Background
Methods
Generalized additive mixed models (GAMMs)
Estimation of GAMMs
Analysis of twins perinatal mortality data
Methods
Data and models
Data analysis
Results of the data analysis
Characteristic | Mothers | Twins | |
---|---|---|---|
First Born | Second Born | ||
Mothers, n (%) | 188480 | ||
Race | |||
White | 149459 (79.3) | ||
Black | 31912 (16.9) | ||
Other | 7109 (3.8) | ||
Age | |||
< 20 | 13192 (7.0) | ||
20–34 | 140992 (74.8) | ||
≥ 35 | 34296 (18.2) | ||
Newbornsa | 188480 | 188480 | |
Sex, boy | 94326 (50.1) | 94654 (50.2) | |
Gestational age, week | 35.7 (3.2) | 35.7 (3.2) | |
Birth weight, gram | 2407.5 (615.5) | 2383.9 (618.5) | |
Breech/Malpresentation | 40832 (21.7) | 51661 (27.4) | |
Cesarean | 100271 (53.2) | 108413 (57.5) |
Variable | Twin births n(%) | Perinatal death n (per 1000) | ORa (95% CI) | Variance of random intercepts | |||
---|---|---|---|---|---|---|---|
Firstborn | Secondborn | Laplace Fit | Bayesian Fitb | Laplace Fit | Bayesian Fit | ||
Birth weight, heavier in %c | |||||||
Heavier firstborn twin | |||||||
≥ 25% | 32,940 (8.74) | 358 (21.74) | 989 (60.05) | 4.15 (2.31, 6.13) | 3.42 (2.47, 4.70) | 104.2 | 3.5 |
15 to < 25% | 35,810 (9.50) | 295 (16.48) | 490 (27.37) | 2.31 (1.46, 3.65) | 1.97 (1.58, 2.49) | 74.7 | 5.5 |
5 to < 15% | 72,230 (19.16) | 565 (15.64) | 723 (20.02) | 1.68 (1.33, 2.12) | 1.39 (1.20, 1.62) | 42.3 | 4.4 |
Similar birth weight | |||||||
within ±5% | 109,998 (29.18) | 1040 (18.91) | 1174 (21.35) | 1.48 (1.28, 1.72) | 1.27 (1.13, 1.43) | 31.8 | 5.4 |
Heavier secondborn twin | |||||||
5 to < 15% | 69,804 (18.52) | 617 (17.68) | 608 (17.42) | 1.16 (0.90, 1.50) | 1.19 (0.97, 1.40) | 69.9 | 4.7 |
15 to < 25% | 32,118 (8.52) | 354 (22.04) | 334 (20.80) | 0.86 (0.67, 1.12) | 0.91 (0.71, 1.20) | 73.9 | 5.6 |
≥ 25% | 24,060 (6.38) | 506 (42.06) | 351 (29.18) | 0.14 (0.07, 0.26) | 0.33 (0.25, 0.45) | 107.5 | 3.3 |
Simulation study
Methods
Data generation: mimicking twin-pairs data setting
Analysis of the simulated data
Performance indicators
Results of the simulation study
Method | \( {\sigma}_{int}^2=0.75 \) | βtrt = 0.7 | f1(x1) | f2(x2) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
\( {\hat{\sigma}}_{int}^2 \) | PRB | 95% CI | \( {\hat{\beta}}_{trt} \) | PRB | 95% CI | MASE | MACP | MACL | MASE | MACP | MACL | |
Event probability = 0.05 | ||||||||||||
DPQL (ML) | 15.83 | 2010.60 | (4.56, 27.10) | 1.24 | 76.44 | (0.23, 2.24) | 7.510 | 0.32 | 1.71 | 11.784 | 0.33 | 1.72 |
DPQL (REML) | 30.45 | 3959.66 | (16.39, 44.56) | 1.07 | 52.38 | (0.01, 2.13) | 6.472 | 0.34 | 1.79 | 12.584 | 0.34 | 1.70 |
Laplace ML | 56.02 | 7369.66 | (5.71, 106.34) | 0.79 | 13.21 | (0.07, 1.51) | 0.763 | 0.70 | 1.76 | 0.907 | 0.73 | 1.82 |
Bayesian (Uniform Prior) | 0.96 | 27.42 | (0.06, 2.88) | 0.75 | 6.54 | (0.28, 1.25) | 0.148 | 0.94 | 1.39 | 0.112 | 0.94 | 1.24 |
Bayesian (Half-Cauchy Prior) | 0.87 | 15.40 | (0.06, 2.71) | 0.72 | 3.25 | (0.29, 1.22) | 0.142 | 0.94 | 1.27 | 0.103 | 0.94 | 1.15 |
Bayesian (IG Prior) | 0.39 | −48.40 | (0.01, 2.20) | 0.71 | 1.71 | (0.27, 1.18) | 0.149 | 0.93 | 1.25 | 0.103 | 0.93 | 1.13 |
Event Probability = 0.5 | ||||||||||||
DPQL (ML) | 0.87 | 15.70 | (0.40, 1.34) | 0.64 | −8.55 | (0.42, 0.86) | 0.032 | 0.89 | 0.57 | 0.023 | 0.88 | 0.48 |
DPQL (REML) | 0.98 | 30.92 | (0.52, 1.44) | 0.66 | −5.86 | (0.42, 0.90) | 0.028 | 0.91 | 0.58 | 0.024 | 0.90 | 0.47 |
Laplace ML | 0.36 | −52.49 | (0.12, 0.60) | 0.66 | −5.77 | (0.43, 0.89) | 0.037 | 0.87 | 0.58 | 0.024 | 0.87 | 0.49 |
Bayesian (Uniform Prior) | 0.82 | 8.99 | (0.33, 1.40) | 0.71 | 1.35 | (0.47, 0.97) | 0.032 | 0.95 | 0.70 | 0.024 | 0.95 | 0.61 |
Bayesian (Half-Cauchy Prior) | 0.80 | 6.04 | (0.34, 1.36) | 0.71 | 0.76 | (0.47, 0.96) | 0.032 | 0.95 | 0.67 | 0.023 | 0.95 | 0.58 |
Bayesian (IG Prior) | 0.72 | −6.50 | (0.19, 1.30) | 0.69 | −0.92 | (0.47, 0.95) | 0.033 | 0.94 | 0.68 | 0.023 | 0.95 | 0.58 |