Table II.

Ratio of required sample sizes obtained by dividing the required sample size assuming CS or time-invariant exposure by the required sample size obtained using the observed exposure distribution for the MSCM study (r = 27, p̄_e = 0.13, ρ_e = 0.1). The cumulative exposure effect model (4) or the acute exposure effect model (5) are assumed. Calculations are reported for different scenarios of the response covariance. The true prevalence of exposure at each time point is used except for the the time-invariant exposure case, where p̄_e is used. For model (5), V (t₀) = 0 is assumed.

Exposure Covariance Assumption	Response Covariance
	ρ = 0.8					ρ = 0.5
	CS	DEX	AR(1)	RS1	RS1	CS	DEX	AR(1)	RS1	RS1
		θ = 0.5		ρb1 = 0.1	ρb1 = 0.5		θ = 0.5		ρb1 = 0.1	ρb1 = 0.5
Cumulative exposure effect (model (4))
Time-invariant	0.16	0.26	0.27	0.53	3.48	0.16	0.20	0.18	0.53	3.48
CS	1.01	1.04	1.01	1.17	1.25	1.01	1.03	1.02	1.17	1.25
Acute exposure effect (model (6))
Time-invariant	0.97	9.09	14.4	10.2	84.5	0.97	4.02	3.31	10.2	85.6
CS	0.98	0.91	0.90	0.97	0.97	0.98	0.93	0.92	0.97	0.97

¹ρ_b0,b1 = −0.5