Table 1 Application of the skew-normal method to some common outcomes and comparison with the normal method applied to transformed data
From: Dichotomisation using a distributional approach when the outcome is skewed
a. Proportions of low birthweight babies | ||||||
|---|---|---|---|---|---|---|
N | Mean (SD) | Difference | ||||
Non-smoker | Smoker | Non-smoker | Smoker | in means (SE) | 95% conf. int. | p-value |
983 | 494 | 3452g (435) | 3267g (441) | 184 (24) | [137, 232] | <0.001 |
Difference proportions | Risk ratio | Odds ratio | ||||
Normal distributional estimates (no transformation) | ||||||
0.025 (0.004) | [0.017, 0.033] | 2.68 (0.13) | [2.09, 3.43] | 2.74 (0.13) | [2.13,3.54] | |
Skew-normal distributional estimates | ||||||
0.024 (0.004) | [0.016,0.032] | 2.87 (0.16) | [2.09,3.92] | 2.94 (0.16) | [2.13,4.05] | |
b. Proportions of patients with high blood pressure | ||||||
N | Mean (SD) | Difference | ||||
Non-whites | Whites | Non-whites | Whites | in means (SE) | 95% conf. int. | p-value |
661 | 1235 | 149.2 (25.7) | 144.1 (24.8) | 5.11 (1.21) | [2.74, 7.49] | <0.001 |
Difference proportions | Risk ratio | Odds ratio | ||||
Normal distributional estimates on the transformed scale | ||||||
0.068 (0.016) | [0.036,0.100] | 1.28 (0.06) | [1.14,1.43] | 1.40 (0.08) | [1.19,1.64] | |
Skew-normal distributional estimates | ||||||
0.061 (0.017) | [0.028,0.093] | 1.25 (0.06) | [1.11,1.40] | 1.36 (0.08) | [1.15,1.60] | |
c. Proportions of obesity | ||||||
N | Mean (SD) | Difference | ||||
Primipari | Multipari | Primipari | Multipari | in means (SE) | 95% conf. int. | p-value |
891 | 890 | 22.96 (3.40) | 23.84 (4.01) | 0.88 (0.18) | [0.53,1.22] | <0.001 |
Difference proportions | Risk ratio | Odds ratio | ||||
Normal distributional estimates on the transformed scale | ||||||
0.022 (0.005) | [0.013, 0.031] | 1.66 (0.10) | [1.36, 2.02] | 1.70 (0.11) | [1.38,2.09] | |
Skew-normal distributional estimates | ||||||
0.020 (0.004) | [0.012,0.028] | 1.40 (0.07) | [1.23,1.60] | 1.44 (0.07) | [1.25,1.66] | |
d. Proportions of premature births | ||||||
N | Mean (SD) | Difference | ||||
Primipari | Multipari | Primipari | Multipari | in means (SE) | 95% conf. int. | p-value |
856 | 874 | 39.40 (1.96) | 39.52 (2.12) | 0.12 (0.10) | [-0.08, 0.31] | 0.23 |
Difference proportions | Risk ratio | Odds ratio | ||||
Normal distributional estimates on the transformed scale | ||||||
-0.019 (0.009) | [-0.037,-0.003] | 0.82 (0.08) | [0.70,0.98] | 0.81 (0.09) | [0.67,0.97] | |
Skew-normal distributional estimates | ||||||
-0.010 (0.007) | [-0.024,0.006] | 0.99 (0.06) | [0.97,1.01] | 0.92 (0.07) | [0.80,1.05] | |