
 If,
over the past week, a subject exposed x hours to the effect of exertion, and
the other y hours were not exposed to. The assumption that "the disease is a
random event" means the disease can happen any time over the past week. In
another words, any hour over the past week would have the same chance to
have the disease fallen in that particular hour. Therefore, the odds that
the disease occurred in the effect period after the exposure would be x:y.
 Thus, algebraically, in the expected odds (x:y), x is the amount of
persontime exposed to the exposure effect and y is the unexposed
persontime. To estimate the amount of "exposed" persontime, we will
multiply the reported usual frequency of exposure, say exertion, by the
length of exposure effect period; and the unexposed persontime is then
calculated by subtracting the exposed persontime from the total
persontime.
