Analysis of pre and post treatment I have the following data:


*

*A random group of patients with a certain disease who receive a drug at a certain time.

*Dose of the drug given to the patient. This drug has an affect to the heart which puts the patient to the risk of cardio attack.

*Four parameters ($p_1,...,p_4$) that are measured before and after the drug is given to the patient. These parameters determine patient's condition.

*General information about the patients (age, BMI, etc.).

*A binary variable indicating whether the patient survived or not.


The data looks like this:
d1 = data.frame(age= sample(20:50,5), BMI = rnorm(5,20,40),p1_pre= rnorm(5,0.5,2),p2_pre=rnorm(5,0.5,2),
                p3_pre=rnorm(5,0.5,2),p4_pre=rnorm(5,0.5,2),p1_post=rnorm(5,0.5,2),p2_post=rnorm(5,0.5,2),
                p3_post=rnorm(5,0.5,2),p4_post=rnorm(5,0.5,2),survived=c(1,1,0,0,1))



Goal:
Current approach: the current believe is that only one of the four parameters, (in item 3 of the above list; let’s call it p1) is an important indicator for knowing the patient's condition who has taken the drug is bad and therefore we should stop giving him/her the drug.
So the practice is that p1 is calculated before and after the treatment and if the value of p1 falls below an acceptable value, the drug is stopped
Hypothesis: the hypothesis is that 1 is not the only indicator, but the other 3 parameters (in item 3 of the above list) are also important indicators for knowing the patient's condition after taking the drug.
Question: What is the best way to study this data? how can I use the general information of the patients and the binary outcome?
Any help is greatly appreciated.
Thanks in advance.
 A: The first problem here is not what statistical model to use, but what experiment to conduct/what to measure when. The current proposal lacks data without treatment from comparable patients (ideally randomized controls), which makes it extremely challenging to find out anything about causal effects. While historical controls might help in case causal effects are extremely strong and so striking that they exceed any other source of variation/differences, this is usually very hard to be certain about. Furthermore, measuring the parameters repeatedly over time would be very helpful, if it is possible that the event that potentially occurs could also affect the values and/or the event might be fatal (=could preclude further measurements).
If you had the right data, then methods for principal stratum estimands would be what you'd want to look for (see e.g. the example here and this one).
A: From your comment...

I mean how can I find out these variables first change significantly between pre and post treatment

Because you measure them before and after, you can take the difference between the $p_i$ in the pre and post measurements and then build a model.  If the $p$ are continuous then a linear regression might be fine.  You will want to look at the intercept of this model to see the average change in the $p$ conditioned on the covariates.

and second if I can associate then with the survival.

If I am not mistaken, you don't know the post $p$ before you know if they survive, right?  
