Imputation of Truncated Tumor Growth Data Via Bayesian Mixed Modelling
ML Bleile1,2*, Yixun Xing 2,3, Casey Timmerman4, Dan Nguyen 2,5, Benjamin Chen 5, Michael Story 5, Robert Timmerman 5, Debabrata Saha 5, Steve Jiang 2,5, Daniel Heitjan 1,6 (1) Southern Methodist University Statistical Science Department, Dallas, TX, (2) UT Southwestern MAIA lab, Dallas, TX, (3) Texas Wesleyan University Applied Statistics and Chemistry, Fort Worth, TX, (4) UT Southwestern Pathology, Dallas, TX, (5) UT Southwestern Radiation Oncology, Dallas, TX, (6) UT Southwestern Population and Data Sciences, Dallas, TX
Presentations
TU-IePD-TRACK 6-1 (Tuesday, 7/27/2021) 3:00 PM - 3:30 PM [Eastern Time (GMT-4)]
Purpose: Dropout occurs when an experimental unit, on which one is taking serial measurements, becomes unavailable for further evaluation prior to the planned end of follow-up. A common instance of dropout is the removal of mice from tumor xenograft experiments, which occurs when the animals either naturally die or undergo sacrifice for morbidity. The unobserved tumor volumes from the lost animals are not, strictly speaking, missing, because the animals are no longer alive. Nevertheless, one approach to analyzing such studies is to treat these truncated data values as missing observations and apply techniques from the statistical modeling of dropout in longitudinal studies. We introduce a novel method for imputing the lost tumor volume values, as well as an R package that implements the method.
Methods: Based on data of measured tumor volumes of mice at multiple prescribed times, we modeled the series of log tumor volumes for each mouse as a set observations from a multivariate Gaussian distribution. We estimated this model using a Bayesian approach, and sampling values from the posterior distribution of the mean and variance. Using these, for each mouse with dropout we impute the counterfactual tumor volumes (i.e., sample from its predictive distribution), conditional on its observed sequence. We have implemented the method in an R package.
Results: Plots of the imputed values reveal consistency with the trend of the observed data. Simulation revealed that the method captures true values reliably. Our R package, tgmix, is available on Github.
Conclusion: We have created a computational tool which allows users to impute counterfactual values in longitudinal datasets with dropout. Further directions may include computational optimization of efficiency in implementation, more extensive tests of the method via simulation, and modification of the method to account for different types of dropout, potentially including nonignorable (biased) dropout.
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