We are also providing the equations underpinning the BPD calculator for other researchers who wish to do their own calculations. The variables for these equations are summarized in Table 1:
Table 1. Format for Inputting Variables
|
Variable |
Units |
Range of Valid Values |
Example(s) |
|
Continuous Variables |
|
|
|
|
Birthweight |
Grams/100 |
5.01 – 12.50 |
Enter 8.0 for 800g |
|
Gestational Age |
Completed weeks |
23 - 28 |
Enter 26 for 26 weeks |
|
FiO2 |
Decimal value multiplied by 5 |
1.05 - 5.0 |
Enter 2.5 for 50% FiO2 |
|
|
|
|
|
|
Dichotomous Variables |
|
|
|
|
Male sex |
Yes/No |
1 for yes, 0 for no, 0.5 for missing |
Enter 1 for Male |
|
Antenatal Steroids (ANS) – Day 1 models only |
Yes/No |
1 for yes, 0 for no, 0.5 for missing |
Enter 0 for No ANS |
|
Surgical NEC – Day 14 and Day 28 models only |
Yes/No |
1 for yes, 0 for no, 0.5 for missing |
Enter 0.5 for Surgical NEC unknown |
|
Type of respiratory support* - High frequency ventilation (HFV) - Conventional ventilation (CV) - Non-invasive positive pressure ventilation (NIPPV) - Continuous positive airway pressure (CPAP) - Nasal cannula (NC) - Hood - No support |
Yes/No Yes/No Yes/No
Yes/No
Yes/No Yes/No Yes/No |
1 for yes, 0 for no 1 for yes, 0 for no 1 for yes, 0 for no
1 for yes, 0 for no
1 for yes, 0 for no 1 for yes, 0 for no 1 for yes, 0 for no |
Enter 1 for Yes Enter 0 for No Enter 0 for No
Enter 0 for No
Enter 0 for No Enter 0 for No Enter 0 for No |
*For type of respiratory support, the highest mode on the postnatal day of the model should be yes (1), and the rest should be no (0).
There are 5 regression models, corresponding to postnatal day 1, 3, 7, 14, and 28. Each one is a multinomial model with 5 possible levels of outcome: survival without BPD, grade 1 BPD, grade 2 BPD, grade 3 BPD, death. This results in a total of 20 regression equations with a regression coefficient for each variable. These regression coefficients are summarized in Table 2:
Table 2. Regression Coefficients by Postnatal Day and Outcome
|
Postnatal Day/ Outcome |
|
Input Variables* |
||||||||||||
|
Intercept |
Birthwt |
GestAge |
FiO2 |
Male |
ANS |
SurgNEC |
HFV |
CV |
NIPPV |
CPAP |
NC |
Hood |
No Support |
|
|
Day 1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Grade 1 BPD |
4.9291 |
-0.2294 |
-0.215 |
0.2058 |
0.3449 |
0.0416 |
|
3.0396 |
2.2306 |
1.6518 |
1.9743 |
2.2903 |
0.5254 |
0 |
|
Grade 2 BPD |
5.0616 |
-0.4245 |
-0.1912 |
0.2193 |
0.7437 |
0.00574 |
3.5266 |
2.3098 |
1.3756 |
1.6092 |
1.251 |
-0.9808 |
0 |
|
|
Grade 3 BPD |
6.2967 |
-0.4503 |
-0.3043 |
0.4125 |
0.6998 |
0.4912 |
3.3379 |
2.4123 |
0.9667 |
1.6672 |
2.0211 |
0.8203 |
0 |
|
|
Death |
12.7791 |
-0.5137 |
-0.4463 |
0.5407 |
0.7472 |
-0.2521 |
1.9929 |
0.7088 |
-0.0387 |
0.1949 |
0.6494 |
-1.0758 |
0 |
|
|
Day 3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Grade 1 BPD |
4.5351 |
-0.1958 |
-0.2097 |
0.2449 |
0.3291 |
|
|
2.8612 |
2.2455 |
1.7769 |
1.8263 |
1.9242 |
0.5198 |
0 |
|
Grade 2 BPD |
