# Table 3 Cox regression multivariable prediction model for patients with negative FOBTs only n = 187,470, 735 events

VariableHazard RatioObserved CoefficientBootstrapped Standard ErrorzP > z[95% Confidence Intervals]
Smoking Status
Ex-smoker (reference category non-smoker)1.2380.2140.0782.750.0060.0610.366
Current smoker (reference category non-smoker)1.4990.4050.1482.740.0060.1160.694
Sex Female (reference category male)0.777−0.2520.074−3.420.001−0.397−0.108
(Age/10)− 2*− 1581.596639.251−2.470.013− 2834.505− 328.687
(Age/10)− 2x ln(Age/10) *1094.918460.9292.380.018191.5141998.322
Previous Negative BCSP FOBTs *0.761−0.2720.066−4.11<0.001−0.403− 0.142
GP ordered Blood Test1.2860.2510.0673.76<0.0010.1210.382
IBS Diagnosis1.4150.3470.1232.830.0050.1060.588
1. Abbreviations: CI = confidence intervals, FOBT = faecal occult blood test (specifically guaiac). The continuous variables (Age/10)−2has been centred at 0.023, (Age/10)− 2x ln(Age/10) at 0.043, Previous negative BCSP FOBTs at 0.510. A ‘*’ indicates that the variable is treated as continuous
2. Survival Probability
3. $$S(2)={0.9909}^{\exp \left(0.21{x}_1+0.41{x}_2-0.25{x}_3-1582\left(\ {\left(\frac{x_4}{10}\right)}^{-2}-0.023\right)+1095\left(\ {\left(\frac{x_4}{10}\right)}^{-2}\ast \ln \left(\frac{x_4}{10}\right)-0.043\right)-0.27\left({x}_5-0.510\right)+0.251{x}_6+0.347{x}_7\right)}$$
4. 0.9909  baseline CRC free survival at 2 years S0(2) (the re-estimated shrunken baseline CRC free survival at 2 years was also 0.9909 when rounded) the heuristic shrinkage factor was 0.914 where S(2) is the survival probability at 2 years (probability of not being diagnosed with colorectal cancer/polyps)
5. Event Probability
6. P = 1 – S(2).
7. Where P is the probability of colorectal cancer/polyp being diagnosed within 2 years of the latest FOBT date; x1ex-smoker; x2current smoker; x3sex; x4age at FOBT; x5Previous negative BCSP FOBT; x6GP ordered blood test; x7presence of IBS.
8. There were 735 events (sample population = 187,470) and considered 16 degrees of freedom giving 45.94 events. The final model had 8 degrees of freedom with an AIC of 16,686.66 and BIC of 16,723.46 (N = 735 when calculating BIC)). Overall model fit was assessed using adjusted R2which was 0.066 (bootstrapped CI 100 reps: 0.046, 0.100). Regular R2was 0.072 (95% CI: 0.047, 0.102) with D statistic of 0.572. The linear predictor from this model had a mean of − 0.021 and a standard deviation of 0.363 (range: -1.418 to 1.206, IQR: -0.287 to 0.211).