval lengths between two doses given by 0. The working model is the logistic model. The feasibility strategy C 0. The distributions are illustrated in Fig 1.

In the discrete dose scheme, the rounding to the nearest dose approach was applied and skipping doses was not allowed. A Monte Carlo study was performed with replicates for each study de. Posterior distribution was sampled using JAGS [ 35 ], in particular the algorithm Slice Sampling, with iterations for the adapt phase, and iterations for burn-in resulting in a sample of values for each parameter of interest without thinning.

In addition, the correct MTD recommendation was quantified using the percentage of trials with the estimated MTD within the optimal MTD interval defined as 9 and the optimal target toxicity level interval defined as 10 and the percentage of patients receiving optimal doses defined by those optimal intervals. Notice that these two criteria of optimality for doses are different measures of the distance between the true MTD and a dose.

The optimal MTD interval defines a interval around the MTD, while the optimal toxicity interval defines a interval around the target toxicity level. From the perspective of a patient participating in a dose finding trial, the best de is the one with the highest proportion of patients receiving optimal doses.

Therefore, it is important to characterize the discrete dose schemes based on the of possibles doses that could be considered optimal. Table 1 presents the of possible optimal doses using the optimal MTD interval for all four true distributions. Dose schemes D0. The dose scheme D0. The dose schemes are evaluated based on the optimal toxicity interval in Table 2.

All discrete dose schemes contain at least one optimal dose under the definition of the optimal toxicity interval if the true distribution is logistic 0, 1 or skew-normal 0, 2, 3. There are scenarios where the dose schemes D0. Percentage of trials in which the estimated MTD is inside the optimal toxicity interval and average percentage of patients receiving doses inside the optimal toxicity interval are in Fig 5. The differences in absolute bias are negligible among the dose schemes for both des.

It is still possible to observe some patterns. The dose schemes D0. In addition, D0. Moreover, D0. However, the performance of discrete des decreases compared to the continuous dose as the sample sizes increases, except D0. It is noteworthy that D0. On the other hand, D0. As expected based on Table 1D0.

Furthermore, D0. The variability of performance for D0. The under D0. CRM: The continuous dose presents a median value close to D0. For both des, D0. Therefore, they offer an ideal framework to compare the loss of information incurred by using a discrete set of doses to estimate the MTD in phase I trials, instead of a continuous dose support. This work compared such dose schemes considering sixteen scenarios and three samples sizes, with a conditional feasibility strategy for EWOC.

The six doses schemes were one with continuous dose and five different pre-specified set of doses. The set of doses are equally spaced between the minimum and maximum doses, with two dose schemes that do not contain the true MTD values. The dose schemes were evaluated based on safety and efficiency measures. Phase I clinical trials usually are performed with 5 or 6 doses chosen based on arbitrary criteria. Based on the simulations, discrete dose schemes containing 9 or 11 doses equally spaced between the minimum and maximum doses produce operating characteristics similar to the continuous dose.

A dose scheme containing 6 pre-specified doses performed well, but with an increased RMSE. Nonetheless, the assumption that the pre-specified set of doses contains the true MTD is essential to obtain acceptable operating characteristics such as: the percentage of trials such that the MTD is inside the optimal MTD and toxicity intervals, and average percentage of patients receiving optimal MTD and toxicity doses. The challenge with this assumption is that it cannot be verified in the real world, outside a simulation setup. Theoretically, the probability of selecting a point for a continuous random variable is equal to zero.

Thus, defining a pre-specified set of doses that contains the exact true MTD value seems improbable.

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