Compare mean heart rate after drug administration with multiple time points against baseline I want to compare mean heart rate change from baseline (T0) within the group. There are 10 continuous time points (T0,T1,....T10.) like t1 vs t0, t2 vs t0, t3 vs t0.. what test should i apply ? paired t test is appropriate? The studied drug was given at t2.
 A: I will assume that you do not have a control group (otherwise, you could proceed as similarly but add a group variable to the fit). This makes this kind of tricky, but here's an idea:
Denote with $h_{p,t}$ the heart rate of patient $p \in \mathcal{P}$ at time $t \in \{1, ..., 10\}$, and with $a_{t}$ an indicator variable that takes value one after treatment (i.e. for $t \ge 2$) and zero otherwise. Let the patient mean $m_p \sim \mathcal{N}(0, \sigma^2)$, follow a normal distribution with mean zero and unknown standard deviation $\sigma$. Finally let $\beta$ and $\mu$ be two fitted parameters.
Now fit the following mixed model:
$$
h_{p, t} = \mu + \beta a_t + m_p
$$
You can now test whether the drug had an effect by testing against the null hypothesis $\beta = 0$.
Intuitively, what this does is it assumes that the heart rate is distributed normally between patients with an unknown mean $\mu$ and standard deviation $\sigma$. Furthermore, after the drug has been administered, the heart rate is modulated by a constant $\beta$. However, it does not discriminate between any time-points after administration. I am not sure how one could a time dependency and also test for a drug effect without control group.
The above model can be implemented using the lme4 package in R, where $m_p$ is a random effect. If you absolutely need p-values, you can use lmerTest.
