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