Table 3.

GEE^a models for the primary and main secondary outcomes. Binomial GEEs with a logit link, scenario as the clustering unit, an exchangeable working correlation structure, and robust SEs. Both primary main-effects models converged without warnings. Estimates involving strata with no observed unsafe major errors should be interpreted with caution. Nine of the 18 model-by-arm-by-complexity cells contained no unsafe major errors: GPT-5.3 in the low- and medium-complexity strata of arm 1 and in all 3 strata of arm 2, Gemini 3 Flash in the low-complexity stratum of arm 1 and in the low- and medium-complexity strata of arm 2, and DeepSeek V3.2 in the low-complexity stratum of arm 2. A model-by-arm interaction was examined for exact concordance and was not statistically significant (Table S5 in Multimedia Appendix 5); the corresponding interaction model for the unsafe major error-free outcome was not estimable because 9 of 18 model-by-arm-by-complexity cells contained 0 unsafe major errors.

Outcome and term		ORb (95% CI)	P value
Unsafe major error-free
	Gemini 3 Flash vs GPT-5.3	0.269 (0.162-0.447)	<.001
	DeepSeek V3.2 vs GPT-5.3	0.051 (0.022-0.119)	<.001
	Arm 2 vs arm 1	3.756 (2.446-5.767)	<.001
	Medium vs low complexity	0.303 (0.067-1.369)	.12
	High vs low complexity	0.047 (0.009-0.242)	<.001
Exact concordance
	Gemini 3 Flash vs GPT-5.3	0.145 (0.073-0.289)	<.001
	DeepSeek V3.2 vs GPT-5.3	0.014 (0.004-0.045)	<.001
	Arm 2 vs arm 1	8.269 (4.140-16.518)	<.001
	Medium vs low complexity	0.056 (0.010-0.329)	.001
	High vs low complexity	0.005 (0.001-0.032)	<.001

^aGEE: generalized estimating equation.

^bOR: odds ratio.