Table 2. Logistic regression likelihood ratio test and leave-one-out cross-validation (LOOCV) error (n = 103 patients).

Model	AIC	Residual df	Residualdeviance	Deviance	p-Value	LOOCV error
Null model${\displaystyle (l={\beta }_0)}$	141.26	102	139.26			0.246
Linear model${\displaystyle (l={\beta }_0+{\beta }_{1}x)}$	134.8	101	130.80	8.46(vs. null model)	0.0036**(vs. null model)	0.231
Quadratic model${\displaystyle (l={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2)}$	128.48	100	122.48	8.32(vs. linear model)	0.0039**(vs. linear model)	0.210
Cubic model${\displaystyle (l={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2+{\beta }_3{x}^3)}$	126.97	99	118.97	3.50(vs. quadratic model)	0.061(vs. quadratic model)	0.213
Natural Spline model (df = 2)${\displaystyle (l={\beta }_0+f_1\left(x\right))}$	128.29	100	122.29	8.50(vs. linear model)	0.0035**(vs. linear model)	0.210
Natural Spline model (df = 3)${\displaystyle (l={\beta }_0+f_1\left(x\right))}$	127.13	99	119.13	3.34(vs. quadratic model)	0.067(vs. quadratic model)	0.213

** p < 0.01.