Table 1

A comparison of mean root-mean-squared error, Brier score, C-statistic and coverage of prediction intervals for 1900 permutations of modelling the relationship between training load and risk of injury in seven different ways, with predetermined relationship shapes

Relationship	Sample size	Method	RMSE	Brier score	C-statistic	Coverage (%)
U shape	22 500	Linear model	2.344	0.097	0.827	100.000
		Categorised (quartiles)	0.995	0.101	0.809	99.678
		Categorised (subjectively)	0.996	0.102	0.758	94.600
		Quadratic model	0.993	0.097	0.826	100.000
		Fractional polynomials	0.994	0.096	0.829	100.000
		Restricted cubic splines (data driven)	1.065	0.097	0.826	100.000
		Restricted cubic splines (subjectively)	0.981	0.097	0.827	100.000
	8494	Linear model	2.935	0.093	0.851	98.048
		Categorised (quartiles)	0.958	0.096	0.838	98.769
		Categorised (subjectively)	0.965	0.098	0.809	84.600
		Quadratic model	0.956	0.092	0.850	98.937
		Fractional polynomials	0.956	0.092	0.852	98.942
		Restricted cubic splines (data driven)	1.079	0.092	0.849	98.686
		Restricted cubic splines (subjectively)	0.936	0.092	0.851	98.687
J shape	22 500	Linear model	1.044	0.063	0.618	77.694
		Categorised (quartiles)	0.993	0.064	0.689	88.652
		Categorised (subjectively)	0.993	0.063	0.690	96.404
		Quadratic model	0.984	0.061	0.732	99.997
		Fractional polynomials	0.986	0.061	0.740	100.000
		Restricted cubic splines (data driven)	0.992	0.061	0.735	99.999
		Restricted cubic splines (subjectively)	0.993	0.061	0.721	99.869
	6308	Linear model	0.942	0.060	0.774	54.493
		Categorised (quartiles)	0.919	0.060	0.791	79.120
		Categorised (subjectively)	0.917	0.059	0.795	89.393
		Quadratic model	0.912	0.057	0.817	93.272
		Fractional polynomials	0.915	0.057	0.821	95.517
		Restricted cubic splines (data driven)	0.918	0.057	0.818	94.281
		Restricted cubic splines (subjectively)	0.919	0.057	0.812	89.959
Linear	22 500	Linear model	0.999	0.239	0.591	100.000
		Categorised (quartiles)	0.999	0.240	0.588	25.000
		Categorised (subjectively)	0.999	0.241	0.579	99.995
		Quadratic model	0.999	0.239	0.591	99.999
		Fractional polynomials	0.999	0.239	0.592	100.000
		Restricted cubic splines (data driven)	0.999	0.239	0.591	100.000
		Restricted cubic splines (subjectively)	0.999	0.239	0.591	99.997
	8494	Linear model	0.991	0.228	0.655	99.795
		Categorised (quartiles)	0.991	0.228	0.653	24.957
		Categorised (subjectively)	0.991	0.229	0.649	99.678
		Quadratic model	0.991	0.228	0.656	99.786
		Fractional polynomials	0.991	0.228	0.656	99.788
		Restricted cubic splines (data driven)	0.991	0.228	0.656	99.789
		Restricted cubic splines (subjectively)	0.991	0.228	0.656	99.791

RMSE, root-mean-squared error.