# Analysis of pre and post treatment

I have the following data:

1. A random group of patients with a certain disease who receive a drug at a certain time.
2. 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.
3. 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.
4. General information about the patients (age, BMI, etc.).
5. 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 𝑝1 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.

• I would approach this with logistic regression. For getting a clear idea of whether something is important, there are a few approaches that make sense. One is to generate a bunch of models that include different reasonable combinations of those factors and compare them using likelihood with AIC or BIC or the like. A second is to fit the model that makes the most sense to you based on your understanding of the system and compare the model coefficients and their CI. For this approach to make any sense you have to scale your predictors so that the betas are comparable. Nov 16, 2019 at 14:47
• @Michael I don’t want to solely fit a model and find out whether a variable is important or not. What I want to prove is that these variables are important in terms of pre treatment and post treatment. I mean how can I find out these variables first change significantly between pre and post treatment, and second if I can associate then with the survival.
– H_A
Nov 16, 2019 at 15:15

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).

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?

• I do have the post $p$ from the historical data, since if the death occurs it happens after the drug is given (thus after the measurement of post $p$).
– H_A
Nov 16, 2019 at 15:37
• OK. Depends on what you hypothesize about the pre/post measurements. If you think differences are important, then put the differences in a logistic regression. Else, you can put the raw data in a logistic regression. Nov 16, 2019 at 15:40
• Thanks. I’ll try and let you know about the results
– H_A
Nov 16, 2019 at 15:42
• I think you have a 3rd option which is to keep the "raw" data, but to code pre/post as an indicator variable. Then it can be something like glm(survived~age*BMI+p1*pre+p2*pre+p3*pre+p4*pre, family="binomial") obviously you know your data so carefully selecting which interactions to include etc. will be kind of important because you could have a very big model very quickly. It seems conceivable that with an interaction between an indicator pre and the p's, you could ask both "is p_blah important in general" and "is the change in p_blah before and after treatment important." Nov 16, 2019 at 17:10