3.0987 |
-0.3648 |
-0.1935 |
0.2401 |
0.7229 |
4.9894 |
3.8294 |
2.9662 |
3.0618 |
2.1682 |
1.4126 |
0 |
||
|
Grade 3 BPD |
-3.3371 |
-0.3817 |
-0.291 |
0.3401 |
0.6741 |
12.7545 |
11.8005 |
10.6459 |
10.5963 |
10.5738 |
9.7391 |
0 |
||
|
Death |
11.8691 |
-0.4317 |
-0.473 |
0.7273 |
0.6238 |
1.9177 |
0.8703 |
-0.065 |
0.3432 |
0.3011 |
0.7349 |
0 |
||
|
Day 7 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Grade 1 BPD |
1.144 |
-0.1866 |
-0.0912 |
0.4595 |
0.3321 |
|
|
3.0036 |
2.5416 |
2.0242 |
1.823 |
1.5886 |
0.8681 |
0 |
|
Grade 2 BPD |
-1.2235 |
-0.3321 |
-0.0226 |
0.5762 |
0.7067 |
4.3533 |
3.4638 |
2.4279 |
2.1694 |
1.4526 |
0.2076 |
0 |
||
|
Grade 3 BPD |
-1.6145 |
-0.3433 |
-0.0885 |
0.7834 |
0.6661 |
5.0163 |
4.3176 |
2.8708 |
2.7186 |
2.4215 |
1.7167 |
0 |
||
|
Death |
4.967 |
-0.3966 |
-0.2435 |
0.9298 |
0.6094 |
2.4941 |
1.7026 |
0.7729 |
0.4705 |
-0.0608 |
0.6065 |
0 |
||
|
Day 14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Grade 1 BPD |
-2.5703 |
-0.1762 |
0.035 |
0.5619 |
0.3118 |
|
-0.2117 |
3.1652 |
2.9005 |
2.2808 |
1.974 |
1.4227 |
0.7885 |
0 |
|
Grade 2 BPD |
-7.4441 |
-0.3211 |
0.1794 |
0.6591 |
0.6909 |
-0.3794 |
5.2531 |
4.4611 |
3.0693 |
2.8811 |
1.5264 |
0.1524 |
0 |
|
|
Grade 3 BPD |
-7.8023 |
-0.3191 |
0.152 |
0.8571 |
0.6327 |
1.1442 |
4.7797 |
4.1855 |
2.1917 |
1.8422 |
1.1852 |
-9.8714 |
0 |
|
|
Death |
-0.8084 |
-0.3862 |
-0.055 |
0.8792 |
0.5066 |
0.3749 |
3.0699 |
2.3286 |
1.4692 |
0.9357 |
-0.3158 |
0.6584 |
0 |
|
|
Day 28 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Grade 1 BPD |
-4.4735 |
-0.1437 |
0.0675 |
0.6873 |
0.2321 |
|
-0.2276 |
4.3301 |
4.0115 |
3.2276 |
3.0016 |
2.1805 |
1.7387 |
0 |
|
Grade 2 BPD |
-10.998 |
-0.2763 |
0.2368 |
0.8902 |
0.5582 |
-0.1591 |
7.5578 |
6.4832 |
5.063 |
4.6981 |
2.8929 |
2.0932 |
0 |
|
|
Grade 3 BPD |
-10.6378 |
-0.2782 |
0.2162 |
1.1343 |
0.4722 |
0.908 |
6.1545 |
5.3745 |
2.8445 |
2.4478 |
1.3087 |
1.5484 |
0 |
|
|
Death |
-4.5017 |
-0.3319 |
0.0183 |
1.3648 |
0.341 |
1.548 |
3.7868 |
2.5009 |
1.1441 |
0.8302 |
-1.0193 |
0.00172 |
0 |
|
*As noted in Table 1, ANS is only in the Day 1 model and Surgical NEC is only in the Day 14 and 28 models.
The corresponding regression equations are provided in Appendix A. Here is the regression equation for Death on Day 1, as an example:
Death = 12.7791 - 0.5137(Birthwt) - 0.4463(GestAge) + 0.5407(FiO2) + 0.7472(Male) - 0.2521(ANS) + 1.9929(HFV) + 0.7088(CV) - 0.0387(NIPPV) + 0.1949(CPAP) + 0.6494(NC) - 1.0758(Hood) + 0(No support)
These regression equations are then used to calculate the probability of each level of outcome using the following equations:
The probability of No BPD:
Prob(No BPD) = 1 / (1+(e^β1+ e^β2+ e^β3+ e^βD ) )
Where β1 is the result from the regression equation for Grade 1 BPD, β2 is the result from the regression equation for Grade 2 BPD, β3 is the result from the regression equation for Grade 3 BPD, and βD is the result from the regression equation for Death.
