Case: Try it yourself

The Create a process tutorial showed how to develop a process. In this case study, you will put this knowledge into practice by developing the endometrial cancer model based on a model description and data. Expected output is given at the end, so you can validate your process.

Model description and data

Each individual has its own hazard rate. For now, we simply assume everyone has a hazard rate of 30.

Two different types of lesion are defined: with and without atypia. The age factors of lesions with atypia are shown below. These are the same for lesions without atypia, but 6.142857143 times higher.

Age

Factor

0

0.0000000

30

0.0000088

40

0.0004550

50

0.0006670

60

0.0042540

70

0.0006250

80

0.8000000

100

0.8000000

These age factors are used as follows to generate onset ages.

  1. The factors are multiplied with the differences between the ages and are made cumulative. For example, at age 40 the result is \((30 - 0) * 0.0000088 + (40 - 30) * 0.0004550 = 0.0048140\).

  2. A random number is drawn from an exponential distribution with the individual hazard rate as rate (or the inverse as scale or mean).

  3. Using linear interpolation, the onset age corresponding to the random number is calculated.

Only a single lesion can develop. If the onset age of a lesion without atypia occurs before the death by other causes, this onset should happen. Otherwise, the onset of the lesion with atypia should be scheduled.

The first state after (the first) onset is hyperplasia. The dwelling time in this state is Weibull distributed with shape 0.75. The distribution has a mean of 114.40339 for lesions without atypia and 7.766915 for lesions with atypia.

After hyperplasia, the lesion will transition to the preclinical state. The dwelling time in this state is Weibull distributed with shape 0.75 and mean 5.

After the preclinical state, the lesion becomes clinical. The probability that the individual will ‘cure’ (i.e. will not die from the disease) depends on the age at which this individual becomes clinical.

Age

Probability

0-20

0.780

20-25

0.811

25-30

0.873

30-35

0.845

35-40

0.815

40-45

0.817

45-50

0.812

50-55

0.833

55-60

0.831

60-65

0.806

65-70

0.761

70-75

0.712

75-80

0.661

80-100

0.442

If the individual does not cure, it will die from the disease. The time until death is distributed as follows.

Cumulative probability

Time (years)

0.000000000

0

0.309278351

1

0.515463918

2

0.659793814

3

0.752577320

4

0.804123711

5

0.840206186

6

0.865979381

7

0.891752577

8

0.912371134

9

0.927835052

10

0.927835052

11

0.927835052

12

0.927835052

13

0.938144330

14

0.948453608

15

0.963917526

16

0.963917526

17

0.963917526

18

0.974226804

19

1.000000000

20

Validation

Now that you have implemented the natural history, it is time to validate the process. Create a model in which you also include the Birth process and the OC process with the us_2017 female life table. Run a simulation with 10 million individuals and compare the outcomes with those shown below.

Age group

Life years

Life years in clinical state

Clinical cases

Deaths

0-5

49746034.95

2531.14

1791

147

5-10

49681082.92

20984.54

6593

867

10-15

49648435.80

58947.19

11263

1766

15-20

49587871.49

114033.51

15288

2801

20-25

49472987.12

183790.38

18931

3282

25-30

49308323.98

269426.89

22207

3038

30-35

49089199.60

484114.33

102038

7928

35-40

48736906.49

1315521.07

263521

31622

40-45

48179047.05

2689546.25

374789

54600

45-50

47391155.86

4383373.21

435791

70623

50-55

46314623.68

6193552.52

470937

75694

55-60

44871626.07

7971053.74

447553

75778

60-65

43017543.38

9403546.44

393968

74715

65-70

40627278.78

10374562.07

338650

76934

70-75

37379781.74

10758321.90

285027

78242

75-80

32813306.93

10392355.98

229977

73702

80-85

26424111.26

9032152.77

172642

79416

85-90

18124660.58

6568945.43

111290

61165

90-95

9320430.27

3548061.71

53842

30684

95-100

2977996.04

1183965.93

16567

9709