. Author manuscript; available in PMC: 2024 Sep 5.

Published in final edited form as: Stat Med. 2024 Mar 15;43(11):2083–2095. doi: 10.1002/sim.10060

Table 1. Type-I error rates in scenarios with a continuous outcome and complete data (nominal α= 0.05).^a.

Covariate–outcome relationship	Unadjusted	Adjust for categories	Linear	FP-2	Cubic splines
f (X) = X, moderate	0.038	0.046	0.048	0.052	0.048
f (X) = X, strong	0.022	0.047	0.046	0.048	0.048
f (X) = e^X, moderate	0.039	0.049	0.048	0.048	0.047
f (X) = e^X, strong	0.029	0.044	0.049	0.052	0.052
f (X) = X², moderate	0.050	0.049	0.050	0.051	0.053
f (X) = X², strong	0.050	0.050	0.050	0.055	0.052
f (X) = X^strat, moderate	0.031	0.051	0.047	0.049	0.049
f (X) = X^strat, strong	0.006	0.051	0.039	0.043	0.052

The maximum Monte Carlo SE across all methods and scenarios was 0.0033.

Table 1. Type-I error rates in scenarios with a continuous outcome and complete data (nominal α= 0.05).a.