Table 2. Traditional (least squares) and quantile regression analyses of spirometric traits between related individuals.a.
| Least-squares regression analysis | Quantile regression analysis | ||||||
|---|---|---|---|---|---|---|---|
| Correlation | Least-squares regression slope | Increase in slope per 1% increase in the offspring or sibling distribution | Difference in slope between the 90th and 10th percentiles | ||||
| Slope ± SE | Pb | Slope ± SE | Pc | Difference ± SE | Pd | ||
| FEV1/FVC | |||||||
| Spouse | 0.04 | 0.047 ± 0.018 | 0.007 | −0.0005 ± 0.0005 | 0.37 | −0.008 ± 0.077 | 0.91 |
| Offspring-parent | 0.17 | 0.134 ± 0.010 | <10−15 | −0.0009 ± 0.0003 | 0.003 | −0.083 ± 0.032 | 0.01 |
| Offspring-midparent | 0.24 | 0.269 ± 0.018 | <10−15 | −0.0021 ± 0.0005 | 4.1 × 10−5 | −0.192 ± 0.059 | 0.001 |
| Full-sibling | 0.27 | 0.266 ± 0.017 | <10−15 | −0.0022 ± 0.0005 | 2.1 × 10−6 | −0.200 ± 0.040 | 5.6 × 10−7 |
| FVC | |||||||
| Spouse | 0.08 | 0.109 ± 0.033 | 0.001 | 0.0008 ± 0.0009 | 0.41 | 0.049 ± 0.089 | 0.58 |
| Offspring-parent | 0.26 | 0.263 ± 0.013 | <10−15 | −0.0002 ± 0.0003 | 0.43 | −0.031 ± 0.027 | 0.24 |
| Offspring-midparent | 0.32 | 0.463 ± 0.022 | <10−15 | −0.0007 ± 0.0006 | 0.23 | −0.050 ± 0.059 | 0.4 |
| Full-sibling | 0.32 | 0.321 ± 0.017 | <10−15 | 0.0001 ± 0.0004 | 0.76 | −0.001 ± 0.039 | 0.99 |
| FEV1 | |||||||
| Spouse | 0.08 | 0.118 ± 0.034 | 0.0005 | −0.0010 ± 0.0008 | 0.23 | −0.073 ± 0.090 | 0.40 |
| Offspring-parent | 0.23 | 0.227 ± 0.012 | <10−15 | −0.0003 ± 0.0003 | 0.29 | −0.026 ± 0.034 | 0.44 |
| Offspring-midparent | 0.30 | 0.407 ± 0.022 | <10−15 | −0.0007 ± 0.0006 | 0.22 | −0.009 ± 0.058 | 0.88 |
| Full-sibling | 0.28 | 0.282 ± 0.017 | <10−15 | −0.0006 ± 0.0004 | 0.17 | −0.070 ± 0.045 | 0.12 |
| PEF | |||||||
| Spouse | 0.05 | 0.078 ± 0.045 | 0.08 | 0.0001 ± 0.0012 | 0.92 | −0.047 ± 0.111 | 0.67 |
| Offspring-parent | 0.19 | 0.180 ± 0.014 | <10−15 | 0.0003 ± 0.0003 | 0.32 | 0.017 ± 0.034 | 0.61 |
| Offspring-midparent | 0.25 | 0.336 ± 0.026 | <10−15 | 0.0006 ± 0.0006 | 0.34 | 0.052 ± 0.055 | 0.34 |
| Full-sibling | 0.23 | 0.228 ± 0.017 | <10−15 | 0.0003 ± 0.0004 | 0.46 | 0.063 ± 0.046 | 0.17 |
| MMEF | |||||||
| Spouse | 0.04 | 0.049 ± 0.038 | 0.20 | −0.0012 ± 0.0009 | 0.20 | −0.106 ± 0.097 | 0.28 |
| Offspring-parent | 0.25 | 0.285 ± 0.015 | <10−15 | 0.0013 ± 0.0004 | 0.0004 | 0.108 ± 0.037 | 0.003 |
| Offspring-midparent | 0.35 | 0.550 ± 0.028 | <10−15 | 0.0014 ± 0.0008 | 0.06 | 0.137 ± 0.071 | 0.05 |
| Full-sibling | 0.30 | 0.296 ± 0.017 | <10−15 | 0.0009 ± 0.0005 | 0.04 | 0.049 ± 0.049 | 0.32 |
| FEF25% | |||||||
| Spouse | 0.07 | 0.101 ± 0.043 | 0.02 | −0.0007 ± 0.0011 | 0.52 | −0.097 ± 0.105 | 0.36 |
| Offspring-parent | 0.21 | 0.200 ± 0.013 | <10−15 | −0.0002 ± 0.0003 | 0.45 | −0.024 ± 0.032 | 0.47 |
| Offspring-midparent | 0.28 | 0.367 ± 0.024 | <10−15 | −0.0005 ± 0.0006 | 0.35 | −0.092 ± 0.060 | 0.13 |
| Full-sibling | 0.24 | 0.241 ± 0.017 | <10−15 | −0.0007 ± 0.0004 | 0.12 | −0.032 ± 0.035 | 0.36 |
| FEF50% | |||||||
| Spouse | 0.06 | 0.077 ± 0.037 | 0.04 | −0.0007 ± 0.0009 | 0.41 | −0.124 ± 0.080 | 0.12 |
| Offspring-parent | 0.25 | 0.253 ± 0.013 | <10−15 | 0.0011 ± 0.0003 | 0.002 | 0.079 ± 0.037 | 0.03 |
| Offspring-midparent | 0.37 | 0.514 ± 0.024 | <10−15 | 0.0010 ± 0.0006 | 0.10 | 0.060 ± 0.060 | 0.32 |
| Full-sibling | 0.28 | 0.284 ± 0.017 | <10−15 | 0.0008 ± 0.0004 | 0.05 | 0.055 ± 0.044 | 0.21 |
| FEF75% | |||||||
| Spouse | 0.01 | 0.015 ± 0.038 | 0.70 | −0.0012 ± 0.0011 | 0.27 | −0.114 ± 0.097 | 0.24 |
| Offspring-parent | 0.20 | 0.249 ± 0.017 | <10−15 | 0.0021 ± 0.0004 | 1.8 × 10−6 | 0.153 ± 0.048 | 0.002 |
| Offspring-midparent | 0.28 | 0.507 ± 0.033 | <10−15 | 0.0035 ± 0.0009 | 0.0001 | 0.228 ± 0.090 | 0.01 |
| Full-sibling | 0.27 | 0.269 ± 0.017 | <10−15 | 0.0019 ± 0.0005 | 0.0002 | 0.147 ± 0.052 | 0.005 |
Notes.
See figure legends for sample sizes.
Significance determined from standard least-squares regression giving each offspring equal weight.
Significance determined from linear contrast from the variance–covariance matrix determined from 1000 bootstrap samples.
Significance determined from difference in coefficients between the 10th and 90th quantiles and their associated standard errors (±SE) and covariance determined from 1,000 bootstrap samples. Significance levels are those reported by Stata, but it is important not to interpret significance levels much less than P < 0.001 literally but rather as indicators of strong significance.