# Compare how fast two time-series grow

I collected data from Pubmed containing articles published about two different topics.

The first is a yearly series of articles about omega 3 supplements. The second is a yearly series of articles published about probiotics supplements.

I want to understand how fast the research has grown over time (in plain English, capture the scientific interest over time) and specifically whether the scientific interest grew somehow "faster" for a topic rather than the other.

Please find here the data in a public gdoc:

https://docs.google.com/spreadsheets/d/1yw2F8a6f0_v_-QmCYpWZfm12ev_qirdRNWcfwR71Qjk/edit?usp=sharing

I don't expect a full solution but at least some indication to where to start looking for my answer.

I assume it is something I can check with the time series slope, but I need some more inputs for going deeper in my research because I am kind of lost. Thank you! • Your linked data shows a large jump in the value of "probiotics" from 1970 to 1974, changing from 59 to 475, but I do not see this on your plot of the data. Both "omega" and "probiotics" show a sudden drop from year 2018 to year 2019 but again I do not see this on your plots. Would you please chech that the posted data link and plots match in this? – James Phillips Jul 31 '19 at 17:49

## 2 Answers

This is very similar to looking at stock prices and other financial variables in econometric analysis. The way to do this would be to plot $$\log(x_{t+1}) - \log(x_t)$$ at each time period $$t = 1,...,T-1$$. This will show the rate of growth of each of the series, which is a good measure of "how fast they are growing". (Note that if you have any zero values in your data then the growth to the next non-zero value is infinite.)

You might typically expect an 'interest' curve to follow an S-shape - interest starts low, accelerates quickly, then reaches a maximum. It might fall again later, but that does not seem to be the case in your time period.

To model this, you could try to fit a logistic function to each of the data sets - one of the parameters of the logistic is the 'steepness' or rate of increase.

• Thank you! I dont understand tho, to my knowledge a logistic function models a dicotomous outcome - either 0 or 1; how would it work with a continuous variable like the dataset here? – xxxvinxxx Jul 31 '19 at 14:57
• The logistic function is a continuous function, so it allows all values between 0 and 1. You would need to scale it to represent the range of your data, so multiply the logistic function by, say 200 or what you think might be a reasonable upper limit for the phenomenon you are modelling. If you want to compare the rates between the two data sets, it might make sense to use the same maximum for both data sets, as long as you think it is reasonable that both data sets have the same theoretical maximum interest. – Jonathan Moore Aug 1 '19 at 8:42