Terms | Definitions |

Zw | Penetrance of MS for the subset of susceptible women (F, G) within (Z) during (E_{T})– Also called the ‘ failure-probability’ for susceptible women during (E_{T}). |

Zm | Penetrance of MS for the subset of susceptible men (M, G) within (Z) during (E_{T})– Also called the ‘ failure-probability’ for susceptible men during (E_{T}). |

, cd | Limiting values (constants) for the ‘failure- probability’ in susceptible men (); and csusceptible women ()—that is, (dZm≤≤1) and (cZw≤≤1).dlimit of (c=Zm) as: (a→∞) & limit of (d=Zw) as: (a→∞). |

p | Proportion of women in the (G) subset—that is, p=P(F│G). |

(E) | Event that a randomly-selected member of (G)—the proband—experiences an environment ‘sufficient’ to cause MS in them. |

P(E│G, E_{T}) | Probability that the event (E) occurs during (E_{T}) for a proband randomly-selected from (G). |

u | Variable, which represents the environmental exposure-level as measured by the odds that the event (E) occurs during any (E_{T}). |

a | Environmental exposure-level during some specific (E_{T})—that is, when: (u=a). |

h(u), k(u) | Unknown (and unspecified) hazard functions for susceptible men—h(u); and for susceptible women—k(u). |

H(a), K(a) | Cumulative hazard functions for susceptible men – H(a); and for susceptible women – K(a)—defined as the definite integrals of these unknown and unspecified hazard functions from an exposure-level of (u=0) to an exposure-level of (u=a). |

R>0 | Value of the proportionality factor (if the hazards are proportional) —that is, k(u) = R * h(u). |

R^{app} | The ‘apparent’ value of R—that is, the value of R for proportional hazards whenever: (1).c=d≤ |

λ_{w}, λ_{m} | Environmental exposure thresholds for developing MS in susceptible women (λ_{w}) and susceptible men (λ_{m}) (see Methods: Longitudinal models: General considerations). |

λ | Difference in the environmental exposure threshold between susceptible women and susceptible men: that is, λ = λ_{w} – λ_{m}. |

MS, multiple sclerosis.