# How to analyze the longitudinal effect of blood pressure and its treatment on outcome

Say I have an observational dataset over 20 years with blood-pressure measured each year for 1000 men.

Each year a decision is made whether to start antihypertensive drug A, drug B or continue without medication. This decision is based on the blood-pressure, but the exact bloodpressure threshold is left at the discretion of the treating physician.

Moreover, the drugs can also be discontinued or changed from $A->B$ or $B->A$ based on the blood pressure.

Is there a method that allows me to disentangle the isolated effect of bloodpressure from treatment with drug A or drug B on outcome (Dead/Alive)?

Would a marginal structural model allow such complexity ?

• You'll need at the very least to address confounding by indication in any attempt at identifying a causal effect. See e.g. Kyriacou, Demetrios N., and Roger J. Lewis. “Confounding by Indication in Clinical Research.” JAMA 316, no. 17 (November 1, 2016): 1818–19. doi:10.1001/jama.2016.16435. A graphical causal model would be a great place to begin; see bayes.cs.ucla.edu/BOOK-09/causality2-excerpts.htm. – David C. Norris Dec 27 '16 at 19:59
• Let $Y_{it}$ be the outcome of $i$ in period $t$. Let $X_{it}$ be the vector of covariates, including blood pressure, and let $D_{it}$ be the dummy variable of the doctor's decision for individual $i$ in year $t$. If we write $Y_{it} = g(X_{it}, D_{it}) + u_{it}$, where $g$ can be a linear function of $X_{it},D_{it}$, the problem is essentially the endogeneity of $D_{it}$, which could be correlated with $u_{it}$. A natural solution to find instrumental variables that affect the doctor's prescription but are uncorrelated with the patient's unobserved heterogeneity $u_{it}$. – semibruin Dec 27 '16 at 22:13