Sample size calculations based on a difference in medians for positively skewed outcomes in health care studies

Table 2 Results from the simulation study where outcome data have Exponential distributions

Significance level = 0.05, Power = 0.9
						Estimated power from simulation study
Scenario	m ₁	m ₂	ϕ ₁	ϕ ₂	n	log t-test	M-W test	t-test
1	0.1	0.3	\(\frac {0.1}{\log (2)}\)	\(\frac {0.3}{\log (2)}\)	13	0.576	0.600	0.661
2	1	1.5	\(\frac {1}{\log (2)}\)	\(\frac {1.5}{\log (2)}\)	91	0.567	0.650	0.769
3	10	7	\(\frac {10}{\log (2)}\)	\(\frac {7}{\log (2)}\)	117	0.564	0.649	0.768
4	20	15	\(\frac {20}{\log (2)}\)	\(\frac {15}{\log (2)}\)	180	0.565	0.654	0.772
5	60	48	\(\frac {60}{\log (2)}\)	\(\frac {48}{\log (2)}\)	299	0.564	0.653	0.775
6	80	70	\(\frac {80}{\log (2)}\)	\(\frac {70}{\log (2)}\)	833	0.565	0.654	0.778

Here, m _j and ϕ _j denote the median and standard deviation of the outcome data for group j. Estimated powers are shown for a two-sample t-test of log-transformed outcomes (‘log t-test’), a Mann-Whitney U test of untransformed outcomes (‘M-W test’) and a two-sample t-test of untransformed outcomes (‘t-test’)

ISSN: 1471-2288