This scenario seems to be arising more and more with the usage of large datasets in an attempt to identify pilot data for associations, etc. I'm trying to figure out what method - if any - is the most appropriate way to analyze data from this type of scenario.
I have access to a de-identified, prospectively collected dataset with up to ten years of data points at varying intervals of time. There are all sorts of continuous and categorical data collected at each time point for each individual.
I have identified 50 individuals with a rare illness in the complete dataset. There are >5000 individuals in the dataset overall. The outcome measure that I'm interested in changes over time in all patients - in those with the rare illness and without. I'd like to know whether or not this continuous variable changes differently over time between the people with illness and those without the illness.
What is the best method to analyze this single outcome measure over time between the two groups?