Table 5.

MSM for the causal effects of aspirin use on the hearing loss at 4000 Hz

Method
IndCov	16.609 (0.227)	1.317 (0.059)	0.076 (1.312)	0.592 (1.389)	0.541 (1.418)	0.233 (0.880)
ExchCov	16.642 (0.228)	1.306 (0.055)	0.087 (1.045)	0.424 (0.61)	0.335 (0.723)	0.282 (0.918)
Cov	16.642 (0.228)	1.306 (0.054)	0.088 (1.036)	0.409 (0.581)	0.316 (0.702)	0.282 (0.918)
Cov	16.642 (0.228)	1.306 (0.055)	0.088 (1.04)	0.416 (0.594)	0.325 (0.711)	0.282 (0.918)
Cov	16.642 (0.228)	1.306 (0.054)	0.088 (1.036)	0.409 (0.581)	0.316 (0.702)	0.282 (0.918)
Cov	16.642 (0.228)	1.306 (0.055)	0.088 (1.04)	0.416 (0.594)	0.325 (0.711)	0.282 (0.918)
ExchTwoS	16.714 (0.42)	1.358 (0.134)	0.189 (1.401)	1.37 (1.183)	1.321 (1.684)	0.665 (1.177)
TwoS	16.716 (0.419)	1.357 (0.134)	0.09 (1.385)	1.204 (1.281)	1.217 (1.729)	0.665 (1.177)
TwoS	16.715 (0.419)	1.357 (0.134)	0.171 (1.389)	1.417 (1.305)	1.336 (1.724)	0.665 (1.177)
TwoS	16.716 (0.419)	1.357 (0.134)	0.09 (1.385)	1.204 (1.281)	1.217 (1.729)	0.665 (1.177)
TwoS	16.715 (0.419)	1.357 (0.134)	0.171 (1.389)	1.417 (1.305)	1.336 (1.724)	0.665 (1.177)

A mixed-effects model was is to estimate the treatment probability for the weight matrix. For the one-stage method, we consider the following situations: (1) using a working independent covariance matrix (IndCov); (2) using a working exchangeable covariance matrix for within subject correlation and assume independence between subjects (ExchCov); (3) using the four user-defined covariance matrices for within-subject correlation and assume independence between subjects (Cov, Cov, Cov, Cov). For the two-stage method, we consider the following situations: (1) using a working exchangeable covariance matrix for the first stage cluster-specific MSMs and combine the results using mixed-effects meta-analysis (ExchTwoS); (2) using the four user-defined covariance matrices for the first stage cluster-specific MSMs and combine the results using mixed-effects meta-analysis (TwoS, TwoS, TwoS, TwoS).