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)