tumour growth modelling
The difference in baseline tumour growth rate may affect treatment efficacy. However, tumours grow at very different rates. For example, the untreated patient-derived colorectal cancer xenograft tumours in mice, as shown in the Novartis mouse clinical trial in 2014, grew by 0.005-0.172 mm/day. This demonstrates over 30-fold difference! Predicting tumour growth rate using gene expression data is hard. Firstly, which tumour growth rate law should you choose for which type of tumour? Secondly, gene expression data are inherently noisy, which makes constructing gene signature risky.
Tumour growth rate laws
We have tested 5 tumour growth rate laws using 224 untreated patient-derived xenografts grown in mice, which represent 6 histology including
gastric cancer (n = 44)
colorectal cancer (n = 42)
breast cancer (n = 39)
non-small cell lung cancer (n = 29)
pancreatic ductal adenocarcinoma (n = 37)
cutaneous melanoma (n = 33)
To fit this dataset, exponential-linear, logistic and Gompertz models collapse back down to a simpler rule: the exponential growth model. In addition, the cubic model (assuming the diameter changes linearly with time, and hence the tumour volume changes cubically with time) fit the data equally well.
RWR-LASSO regression
The single biggest challenge for gene signature is they are built on noisy data. Unfortunately, most signatures cannot be applied to dataset that are not used for construction. In fact, most signatures for breast cancer metastasis is no better than random guess!
We developed a network-based regression method which combined Random Walk with Restart and LASSO regression. It is a gradient-based method. It is fast. We are testing its utility in predicting the growth rate of untreated patient-derived xenograft tumours in mice.