The probability of the other levels of outcome are:
Prob(Grade 1 BPD) = Prob(No BPD)*e^β1
Where Prob(No BPD) is the probability of No BPD (from above) and β1 is the result from the regression equation for Grade 1 BPD.
Prob(Grade 2 BPD) = Prob(No BPD)*e^β2
Where Prob(No BPD) is the probability of No BPD (from above) and β2 is the result from the regression equation for Grade 2 BPD.
Prob(Grade 3 BPD) = Prob(No BPD)*e^β3
Where Prob(No BPD) is the probability of No BPD (from above) and β3 is the result from the regression equation for Grade 3 BPD.
Prob(Death) = Prob(No BPD)*e^βD
Where Prob(No BPD) is the probability of No BPD (from above)
and βD is the result
from the regression equation for Death.
Appendix A – Regression equations:
Day 1
Death = 12.7791 - 0.5137(Birthweight) - 0.4463(GestationalAge) + 0.5407(FiO2) + 0.7472(Male) - 0.2521(ANS) + 1.9929(HFV) + 0.7088(CV) - 0.0387(NIPPV) + 0.1949(CPAP) + 0.6494(NC) - 1.0758(Hood) + 0(No support)
Grade 3 BPD = 6.2967 - 0.4503(Birthweight) - 0.3043(GestationalAge) + 0.4125(FiO2) + 0.6998(Male) + 0.4912(ANS) + 3.3379(HFV) + 2.4123(CV) + 0.9667(NIPPV) + 1.6672(CPAP) + 2.0211(NC) + 0.8203(Hood) + 0(No support)
Grade 2 BPD = 5.0616 - 0.4245(Birthweight) - 0.1912(GestationalAge) + 0.2193(FiO2) + 0.7437(Male) + 0.00574(ANS) + 3.5266(HFV) + 2.3098(CV) + 1.3756(NIPPV) + 1.6092(CPAP) + 1.251(NC) - 0.9808(Hood) + 0(No support)
Grade 1 BPD = 4.9291 - 0.2294(Birthweight) - 0.215(GestationalAge) + 0.2058(FiO2) + 0.3449(Male) + 0.0416(ANS) + 3.0396(HFV) + 2.2306(CV) + 1.6518(NIPPV) + 1.9743(CPAP) + 2.2903(NC) + 0.5254(Hood) + 0(No support)
Day 3
Death = 11.8691 - 0.4317(Birthweight) - 0.473(GestationalAge) + 0.7273(FiO2) + 0.6238(Male) + 1.9177(HFV) + 0.8703(CV) - 0.065(NIPPV) + 0.3432(CPAP) + 0.3011(NC) + 0.7349(Hood) + 0(No support)
Grade 3 BPD = -3.3371 - 0.3817(Birthweight) - 0.291(GestationalAge) + 0.3401(FiO2) + 0.6741(Male) + 12.7545(HFV) + 11.8005(CV) + 10.6459(NIPPV) + 10.5963(CPAP) + 10.5738(NC) + 9.7391(Hood) + 0(No support)
Grade 2 BPD = 3.0987 - 0.3648(Birthweight) - 0.1935(GestationalAge) + 0.2401(FiO2) + 0.7229(Male) + 4.9894(HFV) + 3.8294(CV) + 2.9662(NIPPV) + 3.0618(CPAP) + 2.1682(NC) + 1.4126(Hood) + 0(No support)
Grade 1 BPD = 4.5351 - 0.1958(Birthweight) - 0.2097(GestationalAge) + 0.2449(FiO2) + 0.3291(Male) + 2.8612(HFV) + 2.2455(CV) + 1.7769(NIPPV) + 1.8263(CPAP) + 1.9242(NC) + 0.5198(Hood) + 0(No support)
Day 7
