What is the test for judicial review of a denial of a statutory preemptory challenge to a trial judge?

In a different context, we note that judicial review of the denial of a statutory preemptory challenge to a trial judge is subject to review only by extraordinary writ and may not be reviewed on direct appeal of the final judgment. (Code Civ. Proc., 170.3; People v. Brown (1993) 6 Cal.4th 322, 334-335, 24 Cal.Rptr.2d 710, 862 P.2d 710.) (However, a "nonstatutory" due process claim of judicial bias may be raised on direct appeal from a final judgment. (People v. Brown, supra, at p. 335, 24 Cal.Rptr.2d 710, 862 P.2d 710.).)