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PD-1 CPI therapy can generate durable responses with fewer side effects compared to conventional cytotoxic chemotherapy. Unfortunately, CPI can induce an objective response in less than 15 - 20% of non-melanoma solid tumor patients [1-3]. Multiple biomarkers have been evaluated as potential factors predicting response, but none has shown reproducible clinical utility across tumor types. Higher PD-L1 expression in tumor tissue is associated with higher response rates, but a single tumor tissue sample may not reflect spatial and temporal variability in PD-L1 expression. Circulating tumor cells can be collected at multiple timepoints with minimal risk and may provide a more comprehensive and dynamic view of tumor heterogeneity. Higher IRF-1 expression in tumor tissue has been correlated with longer progression-free survival (PFS) in metastatic melanoma patients treated with CPIs . We hypothesize that evaluating both PD-L1 and IRF-1 expression on CTCs may better predict patient response to PD-1 CPIs.
We used maximum-likelihood estimation to fit four different models to each individual session ITC choice data: two hyperbolic discounting models and two exponential discounting models. We focused on these two classes of models because they are the most prevalent in the literature. Exponential discounting provides a normative account of discounting grounded in discounted utility theory. Hyperbolic discounting often provides a better fit to behavioral human and animal data [3, 58]. Of the two hyperbolic models, one did not take risk attitude into account (assumed a linear utility function, LH) as in Eq (3) and the other (NLH) used the estimated risk attitude (the utility function curvature parameter α from Eq (1)) as in Eq (4). Similarly, for the exponential type, one model assumed a linear utility function (LE) as in Eq (5), and the other (NLE) used the α as shown in Eq (6). To evaluate these four models, we compared their cross-validated log likelihoods (LL). Note that all four models have the same number of free parameters because the α parameter in the models that incorporated a risk attitude estimate (NLH and NLE) was fixed, taken from the maximum likelihood estimation procedure performed on independent data from the RA task (Eq (1)). We employed cross-validation to avoid over-fitting by iteratively fitting the model on all trials but one and computing the log likelihood of the model for the left-out trial (see Materials and methods section). 2b1af7f3a8