Steve Jiang, Daniel F. Heitjan


Tumor xenograft experiments are a popular tool of cancer biology research. In a typical such experiment, one implants a set of animals with an aliquot of the human tumor of interest, applies various treatments of interest, and observes the subsequent response. Efficient analysis of the data from these experiments is therefore of utmost importance. This dissertation proposes three methods for optimizing cancer treatment and data analysis in the tumor xenograft context. The first of these is applicable to tumor xenograft experiments in general, and the second two seek to optimize the combination of radiotherapy with immunotherapy in the tumor xenograft context.

In tumor xenograft experiments, one commonly observes that growth is exponential (log-linear) initially but later decelerates. For this reason, it is common to model tumor volume using a sigmoid growth curve such as the Gompertz, wherein growth increases in what first appears to be an exponential curve and then decelerates, eventually reaching a plateau. Scientists have advanced multiple biological hypotheses to explain this phenomenon. We propose that a contributing factor in the context of in vivo tumor xenograft studies may be the loss of animals whose tumors are growing most quickly. As they die or require sacrifice, we are left with only the smaller, slower-growing tumors on the remaining animals. To illustrate this point, we show via simulation that the performance of the Gompertz model exceeds that of the exponential when fit to the average of incomplete exponential data where larger tumors are subject to truncation. A log-linear mixed model, however, effectively recovers the individual exponential curves. We conduct an analysis of real tumor xenograft data using these models, which shows that while tumor growth appears Gompertz when analyzing the averages of the available tumor volumes, an exponential mixed model fits well to the individual curves.

The efficacy of a radioimmunotherapy regimen for cancer treatment is sensitive to the radiation fractionation scheme. Chapter 2 develops and evaluates a generalized, adaptive method to identify the optimal radiation regimen for use with immunotherapy in the context of a sequential tumor xenograft experiment. We use a predictive model, updated after each new observation, to forecast future tumor growth under each of a set of candidate radioimmunotherapy regimens, selecting the one that yields the best result. We evaluate and compare three versions of our method, characterized by three different predictive models used for forecasting, in a simulation experiment that models an adaptive in vivo tumor xenograft study. We observe that the predictive system characterized by a linear spline mixed model best balances efficiency and robustness and therefore provides the most use in practical applications.

We also develop a Reinforcement Learning system to learn and generate such personalized optimal radiotherapy regimens, which is described in Chapter 3. This model was developed based on a set of pre-clinical experimental data and can capture, in the context of combination therapy, the dependence of performance on radiotherapy scheduling. The timings chosen by the agent outperform the fixed application of the best-performing timing observed in an in vivo experiment to all individuals. This preliminary endeavor provides methodological foundation for a future adaptive in vivo tumor xenograft experiment, and potentially a subsequent human trial.

Degree Date

Spring 5-13-2023

Document Type


Degree Name



Statistical Science


Daniel F. Heitjan

Second Advisor

Steve Jiang

Subject Area


Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License