Dichotomisation using a distributional approach when the outcome is skewed

Sauzet, Odile; Ofuya, Mercy; Peacock, Janet L

doi:10.1186/s12874-015-0028-8

BMC Medical Research Methodology

Table 2 Summary of the simulation results per sample size per group and skewness (measured by the log-standard deviation)

From: Dichotomisation using a distributional approach when the outcome is skewed

Bias of estimates*		Summary statistic: 3rd quartile of the absolute value
Log standard deviation		0.02	0.05	0.08	0.1	0.2	0.4	0.6	1
	Sample size
Diff. in prop.	20	0.03	0.03	0.05	0.06	0.08	0.38	0.94	2.20
	50	0.02	0.03	0.04	0.04	0.12	0.39	1.03	2.38
	100	0.01	0.03	0.03	0.05	0.11	0.41	1.04	2.46
	500	0.01	0.03	0.03	0.03	0.12	0.40	1.07	2.50
Risk ratio	20	0.09	0.09	0.09	0.09	0.07	0.05	0.07	0.10
	50	0.03	0.03	0.03	0.03	0.02	0.04	0.06	0.11
	100	0.02	0.01	0.01	0.01	0.02	0.03	0.06	0.10
	500	<0.01	<0.01	0.01	0.01	0.01	0.03	0.06	0.10
Odds ratio	20	0.24	0.25	0.25	0.25	0.25	0.22	0.23	0.32
	50	0.09	0.09	0.09	0.09	0.08	0.09	0.13	0.23
	100	0.04	0.04	0.04	0.04	0.04	0.06	0.11	0.21
	500	0.01	0.01	0.01	0.01	0.01	0.04	0.11	0.23
Bias of Standard errors**		Summary statistic: 3rd quartile of the absolute value
Log standard deviation		0.02	0.05	0.08	0.1	0.2	0.4	0.6	1
	Sample size
Diff. in prop.	20	0.02	0.02	0.03	0.03	0.03	0.03	0.04	0.06
	50	0.01	0.01	0.01	0.01	0.01	0.02	0.02	0.09
	100	0.01	0.01	0.01	0.01	0.01	0.02	0.02	0.10
	500	0.01	0.01	0.01	0.01	0.01	0.01	0.02	0.12
Risk ratio	20	0.04	0.05	0.05	0.05	0.04	0.04	0.04	0.07
	50	0.02	0.02	0.02	0.03	0.02	0.02	0.03	0.11
	100	0.01	0.01	0.01	0.01	0.02	0.02	0.03	0.11
	500	0.01	0.01	0.01	0.01	0.01	0.01	0.03	0.13
Odds ratio	20	0.04	0.05	0.05	0.05	0.05	0.04	0.03	0.04
	50	0.02	0.03	0.03	0.03	0.03	0.02	0.01	0.08
	100	0.02	0.02	0.02	0.02	0.03	0.02	0.01	0.08
	500	0.02	0.01	0.02	0.01	0.02	0.01	0.02	0.11
Coverage of the 95% DCI		Summary statistic: Inter-quartile range
Log standard deviation		0.02	0.05	0.08	0.1	0.2	0.4	0.6	1
	Sample size
Diff. in prop.	20	0.936	0.937	0.936	0.936	0.936	0.938	0.940	0.947
		0.946	0.944	0.945	0.947	0.948	0.950	0.951	0.956
	50	0.943	0.944	0.944	0.944	0.943	0.943	0.940	0.928
		0.950	0.948	0.949	0.949	0.949	0.950	0.949	0.955
	100	0.946	0.947	0.946	0.947	0.945	0.942	0.932	0.881
		0.950	0.950	0.950	0.950	0.950	0.948	0.947	0.944
	500	0.948	0.948	0.947	0.947	0.943	0.931	0.840	0.483
		0.951	0.950	0.950	0.950	0.950	0.945	0.935	0.834
Risk ratio	20	0.945	0.944	0.944	0.944	0.945	0.947	0.950	0.956
		0.957	0.956	0.955	0.956	0.959	0.962	0.965	0.972
	50	0.947	0.947	0.946	0.946	0.945	0.939	0.931	0.931
		0.954	0.953	0.952	0.952	0.954	0.954	0.954	0.962
	100	0.947	0.947	0.946	0.947	0.944	0.930	0.909	0.861
		0.951	0.951	0.951	0.952	0.951	0.951	0.953	0.950
	500	0.947	0.948	0.945	0.944	0.933	0.875	0.722	0.376
		0.951	0.950	0.950	0.951	0.950	0.948	0.925	0.850
Odds ratio	20	0.942	0.942	0.941	0.941	0.941	0.942	0.946	0.952
		0.945	0.945	0.945	0.945	0.946	0.946	0.950	0.960
	50	0.945	0.944	0.943	0.943	0.944	0.944	0.943	0.931
		0.949	0.948	0.948	0.948	0.948	0.949	0.951	0.958
	100	0.945	0.946	0.946	0.946	0.944	0.942	0.932	0.884
		0.949	0.949	0.949	0.949	0.949	0.949	0.950	0.945
	500	0.946	0.947	0.946	0.946	0.945	0.929	0.848	0.490
		0.950	0.950	0.950	0.950	0.949	0.948	0.932	0.833

*Mean of the relative difference between estimates and true parameter to the true paramter.
**Relative difference between the mean standard error and the standard deviation to the standard deviation.
Varying parameter include effect size (difference in mean) and cut-point.

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