Following my previous question (How to create a dataset with conditional probability?), now I want to create a dataset in R containing the information about TWO symptoms, and 1 disease.
Symptoms $S_1$ and $S_2$ and independent and conditional independent, so $P(S_1|S_2)=P(S_1)$ and $P(S_2|S_1)=P(S_2)$.
Suppose we have the following data:
Following the method that Henry used to solve my previous question, I think that we have to complete this table:
Disease Yes No | Symptom1 Yes | a b Symptom2 Yes | | | No | c d -------------|-----------------|------------------ | Symptom1 Yes | e f Symptom2 No | | | No | g h
What I'd like to calculate, from the dataset, is the value of $P(D|S_1 and S_2)$. Also I need to calculate the probability of each event, in order to run some simulations.
I tried to find the value for
a...h, but I didn't find enough relationship to solve the 8-parameter system.
What I know is:
a + c + e + g = 0.003
a + b + e + f = 0.005
a + b + c + d = 0.008
(a + e) / (a + c + e + g) = 0.3
(a + c) / (a + c + e + g) = 0.25
a + b + c + d + e + f + g + h = 1
So, my question is: are my data sufficient to create a dataset in R, which simulate a real population? The approach I tried was useful in the case of only 1 symptom (How to create a dataset with conditional probability?), as Henry explained. Is it good for the case of two symptoms? Or n-symptoms? Does it exists another approach to simulate this data?