Table 3.

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

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)− 2x 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)⁻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

Survival Probability

$S\left(2\right)={0.9909}^{exp\left(0.21x_1+0.41x_2-0.25x_3-1582\left({\left(\frac{x_4}{10}\right)}^{-2}-0.023\right)+1095\left({\left(\frac{x_4}{10}\right)}^{-2}\ast ln\left(\frac{x_4}{10}\right)-0.043\right)-0.27\left(x_5-0.510\right)+0.251x_6+0.347x_7\right)}$

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)

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; x₁ex-smoker; x₂current smoker; x₃sex; x₄age at FOBT; x₅Previous negative BCSP FOBT; x₆GP ordered blood test; x₇presence 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 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).