Advice needed for time series correlation

Question

I have two time series data sets that I wish to compare. One is from an automated process of laboratory generated medical test results. The positive test results occur every day over N years.

The second is from manual collection of clinical information about the patients from on which the medical tests were performed.

My null hypothesis is that there is no correlation between the aggregated monthly counts of positive tests results over time and the aggregated monthly number of clinical follow-ups on those patients during the same period.

So, I am not looking for validation of laboratory test results. I am looking for correlation between two data generating processes over time.

Can someone advise if this sounds feasible / appropriate and suggest a strategy to undertake the analysis. Any point me in the direction of a useful resource.

Thanks.

Answer 1

I'd start with a cross-correlation function, because there may be lags involved; data should be pre-whitened to screen out nuisance effects like seasonality. (I think, unless this isn't so much "seasonality" as "tests are always done in the first month of a quarter)

I'm suggesting cross-correlation because you might expect lag effects (test is positive in late March, but follow-up occurs in early April).

There may be some other normalizing needed -- e.g. if the number of patients is twice as large at the end as at the beginning due to the clinic's population base getting larger.