Calculate probability of disease appearance I am a doctor so please be kind with me and my basic understanding of statistics.
I have a dataset consisting of patients and their visits and I have labelled the presence of a specific kind of mole in their left and/or right hand with {0,1} values (0 = not present and 1 = present). The dataset looks like this:
**I removed it since the answers are provided; I can send it upon new request
So, that means that patient A1-001 had 6 visits with no presence of mole in his right hand during all visits and present of mole in his left hand in all visits except the first one. 
I am interested in finding the probability of a hand developing a mole among only the patients that developed a mole in one hand and finding the probability of developing a mole in the other hand (given that the patient had already a mole in the other hand).
Furthermore, I want to know what is the probability of developing a mole within visits among the patients that developed a mole at some point in both hands
Could you help me model these simple questions?
 A: I personally feel this lends itself well to a survival analysis.
You have people without moles in a certain hand at the start of the period (your at risk population); you can select these, and you have time points for follow-up and whether or not they were censored (developed a mole). This gives you a hazard for whatever cohort you've selected.
You can then calculate a hazard ratio (e.g. for developing a right-hand mole in people with a left-hand moles at baseline, versus those without). This could be expressed on a Kaplan-Meier graph and will come with a confidence interval.
A: There is no modeling to be done here, all of your questions are simple conditional probabilities.
Alright, since people did not appreciate that answer, you need to clarify a couple of things.  

I am interested in finding the probability of a hand developing a mole among only the patients that developed a mole in one hand and finding the probability of developing a mole in the other hand (given that the patient had already a mole in the other hand).

Do you mean per visit? Or that they never developed a mole ever?
From your example:
Patients 1 and 3 developed a mole on one hand.  Patient 1 never developed a mole on the other hand but patient 3 did, so you could argue the answer to your question is 50%.  Now, you could also argue that patient 1 had 4 checkups with 1 mole and not on the other and patient 3 had 0 checkups with 1 mole and not the other so the probability could be 1/5 = 20%.  It depends on how you define your question.
A: Personally, I think you can start by studying the multicovariance 
generalized linear models: https://cran.r-project.org/web/packages/mcglm/index.html
https://cran.r-project.org/web/packages/mcglm/vignettes/GLMExamples.html 
http://cursos.leg.ufpr.br/mcglm4aed/slides/2-mcglm.html#(1)
Those models are apropriated for when you have more than one response
variable and they're not gaussian, and this is your case, as you have two binary variables (mole or not mole in each hand). Also, the method lets you deal with intra-individual dependencies, which is given by the longitudinal structure. Here, longitudinal means repeated measures for the same individual, along the time.  
I think the links above will help you to have a good idea about these techniques, and they also provide the computational implementation in R. 
