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 3 Summary of the simulation results comparing skew normal and normal methods of dochotomisation per sample size per group and skewness of the skew-normal data

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

Bias of estimates*		Summary statistic: 3rd quartile of the absolute value
Skewness ( α )		±1	±5	±10	±20	±1	±5	±10	±20
	Sample size	Normal method				Skew normal method
Diff. in prop.	20	0.05	0.28	0.32	0.34	0.40	0.08	0.06	0.03
	50	0.05	0.31	0.34	0.34	0.37	0.02	0.02	0.02
	100	0.05	0.33	0.38	0.39	0.27	0.02	0.03	0.02
	500	0.04	0.33	0.38	0.40	0.09	0.01	0.01	0.01
Risk ratio	20	0.12	0.10	0.12	0.13	0.09	0.04	0.05	0.06
	50	0.02	0.11	0.13	0.12	0.10	0.03	0.03	0.03
	100	0.03	0.18	0.23	0.24	0.08	0.02	0.02	0.02
	500	0.03	0.20	0.23	0.24	0.02	0.01	0.01	0.01
Odds ratio	20	0.20	0.23	0.24	0.23	0.18	0.10	0.10	–
	50	0.09	0.07	0.20	0.25	0.25	0.05	0.0.05	0.05
	100	0.04	0.31	0.35	0.35	0.05	0.09	0.09	0.07
	500	0.01	0.32	0.35	0.34	0.01	0.01	0.02	0.01
Bias of Standard errors**		Summary statistic: 3rd quartile of the absolute value
Skewness ( α )		±1	±5	±10	±20	±1	±5	±10	±20
	Sample size	Normal method				Skew normal method
Diff. in prop.	20	0.02	0.04	0.04	0.04	0.27	0.07	0.07	0.04
	50	0.01	0.03	0.03	0.03	0.34	0.02	0.02	0.02
	100	0.01	0.02	0.02	0.02	0.42	0.02	0.01	0.02
	500	0.01	0.01	0.02	0.02	0.45	0.01	0.02	0.02
Risk ratio	20	0.06	0.06	0.07	0.07	0.29	0.45	0.67	0.85
	50	0.03	0.05	0.05	0.05	0.36	0.05	0.04	0.05
	100	0.02	0.03	0.04	0.04	0.37	0.04	0.04	0.05
	500	0.02	0.02	0.03	0.02	0.38	0.03	0.02	0.03
Odds ratio	20	0.04	0.05	0.05	0.05	0.08	0.27	0.36	0.50
	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	0.10	0.03	0.02	0.03
Coverage of the 95% DCI		Summary statistic: Inter-quartile range
Skewness ( α )		±1	±5	±10	±20	±1	±5	±10	±20
	Sample size	Normal method				Skew normal method
Diff. in prop.	20	0.935	0.918	0.915		0.914	0.917	0.916	0.917
		0.951	0.946	0.945	0.943	0.925	0.947	0.948	0.946
	50	0.943	0.918	0.912	0.907	0.711	0.942	0.937	0.939
		0.950	0.947	0.945	0.945	0.922	0.951	0.952	0.950
	100	0.944	0.889	0.873	0.869	0.720	0.944	0.942	0.942
		0.950	0.945	0.942	0.942	0.911	0.941	0.951	0.951
	500	0.943	0.617	0.571	0.535	0.842	0.948	0.947	0.945
		0.948	0.934	0.936	0.931	0.919	0.951	0.950	0.951
Risk ratio	20	0.942	0.922	0.918	0.918	0.819	0.932	0.934	0.934
		0.952	0.951	0.952	0.951	0.936	0.961	0.963	0.958
	50	0.945	0.900	0.893	0.888	0.778	0.942	0.942	0.940
		0.951	0.947	0.949	0.945	0.929	0.954	0.956	0.954
	100	0.941	0.763	0.709	0.706	0.759	0.943	0.944	0.941
		0.950	0.943	0.942	0.943	0.927	0.952	0.953	0.953
	500	0.947	0.948	0.945	0.944	0.867	0.945	0.945	0.943
		0.947	0.919	0.909	0.907	0.930	0.951	0.951	0.951
Odds ratio	20	0.944	0.931	0.925	0.926	0.938	0.941	0.939	0.939
		0.950	0.946	0.949	0.947	0.944	0.952	0.956	0.959
	50	0.944	0.890	0.888	0.884	0.938	0.944	0.945	0.944
		0.949	0.947	0.945	0.945	0.946	0.950	0.953	0.951
	100	0.942	0.787	0.759	0.768	0.931	0.944	0.945	0.944
		0.949	0.943	0.943	0.942	0.948	0.950	0.952	0.951
	500	0.933	0.293	0.216	0.222	0.932	0.944	0.945	0.944
		0.948	0.922	0.920	0.920	0.948	0.950	0.951	0.951

*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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