Estimating Conditional Power for Sequential Monitoring of Covariate Adaptive Randomized Designs: The Fractional Brownian Motion Approach

Yiping Yang,Hongjian Zhu,Dejian Lai

doi:10.3390/fractalfract5030114

Yiping Yang, Hongjian Zhu + Show 1 more

Open Access

https://doi.org/10.3390/fractalfract5030114

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Abstract

Conditional power based on classical Brownian motion (BM) has been widely used in sequential monitoring of clinical trials, including those with the covariate adaptive randomization design (CAR). Due to some uncontrollable factors, the sequential test statistics under CAR procedures may not satisfy the independent increment property of BM. We confirm the invalidation of BM when the error terms in the linear model with CAR design are not independent and identically distributed. To incorporate the possible correlation structure of the increment of the test statistic, we utilize the fractional Brownian motion (FBM). We conducted a comparative study of the conditional power under BM and FBM. It was found that the conditional power under FBM assumption was mostly higher than that under BM assumption when the Hurst exponent was greater than 0.5.

Highlights

Since the sequential test statistics cannot converge to asymptotically Brownian motion when error terms are correlated, we propose a larger class of fractional Brownian motion for the stochastic structure of the test statistic
Test statistics derived from covariate adaptive randomized clinical trials do not follow a Brownian motion in the sequential monitoring processes when ignoring the error term covariance patterns in the statistics test formula [15]
We investigated the sequential monitoring properties in covariate adapthis study,clinical we investigated monitoring properties covariate adaptive In randomized trials underthe thesequential misspecification scenarios

Summary

Simulations for Misspecification Scenarios

Since the sequential test statistics cannot converge to asymptotically Brownian motion when error terms are correlated, we propose a larger class of fractional Brownian motion for the stochastic structure of the test statistic. Maximum likelihood method was used to estimate the Hurst exponents of the FBM for the sequential monitoring processes under the misspecification assumption. Incorrect estimators (4) and (5) and incorrect classical hypothesis test statistics (2) were used to build the sequential monitoring processes without considering the covariance terms. According to the theoretical derivation results and simulation results, sequential test statistics do not follow a Brownian motion in the covariate adaptive randomized clinical trials sequential monitoring processes when error terms are correlated. Histogramsfor forestimated estimated values design, increments of FBM, no covariate, two discrete covariates, two continuous covariates. Test statistics derived from covariate adaptive randomized clinical trials do not follow a Brownian motion in the sequential monitoring processes when ignoring the error term covariance patterns in the statistics test formula [15]. The independent increment property is not satisfied under the misspecification assumption for the covariate adaptive

Conditional Power for Covariate Adaptive Randomized Clinical Trials with

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