Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer

Abstract

The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.

Fig. 1. Schematic illustrating the family of resistance models.

Sensitive cells are illustrated as blue circles, pre-existing resistant cells as red-striped circles, spontaneously-created resistant cells as black-and-white checkered circles, and drug-induced resistant cells as black-and-white checkered diamonds. Second row contains all models without pre-existing resistance, and the third row contains all models with pre-existing resistance. Second column contains all models with no acquired resistance, third column contains all models with randomly acquired resistance, and fourth column contains all models with drug-induced resistance.

Fig. 2. Best fit exponential, logistic, and Allee model for three representative mice.

a Mouse 23 representing the case where the tumor volume increases. b Mouse 11 representing the case where the tumor volume decreases. c Mouse 22 representing the case where the tumor volume remains relatively stable.

Fig. 3. AIC and BIC comparisons across control models.

a, b The number of mice for which each model has the lowest IC value (i.e., is the most parsimonious model), with (a) using AIC and (b) using BIC. c, d The number of mice for which each model has the highest IC value (i.e., is the least parsimonious model), with (c) using AIC and (d) using BIC. We have low confidence in our classification (blue) when the IC value corresponding to the most parsimonious (or least parsimonious, for high IC) model varies by 5% or less from the other IC values. We have medium confidence (red) when it varies by 5–10%, and high confidence (yellow-orange) when it varies by >10%.

Fig. 4. Best fit of six proposed resistance models to treatment data for three representative mice.

a Mouse 13 representing the case where the tumor volume increases in spite of treatment. b Mouse 23 representing the case where the tumor volume decreases during treatment. c Mouse 24 representing the case where the tumor volume remains relatively stable during treatment.

Fig. 5. AIC and BIC comparisons across treatment models when exponential growth is used.

a, b The number of mice for which each model has the lowest IC value (i.e., is the most parsimonious model), with (a) using AIC and (b) using BIC. c, d The number of mice for which each model has the highest IC value (i.e., is the least parsimonious model), with (c) using AIC and (d) using BIC. Confidence in model selection is also shown, as described in detail in Fig. 3.

Fig. 6. Profile likelihood curves of the initial resistance fraction for a representative mouse, Mouse 1.

a The resistance fraction in Model 1.2 is practically identifiable and places the optimal parameter at approximately 55%. b The resistance fraction in Model 3.2 is not practically identifiable.

Fig. 7. Dose escalation study of median reduction in tumor volume (relative to initial volume) after 2 weeks.

Dose varies from 16 to 20 mg/kg. Growth is assumed to be exponential. a Plausible models involving no pre-existing resistance. b Plausible models including pre-existing resistance.