A simple model of a growing tumour

Explaining in-vitro to in-vivo efficacy correlations in oncology pre-clinical development via a semi-mechanistic mathematical model

In-vitro to in-vivo correlations (IVIVC), relating in-vitro parameters like IC50 to in-vivo drug exposure in plasma and tumour growth, are widely used in oncology for experimental design and dose decisions. However, they lack a deeper understanding of the underlying mechanisms. Our paper therefore focuses on linking empirical IVIVC relations for small-molecule kinase inhibitors with a semi-mechanistic tumour-growth model. We develop an approach incorporating parameters like the compound's peak-trough ratio (PTR), Hill coefficient of in-vitro dose-response curves, and xenograft-specific properties. This leads to formulas for determining efficacious doses for tumor stasis under linear pharmacokinetics equivalent to traditional empirical IVIVC relations, but enabling more systematic analysis. Our findings reveal that in-vivo xenograft-specific parameters, specifically the growth rate (g) and decay rate (d), along with the average exposure, are generally more significant determinants of tumor stasis and effective dose than the compound's peak-trough ratio. However, as the Hill coefficient increases, the dependency of tumor stasis on the PTR becomes more pronounced, indicating that the compound is more influenced by its maximum or trough values rather than the average exposure. Furthermore, we discuss the translation of our method to predict population dose ranges in clinical studies and propose a resistance mechanism that solely relies on specific in-vivo xenograft parameters instead of IC50 exposure coverage. In summary, our study aims to provide a more mechanistic understanding of IVIVC relations, emphasizing the importance of xenograft-specific parameters and PTR on tumor stasis.

Radius additivity score: a novel combination index for tumour growth inhibition in fixed-dose xenograft studies

The effect of combination therapies in many cancers has often been shown to be superior to that of monotherapies. This success is commonly attributed to drug synergies. Combinations of two (or more) drugs in xenograft tumor growth inhibition (TGI) studies are typically designed at fixed doses for each compound. The available methods for assessing synergy in such study designs are based on combination indices (CI) and model-based analyses. The former methods are suitable for screening exercises but are difficult to verify in in vivo studies, while the latter incorporate drug synergy in semi-mechanistic frameworks describing disease progression and drug action but are unsuitable for screening. In the current study, we proposed the empirical radius additivity (Rad-add) score, a novel CI for synergy detection in fixed-dose xenograft TGI combination studies. The Rad-add score approximates model-based analysis performed using the semi-mechanistic constant-radius growth TGI model. The Rad-add score was compared with response additivity, defined as the addition of the two response values, and the bliss independence model in combination studies derived from the Novartis PDX dataset. The results showed that the bliss independence and response additivity models predicted synergistic interactions with high and low probabilities, respectively. The Rad-add score predicted synergistic probabilities that appeared to be between those predicted with response additivity and the Bliss model. We believe that the Rad-add score is particularly suitable for assessing synergy in the context of xenograft combination TGI studies, as it combines the advantages of CI approaches suitable for screening exercises with those of semi-mechanistic TGI models based on a mechanistic understanding of tumor growth.

Exploring a model-based analysis of patient derived xenograft studies in oncology drug development

Purpose

To assess whether a model-based analysis increased statistical power over an analysis of final day volumes and provide insights into more efficient patient derived xenograft (PDX) study designs.

Methods

Tumour xenograft time-series data was extracted from a public PDX drug treatment database. For all 2-arm studies the percent tumour growth inhibition (TGI) at day 14, 21 and 28 was calculated. Treatment effect was analysed using an un-paired, two-tailed t-test (empirical) and a model-based analysis, likelihood ratio-test (LRT). In addition, a simulation study was performed to assess the difference in power between the two data-analysis approaches for PDX or standard cell-line derived xenografts (CDX).

Results

The model-based analysis had greater statistical power than the empirical approach within the PDX data-set. The model-based approach was able to detect TGI values as low as 25% whereas the empirical approach required at least 50% TGI. The simulation study confirmed the findings and highlighted that CDX studies require fewer animals than PDX studies which show the equivalent level of TGI.

Conclusions

The study conducted adds to the growing literature which has shown that a model-based analysis of xenograft data improves statistical power over the common empirical approach. The analysis conducted showed that a model-based approach, based on the first mathematical model of tumour growth, was able to detect smaller size of effect compared to the empirical approach which is common of such studies. A model-based analysis should allow studies to reduce animal use and experiment length providing effective insights into compound anti-tumour activity.