*2.2. Mutational Analysis*

*KRAS* mutational status was determined by Sanger sequencing at each center, following the protocol already used in a clinical trial by our group [10]. Briefly, DNA extraction was performed on histological tumor specimens by using standard phenol–chloroform procedure after macro/microdissection in order to recovery most of the cancer cells and to reduce contamination by normal ones. DNA preparations were verified for their concentration and quality by spectrophotometric measurement. Genomic DNAs were amplified by polymerase chain reaction (PCR) using high-fidelity Taq polymerase and specific primers encompassing intronic regions for KRAS exons 2–4. PCR products were then analyzed electrophoretically on agarose gel, and automated bidirectional sequencing was performed using BigDye Terminator chemistry. Sequences were then automatically compared with wild-type KRAS gene profiles by software analysis to assess the presence of possible mutations.

### *2.3. Immunohistochemical Analysis (IHC)*

IHC was done centrally on single slides at the Fondazione Filarete, as previously reported [11]. Sections were immune-stained with anti-DNA polymerase β antibody ab26343 (Abcam, Cambridge, UK), and incubated with biotinylated secondary goat anti-rabbit antibody (VC-BA-1000-MM15, Vector Laboratories, Burlingame, CA, USA). Sections were labeled by the avidin–biotin–peroxidase (ABC) procedure with a commercial immunoperoxidase kit (VECTASTAIN Elite ABC-Peroxidase Kit Standard, VC-PK-6100-KI01, Vector Laboratories, Burlingame, CA, USA). The immune reaction was visualized with 3,3 -diaminobenzidine peroxidase DAB substrate kit (VC-SK-4100-KI01, Vector Laboratories, Burlingame, CA, USA) substrate and sections were counterstained with Mayer's hematoxylin. Figure S1 shows representative images of negative and positive DNA polymerase β staining.

A semiquantitative H-score (percentage of positive tumoral cells x intensity: 0 = negative, 1 = slight, 2 = moderate, 3 = strong) was calculated independently by two pathologists. In case of disagreement, a third opinion was requested.

### *2.4. Outcomes*

The primary outcome of the study was progression-free survival (PFS). Secondary outcomes were objective response rate (ORR) and overall survival (OS). PFS was defined as the time from the start of the platinum-based first-line therapy to the date of progression or death from any cause, whichever came first. ORR was defined as the proportion of patients with a complete or partial response to treatment. OS was defined as the time from the platinum-based first-line therapy to the date of death from any cause.

### *2.5. Statistical Methods*

Chi-squared and Kruskal–Wallis tests were used to analyze the relations between the DNA polymerase β H-score (Polβ) and categorical clinical variables. The Spearman correlation coefficient was used to measure the correlation between Polβ and continuous clinical variables. Polβ was analyzed as a continuous and dichotomous variable (Polβ = 0 as negative and Polβ > 0 as positive).

Patients who had not died or had no disease progression were censored at their last available information on status. Survival curves were calculated with the Kaplan–Meier method and tested by the log-rank test. Cox proportional hazard models were used to analyze the impact of DNA polymerase β on PFS and OS, adjusting for clinical and pathological characteristics such as ECOG-PS, age, histology, smoking, therapy, and, only for OS, immunotherapy. Results were expressed as hazard ratios (HRs) with their 95% confidence intervals (95% CIs).

The impact of DNA polymerase β on ORR was analyzed with logistic regression models and expressed as odds ratios (ORs) with their 95% CIs, while for dichotomized analysis, the chi-square test was used. A subgroup analysis was done for patients with both Polβ and KRAS mutational status available.

All statistical tests were two-sided, and *p* < 0.05 was considered statistically significant. Statistical analyses were done using SAS version 9.4 (SAS Institute, Cary, NC, USA).
