Table 1.

Model results, by correlation and estimation method

$\rho$	All confounders		No confounders		Observed confounder		IPTW		PSM caliper 0.001
	$\widehat{{\beta }_T}$	RR	$\widehat{{\beta }_T}$	RR	$\widehat{{\beta }_T}$	RR	$\widehat{{\beta }_T}$	RR	$\widehat{{\beta }_T}$	RR
0	0.197 (0.057)	1.069 (0.021)	0.310 (0.043)	1.110 (0.016)	0.262 (0.048)	1.092 (0.018)	0.263 (0.049)	1.093 (0.018)	0.267 (0.064)	1.095 (0.024)
0.1	0.202 (0.057)	1.071 (0.020)	0.327 (0.041)	1.117 (0.016)	0.258 (0.049)	1.091 (0.018)	0.261 (0.053)	1.092 (0.019)	0.263 (0.072)	1.094 (0.027)
0.2	0.206 (0.064)	1.072 (0.023)	0.343 (0.042)	1.123 (0.016)	0.258 (0.057)	1.091 (0.021)	0.260 (0.071)	1.091 (0.027)	0.262 (0.090)	1.092 (0.033)
0.3	0.202 (0.067)	1.070 (0.024)	0.358 (0.041)	1.129 (0.016)	0.247 (0.062)	1.086 (0.023)	0.271 (0.108)	1.097 (0.040)	0.264 (0.142)	1.093 (0.053)
0.4	0.198 (0.073)	1.069 (0.027)	0.370 (0.042)	1.133 (0.016)	0.233 (0.069)	1.082 (0.025)	0.287 (0.110)	1.102 (0.041)	0.239 (0.154)	1.084 (0.057)
0.5	0.201 (0.074)	1.070 (0.027)	0.383 (0.043)	1.138 (0.017)	0.224 (0.073)	1.078 (0.027)	0.314 (0.109)	1.112 (0.041)	0.242 (0.173)	1.085 (0.064)
0.6	0.201 (0.080)	1.070 (0.029)	0.393 (0.043)	1.142 (0.017)	0.217 (0.079)	1.076 (0.029)	0.342 (0.108)	1.122 (0.041)	0.246 (0.195)	1.086 (0.072)
0.7	0.200 (0.085)	1.070 (0.031)	0.401 (0.043)	1.145 (0.017)	0.206 (0.085)	1.072 (0.031)	0.366 (0.097)	1.131 (0.038)	0.236 (0.233)	1.081 (0.087)
0.8	0.200 (0.086)	1.070 (0.031)	0.414 (0.043)	1.150 (0.017)	0.203 (0.086)	1.070 (0.031)	0.384 (0.089)	1.138 (0.035)	0.217 (0.309)	1.074 (0.119)
0.9	0.204 (0.084)	1.071 (0.030)	0.426 (0.043)	1.155 (0.017)	0.205 (0.084)	1.071 (0.030)	0.411 (0.070)	1.148 (0.027)	0.235 (0.491)	1.079 (0.188)

Median and standard deviation of coefficients and Odds ratios of 1,000 simulations results. RR: Risk ratio. IPTW: Inverse probability treatment weighting. PSM: Propensity score matching