Table 3.

Sample Sizes Required to Achieve Adequate Power for Main Effects, Versus Interaction Effects

Proportion of Sample with Multimorbidity	Subgroup Analyses (No.)	Sample Size Needed for Test of Main Treatment Effect (A)	Sample Size Needed for Test of Treatment Effect Modification by Multimorbidity (B)	Sample Size Multiplier to Study Multimorbidity Interaction (B / A)
0.0	n/a	800	n/a	n/a
0.2	1	800	9,700	12.1
	2	1,000	11,400	11.4
	3	1,100	12,800	11.6
0.5	1	1,300	6,400	4.9
	2	1,600	7,600	4.8
	3	1,800	9,100	5.1

Assumptions are: study power = 0.8; the main treatment effect is a RR of 0.7; multimorbidity increases the outcome by a RR of 1.25; multimorbidity has a synergistic effect, increasing the treatment effect by a factor of 0.8 from 0.7 to 0.56; the baseline hazard rate is five events per 100 person-years; proportion of sample censored is 0.6. For two or three subgroup analyses, the family-wise type I error probability is kept at 0.05 according to a Bonferroni correction. Estimates are based on 10,000 simulations using the Cox proportional hazards model