If a disease follows a logistic distribution in its age of onset and penetrance, then these can be calculated if the mean age of onset and standard deviation for age of onset are known.


Penetration at Given Age


penetrance at age x =

= 1 / (1 + EXP(-Y))


Y =

= 1.8138 * ((age x) - (mean age of onset)) / (standard deviation in age of onset)



• 1.8138 = (pi) / SQRT(3)

• The penetrance is the decimal fraction of all susceptible individuals who have expressed the disease.


Age for Given Penetrance


age for given penetrance =

= (mean age of onset) - (((standard deviation in age of onset) / 1.8138 ) * LN((1 - (given penetrance)) / (given penetrance)))


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