Document Y9J1nDd2400kJm72Law56JRRy

110 G. Berry, J. C. Gilson, S. Holmes, H. C. Lewinsohn, and S. A. Roach Ashestc evaluated. In this example some of the concentra tions could be zero to cope with a break in exposure, C2 or cs = 0, or with retirement, a = 0. Then the cumulative dose is given by: but is assumed to be proportional to the concentra tion. Then the amount of dust in the lungs at time v is, apart from a constant of proportionality, a(v\ given by: with a' some n The cumulative dose =, ci/i + cz(tz - h) + cs(l3 - tz) + 04(14 -- tz) JA(y) = c(u) e~A du This i: This is how the cumulative dose would be evaluated in practice, but to simplify a more general approach it may also be written as an integral. Suppose exposure started at time zero and is to be evaluated up to time t, and that the concentration at time u is c(u) for 0 u < t\ again c(u) would be zero during breaks in exposure or after retirement. Then If it is supposed that each component of dust which was deposited in the lungs contributes to the dose for the time it remains in the lungs then the dose D(t) evaluated at time t is given by: JD(t) = ` /4(v)[dv Occup; based dose a The re that a instead and p equivai cumulative dose = f c(u) du Jo t rv c(u) e~A 0 Jo du dv differei used tc An i This measure attaches no more importance to exposure a long time ago than to recent exposure, and does not alter after exposure has ended. Both t ct c(u) I e-A (v~") dv du 0 J to cons of the are relf of these properties are unrealistic for a disease, such = T c(u) {1 - e"A } du ! i as asbestosis, which is dependent more on early exposure than on recent exposure and which may A J0 i develop after exposure has ended. The simplest way of allowing for both of these points was given by Jahr (1974) who suggested that each component This is the generalised measure which, except for infinite A, has the properties that, first, it gives more It can relatioi tt t of exposure should be weighted by the time which has elapsed since the exposure occurred. Thus, cumulative dose weighted by time since exposure is given by weight to exposure a long time ago than to recent exposure and, second, it continues to increase after exposure has ended. If A tends to infinity then D tends to zero, but in such a way that AD tends to cumulative dose. Thus, in effect the cumulative j where. earlier. dose may be considered as a special case of the ' If, i: (t -- u) c(u) du 0 generalised dose when elimination of dust from i the lungs takes place very quickly. If A tends to ' dose a norma zero, then D tends to the cumulative dose weighted propoi and, in practice, evaluated by summing contributions by time since exposure which, therefore, is also a then a of the form special case of the generalised measure when there obtaim is no elimination of dust from the lungs. I cz(tz -- t\) {t -- i(ti + tz)} To summarise, the generalised measure consists I of a family of dose measures with each member of the over each period of exposure to a fixed concentration. family defined by the parameter A, or, in an equiva which The weighting factor could be regarded as the lent manner, by the half-life time T. The full family time that the dust has been in the lungs if elimination is obtained by allowing T to vary from zero to has not taken place. Looking at the measure in this infinity. The approach followed here is akin to that way, and postulating that elimination does occur, leads to a generalisation. Suppose that, over the long term, dust is eliminated from the lungs at a rate proportional to the amount in the lungs, and the constant of proportionality is A; in other words, in the absence of further exposure the amount of dust in the lungs declines exponentially at rate A and will be reduced to one half of its level in time T = In2/A, the half-life time. The actual amount of dust deposited in the lungs is unknown, of the British Thoracic and Tuberculosis Association (1975). DOSE-RESPONSE RELATIONSHIPS If P is the prevalence of a sign at dose D, then a dose-response relationship is defined by a functional relationship between P and D, that is, P = f(D). All the relationships considered are such that P is zero when D is zero, and as D increases above zero then so also does P; this excludes relationship | f > ! Botl prevalt dose e assumi lungs : and, ir period observ' attaine the for )