SUPPLEMENTARY MATERIALS
METHODS
Details of the cure-fraction model
In the non-mixture cure fraction model, the all-cause survival is:
S(t) = S*(t) exp {ln(π)Fz(t)}(1)
Where π is the cure fraction and Fz is the cumulative distribution function chosen to be 1- Sz(t) and where Sz(t) is the parametric survival function fitted using the Weibull distribution.8,12 The estimated cure fraction of patients occurs when t equals infinity, which is the asymptote of the Weibull curve. The survival function for the non-mixture model can also be written as:
S(t) = S*(t) (π + (1- π )((π^Fz(t) – π) /(1- π)))(2)
which enables estimation of both the cure proportion (π) and the survival of the "uncured" (1- π). The λ (scale parameter) and γ (location parameter) coefficients of the Weibull model were appropriately fitted. 8,12 The impact of the clinical and the tumoral variables in determining the cure fraction of the subgroups was also calculated using a proportional excess hazards model.Median survival of the “uncured” patients was obtained from the cure model by solving the following equation:
tMedian = (-ln(0.5)/ λ) ^ (1/γ) (3)
Finally, time to cure was assessed. Time to cure must be interpreted as the minimum time a patient must survive before a clinician can assess the patient for a possible presence of a cure. Cure models define cure as occurring when time tends to infinite and time to cure was here calculated assuming a 99% level of confidence (alpha=0.01).
The estimations of expected survival, S*(t), and of the expected hazard of the general population, h*(t), at the time of patient event (death or recurrence) were derived from population survival tables obtained from the Italian National Institute of Statistics, matched by age and sex.14
Statistical analysis
Differences between categorical features were compared with the Fisher’s exact test. Since a normal distribution could not be confirmed for the majority of the continuous variables (Kolmogorov-Smirnov test), these are reported as medians and interquartile ranges (25th and 75th percentiles), and differences were compared with a non-parametric test (Mann-Whitney test). Overall survival (OS) was computed from the day of hepatic resection until death or the most recent follow-up visit. Survival rates at different temporal end-points were obtained using the Kaplan-Meier method. The estimations of expected survival of the general population at the time of patient event (death or recurrence) were derived from population survival tables obtained from the Italian National Institute of Statistics, matched by age and sex.14 Variables having a non-negligible effect (p<0.05) on the cure fraction were entered into the multivariate cure model. Statistical analyses were computed using STATA software (StataCorp. 2011. College Station, TX: StataCorp LP). The cure model was computed using the strsnmix package.12 A p-value <0.05 was considered statistically significant. The study was approved by the Institutional Review Boards of all three participating centres.
RESULTS
Relationship between variables
Compared to older patients, those <60 years of age were more frequently N+ (76.2% vs. 65.2%; p=0.001), and had synchronous metastases (61.0% vs. 48.6%; p=0.001) and 4 or more metastases more frequently (35.1% vs. 24.2%; p=0.001). Data regarding adjuvant chemotherapy after hepatic resection were available for 830 patients. Patients receiving adjuvant chemotherapy had a more aggressive and advanced tumour at the time of colonic and hepatic surgery as indicated by a higher prevalence of primary T3-T4 tumours (91.6% vs. 84.7%;p=0.008), higher primary tumour node invasion (71.8% vs. 64.6%; p=0.058), a higher prevalence of synchronous metastases (56.0% vs. 44.4%; p=0.006), a lower prevalence of disease-free survival, from primary colonic surgery, >24months (20.6% vs. 30.2%; p=0.008) and a higher prevalence of metastases ≥4 (30.4% vs. 19.6%; p=0.003). Patients who experienced at least one postoperative complication had synchronous metastases (59.4% vs. 50.0%; p=0.006) and a tumour size ≥5cm (37.0% vs. 23.6%; p=0.001) more frequently in comparison to patients who experienced an uneventful postoperative course.
Cure model results on overall survival
Considering overall survival, instead of DFS, as a survival measure, the time to equalize the death-rate after surgery for CLM of the whole study population to the death-rate of the general population was 7.9 years (95%C.I.6.3 –10.1). Using the same survival end-point, in the multivariate final model of Table 3, the constant term was 78.9% (95%C.I.68.3 – 89.3), representing the probability to equalize the death-rate of the general population, regardless of tumour recurrence, for patients with an N0 primary tumour and the metachronous presentation of a single lesion not larger than 3cm. Additional covariate effects were as follows: N+ = -22.1% (95%C.I.-31.3 – -12.9); synchronous metastases = -2.8% (95%C.I.-10.6 – -0.5); 2 or 3 liver metastases = -10.0% (95%C.I.-14.5 – -5.9); metastases ≥4 = -20.0% (95%C.I.-29.0 – -11.8); tumour size 3 – 5cm = -13.5% (95%C.I.-18.9 – -8.9);, tumour size ≥ 5cm= -27.0% (95%C.I.-37.8 – -17.8).