Death = 4.967 - 0.3966(Birthweight) - 0.2435(GestationalAge) + 0.9298(FiO2) + 0.6094(Male) + 2.4941(HFV) + 1.7026(CV) + 0.7729(NIPPV) + 0.4705(CPAP) - 0.0608(NC) + 0.6065(Hood) + 0(No support)
Grade 3 BPD = -1.6145 - 0.3433 (Birthweight) - 0.0885(GestationalAge) + 0.7834(FiO2) + 0.6661(Male) + 5.0163(HFV) + 4.3176(CV) + 2.8708(NIPPV) + 2.7186(CPAP) + 2.4215(NC) + 1.7167(Hood) + 0(No support)
Grade 2 BPD = -1.2235 - 0.3321(Birthweight) - 0.0226(GestationalAge) + 0.5762(FiO2) + 0.7067(Male) + 4.3533(HFV) + 3.4638(CV) + 2.4279(NIPPV) + 2.1694(CPAP) + 1.4526(NC) + 0.2076(Hood) + 0(No support)
Grade 1 BPD = 1.144 - 0.1866(Birthweight) - 0.0912(GestationalAge) + 0.4595(FiO2) + 0.3321(Male) + 3.0036(HFV) + 2.5416(CV) + 2.0242(NIPPV) + 1.823(CPAP) + 1.5886 (NC) + 0.8681(Hood) + 0(No support)
Day 14
Death = -0.8084 - 0.3862(Birthweight) - 0.055(GestationalAge) + 0.8792(FiO2) + 0.5066(Male) + 0.3749(Surgical NEC) + 3.0699(HFV) + 2.3286(CV) + 1.4692 (NIPPV) + 0.9357(CPAP) - 0.3158(NC) + 0.6584(Hood) + 0(No support)
Grade 3 BPD = -7.8023 - 0.3191 (Birthweight) + 0.152(GestationalAge) + 0.8571(FiO2) + 0.6327(Male) + 1.1442(Surgical NEC) + 4.7797(HFV) + 4.1855(CV) + 2.1917(NIPPV) + 1.8422(CPAP) + 1.1852(NC) - 9.8714(Hood) + 0(No support)
Grade 2 BPD = -7.4441 - 0.3211(Birthweight) + 0.1794(GestationalAge) + 0.6591(FiO2) + 0.6909(Male) - 0.3794(Surgical NEC) + 5.2531(HFV) + 4.4611(CV) + 3.0693(NIPPV) + 2.8811(CPAP) + 1.5264(NC) + 0.1524(Hood) + 0(No support)
Grade 1 BPD = -2.5703 - 0.1762(Birthweight) + 0.035(GestationalAge) + 0.5619(FiO2) + 0.3118(Male) - 0.2117(Surgical NEC) + 3.1652(HFV) + 2.9005(CV) + 2.2808(NIPPV) + 1.974(CPAP) + 1.4227(NC) + 0.7885(Hood) + 0(No support)
Day 28
Death = -4.5017 - 0.3319(Birthweight) + 0.0183(GestationalAge) + 1.3648(FiO2) + 0.341(Male) + 1.548(Surgical NEC) + 3.7868(HFV) + 2.5009(CV) + 1.1441 (NIPPV) + 0.8302(CPAP) - 1.0193(NC) + 0.00172(Hood) + 0(No support)
Grade 3 BPD = -10.6378 - 0.2782 (Birthweight) + 0.2162(GestationalAge) + 1.1343(FiO2) + 0.4722 (Male) + 0.908(Surgical NEC) + 6.1545(HFV) + 5.3745(CV) + 2.8445(NIPPV) + 2.4478(CPAP) + 1.3087(NC) + 1.5484(Hood) + 0(No support)
Grade 2 BPD = -10.998 - 0.2763(Birthweight) + 0.2368(GestationalAge) + 0.8902(FiO2) + 0.5582(Male) - 0.1591(Surgical NEC) + 7.5578(HFV) + 6.4832(CV) + 5.063(NIPPV) + 4.6981(CPAP) + 2.8929(NC) + 2.0932(Hood) + 0(No support)
Grade 1 BPD = -4.4735 - 0.1437(Birthweight) + 0.0675(GestationalAge) + 0.6873(FiO2) + 0.2321(Male) - 0.2276(Surgical NEC) + 4.3301(HFV) + 4.0115(CV) + 3.2276(NIPPV) + 3.0016(CPAP) + 2.1805(NC) + 1.7387 (Hood) + 0(No support)