 ### Description

Wilcox et al studied the probability that a woman would be in her 6 day fertile window on a specific day in her menstrual cycle. The timing of the fertile window can be highly unpredictable, with only a third of women having the fertile window entirely between days 10 and 17. The authors are from the National Institute of Environmental Health Sciences in Durham, North Carolina.

Parameters:

(1) cycle regular vs irregular

(2) if regular, the number of days in the cycle

Probability of Being in the Fertile Window

day of cycle

irregular cycle

regular cycle < 28 days

regular cycle of 28 days

regular cycle of 29 days

regular cycle  >= 30 days

0

0.000

0.000

0.000

0.000

0.000

1.75

0.000

0.002

0.001

0.001

0.001

3.5

0.002

0.025

0.022

0.019

0.009

5.25

0.013

0.119

0.075

0.056

0.028

7

0.041

0.350

0.216

0.134

0.063

8.75

0.100

0.616

0.475

0.375

0.172

10.5

0.194

0.703

0.631

0.566

0.363

11.5

0.269

0.688

0.663

0.628

0.450

12.25

0.300

0.631

0.656

0.644

0.503

12.8

0.341

0.541

0.625

0.656

0.541

14

0.388

0.398

0.519

0.594

0.556

15.75

0.428

0.219

0.313

0.428

0.475

17.5

0.409

0.128

0.194

0.288

0.350

19.25

0.356

0.075

0.122

0.175

0.228

21

0.291

0.050

0.074

0.097

0.153

22.75

0.211

0.038

0.044

0.060

0.106

24.5

0.156

0.034

0.031

0.041

0.081

26.25

0.116

0.038

0.025

0.024

0.063

28

0.091

0.049

0.031

0.022

0.063

29.75

0.075

0.056

0.044

0.019

0.064

31.5

0.066

0.069

0.056

0.019

0.069

33.25

0.069

0.075

0.075

0.021

0.088

35

0.077

0.081

0.103

0.026

0.103

approximated from Figures 2 and 3, pages 1260-1261

Approximating Equations from JMP: Irregular Cycle

probability in fertile window for day 0 to 11.5 =

= (0.0002876 * ((day of cycle) ^3)) – (0.001458 * ((day of cycle) ^2)) + (0.002127 * (day of cycle)) – 0.000208

probability in fertile window for day 11.5 to 19.25 =

= (-0.000122 * ((day of cycle) ^3)) – (0.001685 * ((day of cycle) ^2)) + (0.1520585 * (day of cycle)) – 1.075533

probability in fertile window for day 19.25 to 29.75 =

= (0.0000726 * ((day of cycle) ^3)) – (0.003195 * ((day of cycle) ^2)) - (0.002957 * (day of cycle)) + 1.0822857

probability in fertile window for day 29.75 to 35 =

= (-0.000218 * ((day of cycle) ^3)) + (0.0225306 * ((day of cycle) ^2)) - (0.772476 * (day of cycle)) + 8.847

Approximating Equations from JMP: Regular Cycle of < 28 Days

probability in fertile window for day 0 to 8.75 =

= (0.000463 * ((day of cycle) ^3)) + (0.006471 * ((day of cycle) ^2)) - (0.021504 * (day of cycle)) + 0.0046984

probability in fertile window for day 8.75 to 12.25 =

= (-0.003236 * ((day of cycle) ^3)) + (0.0759629 * ((day of cycle) ^2)) - (0.510844 * (day of cycle)) + 1.4375909

probability in fertile window for day 12.25 to 21 =

= (-0.000491 * ((day of cycle) ^3)) + (0.0334244 * ((day of cycle) ^2)) - (0.761041 * (day of cycle)) + 5.8401134

probability in fertile window for day 21 to 28 =

= (-0.000016 * ((day of cycle) ^3)) + (0.0024023 * ((day of cycle) ^2)) - (0.089667 * (day of cycle)) + 1.0175857

probability in fertile window for day 28 to 35 =

= (-0.000093 * ((day of cycle) ^3)) + (0.0086064 * ((day of cycle) ^2)) - (0.258776 * (day of cycle)) + 2.595

Approximating Equations from JMP: Regular Cycle of 28 Days

probability in fertile window for day 0 to 8.75 =

= (0.0011368 * ((day of cycle) ^3)) – (0.0046 * ((day of cycle) ^2)) + (0.0075616 * (day of cycle)) – 0.000921

probability in fertile window for day 8.75 to 14 =

= (-0.000583 * ((day of cycle) ^3)) – (0.003965 * ((day of cycle) ^2)) + (0.3287014 * (day of cycle)) – 1.707444

probability in fertile window for day 14 to 26.25 =

= (-0.000402 * ((day of cycle) ^3)) + (0.0290718 * ((day of cycle) ^2)) - (0.706321 * (day of cycle)) + 5.808474

probability in fertile window for day 26.25 to 35 =

= (0.0000587 * ((day of cycle) ^3)) – (0.004615 * ((day of cycle) ^2)) + (0.1252305 * (day of cycle)) – 1.144889

Approximating Equations from JMP: Regular Cycle of 29 Days

probability in fertile window for day 0 to 10.5 =

= (0.0003991 * ((day of cycle) ^3)) + (0.0020603 * ((day of cycle) ^2)) - (0.010923 * (day of cycle)) + 0.005

probability in fertile window for day 10.5 to 15.75 =

= (0.0009901 * ((day of cycle) ^4)) –  (0.051103 * ((day of cycle) ^3)) + (0.9607751 * ((day of cycle) ^2)) - (7.796999 * (day of cycle)) + 23.633397

probability in fertile window for day 15.75 to 29.75 =

= (-0.000219 * ((day of cycle) ^3)) + (0.0183492 * ((day of cycle) ^2)) - (0.512868 * (day of cycle)) + 4.8137222

probability in fertile window for day 29.75 to 35=

= (0.0000311 * ((day of cycle) ^3)) – (0.002612 * ((day of cycle) ^2)) + (0.0724762 * (day of cycle)) – 0.644

Approximating Equations from JMP: Regular Cycle of >= 30 Days

probability in fertile window for day 0 to 11.5 =

= (0.0004607 * ((day of cycle) ^3)) – (0.001963 * ((day of cycle) ^2)) + (0.0019073 * (day of cycle)) + 0.0014143

probability in fertile window for day 11.5 to 15.75 =

= (-0.000406 * ((day of cycle) ^3)) – (0.004533 * ((day of cycle) ^2)) + (0.357417 * (day of cycle)) – 2.444863

probability in fertile window for day 15.75 to 29.75 =

= (-0.00015 * ((day of cycle) ^3)) + (0.0135822 * ((day of cycle) ^2)) - (0.408112 * (day of cycle)) + 4.1223968

probability in fertile window for day 29.75 to 35 =

=  (0.0008163 * ((day of cycle) ^2)) - (0.045086 * (day of cycle)) + 0.6819