Not sure that my answer is in the format you want but here goes. If P1 is the probability of event 1 happening then the probability of the event not happening is P3 = (1 - P1) or P3 = (100% - P1) if you have defined your risk as a percentage. Similarly, if P2 is the probability of event 2 happening then the probability of it not happening is P4 = (1 - P2). The probability of neither event happening is P5 = P3 x x P4. Hence, the probability of one of the events happening is P6 = (1 - P5). The probability that both events happen is P7 = P1 x P2. Hope that makes sense.

HI,

Thank you for the answer. Is this valid only when events are independent? Both biomarkers are from the same patient

Hi Indra, my answer is based on statistics, I can't comment on the medical side. If medically, event 1 is based on biomarker 1 and event 2 is based on biomarker 2 then the events are independent, even though they are for the same patient. If there is some interdependency, i.e. there is a probability P1a of event 1 based on biomarker 1 and a probability P1b of event 1 based on biomarker 2 then the probability of event 1 when both biomarkers are present is P1 = 1 - (1 - P1a) x (1 - P1b). Notice that if the presence of biomarker 2 has no effect on the probability of event 1 then P1b = 0 and the equation reduces to P1 = P1a. The same applies to event 2. Once the probabilities P1 and P2 have been established they can be considered as independent, the interdependency has been accounted for by combining P1a with P1b and P2a with P2b.

For an individual you would have to know if the factors are independent of each other or not (eg if they are highly correlated, then the combined information is no more useful than that gleaned from one of them). If you have a lot of data on a lot of people with outcome measures then a logistic regression model can be constructed. This allows probabilities of the outcome to be calculated for any individual.