Translational tumor control probability modeling for NSCLC: A two-dimensional maximum-likelihood framework

Tumor control probability (TCP) modeling for early-stage non-small cell lung cancer (NSCLC) is usually performed by one-dimensional (1D) fitting that assumes error-free dose and assigns all uncertainty to the local control (LC) axis. Neglecting dose-axis uncertainties leads to a classical errors-in-variables (EIV) problem that can bias both the dose required for 50% TCP ( $\mathrm{TC}{D}_{50}$ ) and curve steepness. Furthermore, the mechanistic origins of TCP steepness remain incompletely characterized, limiting the translational link between cellular radiobiology and clinical dose-response.

To develop a mechanistic TCP framework that (i) mitigates EIV bias by explicitly modeling uncertainties in both dose and LC, (ii) decomposes TCP steepness into contributions from clonogenic heterogeneity and inter-patient radiosensitivity, and (iii) validates the translational consistency.

Cell-survival data from A549 NSCLC cells were fitted with three radiobiological models-saturable repair and repairability (SRR), universal survival curve (USC), and linear-quadratic (LQ)-using maximum-likelihood estimation. Clinical TCP modeling used 34 early-stage NSCLC studies (41 data points, 3-year LC). Prescriptions were converted to EQD2 using each model's formalism, and TCP curves were fitted by a two-dimensional (2D) maximum-likelihood framework. The LC-axis uncertainty was constructed from binomial sampling uncertainty and an intrinsic scatter, the latter co-estimated with the effective dose-axis uncertainty. TCP steepness was measured by the inter-patient variability ${\sigma }_{\varphi }$ of the TCP exponent and decomposed into clonogenic heterogeneity ( ${\sigma }_{\ln N}$ , from reported tumor volumes) and inter-patient radiosensitivity variability ( ${\sigma }_{E_2}$ ).

In cell-survival fitting, the SRR and USC models accurately reproduced A549 survival (AIC = $-0.49$ and 0.21); the LQ model achieved the lowest AIC ( $-5.17$ ) but only by inflating $\alpha /\beta$ to 31.1 Gy. In clinical fitting, the SRR, USC, and LQ models yielded ${\mathrm{TCD}}_{50}$ = 57.1, 51.6, and 50.2 Gy EQD2 and ${\mathrm{TCD}}_{95}$ = 81.4, 71.8, and 60.5 Gy. The effective dose-axis uncertainty (16.6%, 16.9%, and 10.5%) exceeded the mean relative LC-axis uncertainty (5.0%, 5.0%, and 5.8%), supporting the need for a 2D framework. Variance decomposition revealed that clonogenic heterogeneity contributed only 3%-15% of ${\sigma }_{\varphi }^2$ , while inter-patient radiosensitivity dominated (85%-97%); ${\sigma }_{E_2}$ = 0.057-0.120 remained within the CLARIFi-derived inter-cell-line ${\sigma }_{E_2}$ bound of 0.255 (across 41 NSCLC cell lines). Fitted $N_0$ for the SRR and USC models implied mean tumor diameters of 2.6 and 3.2 cm, both falling within approximately one standard deviation of the clinical reference $2.7\pm 0.6$  cm; the LQ-model substantially overestimated the diameter (6.0 cm).

The proposed 2D maximum-likelihood framework mitigates EIV bias and links clinical TCP to mechanistic cell-survival models. In early-stage NSCLC, inter-patient radiosensitivity dominates TCP steepness while clonogenic cell-number variability contributes negligibly. This framework provides a robust basis for future TCP modeling and dose-prescription studies.