Trend analysis using proportions

[Anton-24]

Dear Listers,

I would like to conduct a trend analysis on set of proportions, but don’t
know exactly how to proceed.

I have 5 programs that have measured retention (binary: yes/no), each year,
over a period of 7 years.  One program started in year 2, while another
started in year 3, so I don’t have a complete set of proportions for all
programs for all seven years.  The data are aggregated; I have proportions
and Ns, but not individual student-level data across time.

I would ultimately like to make statements something like: "Program A has
experienced a relatively strong upward trend in the rate of retention, when
compared to Program B with a weaker upward trend, and Program C with varying
periods of high & low rates.

Any thoughts or suggestions on the appropriate analysis are much appreciated.

Anton