Variable | Hazard Ratio | Observed Coefficient | Bootstrapped Standard Error | z | *P* > z | [95% Confidence Intervals] |
---|

**Smoking Status** |

Ex-smoker (reference category non-smoker) | 1.238 | 0.214 | 0.078 | 2.75 | 0.006 | 0.061 | 0.366 |

Current smoker (reference category non-smoker) | 1.499 | 0.405 | 0.148 | 2.74 | 0.006 | 0.116 | 0.694 |

**Sex Female (reference category male)** | 0.777 | −0.252 | 0.074 | −3.42 | 0.001 | −0.397 | −0.108 |

**(Age/10)**^{− 2}***** | − | − 1581.596 | 639.251 | −2.47 | 0.013 | − 2834.505 | − 328.687 |

**(Age/10)**^{− 2}**x ln(Age/10) *** | − | 1094.918 | 460.929 | 2.38 | 0.018 | 191.514 | 1998.322 |

**Previous Negative BCSP FOBTs *** | 0.761 | −0.272 | 0.066 | −4.11 | <0.001 | −0.403 | − 0.142 |

**GP ordered Blood Test** | 1.286 | 0.251 | 0.067 | 3.76 | <0.001 | 0.121 | 0.382 |

**IBS Diagnosis** | 1.415 | 0.347 | 0.123 | 2.83 | 0.005 | 0.106 | 0.588 |

*Abbreviations: CI = confidence intervals, FOBT = faecal occult blood test (specifically guaiac). The continuous variables (Age/10)*^{−2}*has been centred at 0.023, (Age/10)*^{− 2}*x ln(Age/10) at 0.043, Previous negative BCSP FOBTs at 0.510. A ‘*’ indicates that the variable is treated as continuous**Survival Probability*- \( S(2)={0.9909}^{\exp \left(0.21{x}_1+0.41{x}_2-0.25{x}_3-1582\left(\ {\left(\frac{x_4}{10}\right)}^{-2}-0.023\right)+1095\left(\ {\left(\frac{x_4}{10}\right)}^{-2}\ast \ln \left(\frac{x_4}{10}\right)-0.043\right)-0.27\left({x}_5-0.510\right)+0.251{x}_6+0.347{x}_7\right)} \)
- 0.9909 baseline CRC free survival at 2 years S
_{0}(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) *Event Probability**P = 1 – S(2).**Where P is the probability of colorectal cancer/polyp being diagnosed within 2 years of the latest FOBT date; x*_{1}*ex-smoker; x*_{2}*current smoker; x*_{3}*sex; x*_{4}*age at FOBT; x*_{5}*Previous negative BCSP FOBT; x*_{6}*GP ordered blood test; x*_{7}*presence of IBS.**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 R*^{2}*which was 0.066 (bootstrapped CI 100 reps: 0.046, 0.100). Regular R*^{2}*was 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).*