# Bootstrapping with repeated measurements

I am trying to estimate a linear relation between body temperature and body mass, and I have a sample of measurements from subjects, with most subjects having one measurement, but several subjects having two measurements in different times.

In order to estimating the slope 95% confidence interval, I could have used the usual formula, but since my data is partially correlated (due to having two measurements from the same subjects, for some of the subjects), I understand this will not be correct. So I was told it is better to use bootstraping technique.

My question is: How do I use bootstrapping while accounting for the fact that some of the subjects were sampled twice? Should I just take those subjects with 1/2 the probability of other subjects? Is that a common practice, and if so - how is it called? (possibly "Inverse Probability Bootstrap Sampling"?)

(In fact, there is an additional twist here, since I am using Passing-Bablok linear model, due to the nature of data; but answers related to ordinary linear regression, or even bootstrapping of 1 variable alone, are welcome as well).

• In another comment you write that the dataset is "not large." This ought to lead you away from bootstrapping, whose theoretical legitimacy holds only for large datasets (that is, asymptotically). Instead, use an appropriate model. A simple and likely effective one is to suppose independent, homoscedastic measurement errors, permitting direct application of standard (ordinary least squares) modeling.
– whuber
Aug 3, 2021 at 13:35