# Table 1 Transition probability by age

Parameter Description and parameters used to estimate transition probabilities Source
Transitions from the health state (State 1)
x λ 11 Probability of permanence in healthy state without onset of HPV-related diseases (addition to 1 of the remaining probabilities from state 1) 1 −  x λ 12 −  x λ 13 −  x λ 14 −  x λ 15 −  x λ 16 −  x λ 18 Complementary probability
x λ 12 Probability of genital warts onset = incidence of diagnosis by age in genital warts [11, 14, 59, 63, 64]
x λ 13 Probability to contract a CIN 1 = incidence of diagnosis by age of CIN 1 [11, 65,66,67]
x λ 14 Probability to contract a CIN 2/3 = incidence of diagnosis by age of CIN 2/3 [11, 65,66,67]
x λ 15 Probability of cervical cancer onset by age = incidence of cervical cancer by age (assuming all cancers are diagnosed) 
x λ 16 Probability of anal cancer onset by age = incidence of anal cancer by age (assuming all cancers are diagnosed) [60, 68]
Transitions from the genital warts state (State 2)
x λ 22 Probability of permanence of genital warts by age = Recurrence rate of genital warts by age between age x − 1 and x [11, 59, 69]
x λ 21 Probability of healing from genital warts = 1 −  x λ 22 −  x λ 28 Complementary probability
Transitions from state of CIN 1 (State 3)
x λ 33 Probability of permanence of CIN 1 by age =1 −  x λ 31 −  x λ 38 Complementary probability
x λ 34 Transition probability from CIN 1 to CIN 2/3 = progression rate of the disease by age from state CIN 1 to CIN 2/3 [11, 70]
x λ 31 Probability of healing from CIN 1 by age = spontaneous regression rate of the disease by age. In this case women are only observed and not treated. [11, 70,71,72]
Transitions from state of CIN 2/3 (State 4)
x λ 44 Probability of permanence in CIN 2/3 =1 −  x λ 41 −  x λ 48 Complementary probability
x λ 41 Probability of healing from CIN 2/3 by age = efficacy rate of health care intervention on diagnosed women (Constant by age) [11, 70,71,72]
x λ 45 Transition probability from CIN 2/3 to CCU state by age for lack of efficacy of health care intervention = progression rate of the disease by age [11, 66, 70,71,72]
Transitions from Cervical cancer state (State 5)
x λ 55 Probability of permanence of CCU state by age = recurrence rate (recurrence of disease) of CCU [73, 74]
x λ 51 Probability of healing from cervical cancer state by age = 1 −  x λ 55 −  x λ 57 x λ 59 Complementary probability
x λ 57 Probability of death from cervical cancer by age for ill subjects =1 −  x λ 59 − 5 − year survival by age [28, 75]
Transitions from Anal Cancer (State 6)
x λ 66 Probability of permanence in CCU state by age = recurrence rate of anal cancer (recurrence of disease) 
x λ 61 Probability of healing from cervical cancer state by age =1 −  x λ 66 −  x λ 67 x λ 69 [28, 75]
x λ 68 Probability of death from anal cancer by age for ill subjects =1 −  x λ 69 − 5 − year survival by age Complementary probability
Transitions to death for other causes (State i - > State 9)
x λ i9
i = 1, 2, 3, 4, 5,6
Probability of death by age from any state for other causes except for cervical cancer = Probability of general death by age 
1. Legend: i = state of origin; j = state of destination; x = Age group: 0–4, 5–9, 10–14, 15–19, 20–24, 25–29, 30–34, 35–39, 40–44, 45–49, 50–54, 55–59, 60–64, 65–69, 70–74, 75–79, 80–84, ≥85;