Table 1.
Five data sets were used in this study. The original number of patients in each data set and the treatment arm/subgroups are reported in this table. Two of the data sets have more than one treatment arm (Atezolizumab and Docetacxel) and the others have only one arm with a number of subgroups defined by clinical features. No. = Number, Pats. = Patients.
Table 2.
Detailed summary of included studies.
Data from five studies were used in this work. All studies can be identified either by their clinical trial registry number (“NCT …”) or by their Roche ID (“GO …”).
Fig 1.
(A) Longest tumor diameter over time for all lesions in representative patients in each data set. (B) Number of patients in each dataset. (C) Tumors can be categorized in three trajectory types based on their response to the treatment: Up, Down, Fluctuate. (D) Proportions of trajectory type in each dataset. (E) Initial RECIST status does not predict final RECIST status.
Table 3.
Model description and interpretation of the parameters.
For all differential equation models in the current study, the model name, equations and variables are listed. *birth rate and growth rate can be combined to one parameter, the effective growth rate.
Fig 2.
Experimental design and model fit.
(A) In experiment #1, models were fitted to all available data points for each patient (only for patients with at least 3 or 6 data points, respectively). In experiment #2, models were fitted to all but the last 3 data points for all patients with at least 6 data points. Then, the predictions for the last 3 data points were compared with the actual values. (B) Fit and prediction for three representative patients. (C) Plot of real data points and fitted data points for all models for all studies. A larger deviation from the diagonal indicates a worse fit. Models with a “raincloud” appearance systematically underestimate true tumor volume.
Fig 3.
Head-to-head comparison of all models.
(A) Model fit for all treatment arms in all trials, stratified by final RECIST, for all models. The loss function is the Mean Absolute Error (MAE, L1-Loss), after row-wise normalization. (B) Corresponding plot without row-wise normalization, showing the raw MAE. The worst MAE in each figure is indicated with “#” and best one is indicated with “*”. (C) Corresponding plot showing the Akaike Information Criterion (AIC) which penalizes models with a large number of free parameters, row-wise normalized. (D) Corresponding plot without row-wise normalization.
Fig 4.
Fit of the exponential model and the General Bertalanffy model to unseen data.
(A) Fit (blue) of the exponential model to the full timeline of representative patients with “up”, “down” and “fluctuate” trajectories. For the same patients, the prediction (yellow) is shown which was fitted to all points except the last three data points. (B) Corresponding plot for the General Bertalanffy model. The y axis is the relative tumor volume with respect to the largest tumor in the whole dataset, shown as 10^-3.