Table 2.

Cox regression multivariable prediction model for participants with a FOBT result (either positive or negative) N = 191,081, 1676 events

Variable	Hazard Ratio	Observed Coefficient	Bootstrapped Standard Error	z	P > z	[95% Confidence Intervals]
FOBT Result Positive (reference category negative FOBT result)	70.173	4.251	0.057	74.19	<0.001	4.139	4.363
Smoking Status
Ex-smoker (reference category non-smoker)	1.141	0.132	0.050	2.61	0.009	0.033	0.230
Current smoker (reference category non-smoker)	1.265	0.235	0.090	2.61	0.009	0.058	0.411
((Alcohol + 1)/100)2*	−	3.147	1.180	2.67	0.008	0.835	5.460
((Alcohol + 1)/100)3*	−	−4.177	1.557	−2.68	0.007	−7.229	−1.125
Sex Female (reference category male)	0.850	−0.162	0.054	−2.99	0.003	−0.269	−0.056
Age/10 *	−	5.859	2.064	2.84	0.005	1.814	9.904
(Age/10)2*	−	−0.419	0.154	−2.71	0.007	−0.722	−0.116
Previous Negative BCSP FOBTs*	0.862	−0.149	0.049	−3.05	0.002	−0.245	−0.053
Family History of Gastrointestinal Cancer	1.560	0.444	0.168	2.64	0.008	0.115	0.774

Abbreviations: CI confidence intervals, FOBT faecal occult blood test (specifically guaiac). The continuous variables (Age/10) has been centred at 6.639, (Age/10)²at 44.077, ((Alcohol + 1)/100)²at 0.011, ((Alcohol + 1)/100)³at 0.001, Previous negative BCSP FOBTs at 0.507. A ‘*’ indicates that the variable is treated as continuous.

Survival Probability

$S\left(2\right)={0.9932}^{exp\left(4.25x_1+0.13x_2+0.23x_3+3.15\left({\left(\frac{x_4+1}{100}\right)}^2-0.011\right)-4.18\left({\left(\frac{x_4+1}{100}\right)}^3-0.001\right)-0.16x_5+5.86\left(\frac{x_6}{10}-6.639\right)-0.42\left({\left(\frac{x_6}{10}\right)}^2-44.077\right)-0.15\left(x_7-0.507\right)+0.44x_8\right)}$

0.9932  baseline CRC free survival at 2 years S₀(2) (the re-estimated shrunken baseline CRC free survival at 2 years was also 0.9932 when rounded) the heuristic shrinkage factor was 0.998.

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; x₁Latest FOBT result; x₂ex-smoker; x₃current smoker; x₄alcohol consumption; x₅sex; x₆age at FOBT; x₇Number of previous negative BCSP FOBTs < 80 fL; x₈Family History of GI Cancer.

The dataset derived for the multivariable modelling analysis had 1676 colorectal cancers and polyp diagnoses (sample population = 191,081) and considered 17 degrees of freedom in the model building process giving 98.59 events per variable. The final model had 10 degrees of freedom with an AIC of 34,050.33 and BIC 34,104.77 (N = 1676 when calculating BIC). Overall model fit was assessed using adjusted R²which was 0.600 (bootstrapped CI 100 reps: 0.580, 0.622) and adjusted D was 2.509. Regular R²was 0.602 with a D statistic of 2.519. The linear predictor from the final model had a mean of − 0.021 and a standard deviation of 1.630 (range: -446.458 to 5.048, IQR: -0.235 to 0.781).