Statistical Analyses of Non-Static Group Question

I don't have a background in statistics so perhaps someone can lend
some guidance with respect to the issue that I present here or tell me
where I can go to find guidance.

The goal is to determine how well a group of participants for a given
program is performing over a given period of time. The number of
participants is not static. The program has a lifecycle where the
number of participants starts out small, builds to a maximum then
declines through attrition until the program is retired. Participants
tend to participate with greater frequency when first added to the
program then taper off with time. A very small percentage of
participants are extremely active from the time they are added until
they leave the program and to a point where they artificially raise
the norm.

The question then is how does one compare group performance from one
sample to the next if the group dynamic is changing?

How does one account for the influx of new participants and the effect
they have on the group?

How does one correct for the overly active participants?

Is it valid to look at only those participants who appear in
subsequent sample periods (i.e. exclude additions and removals)?

Statistics is a broad subject. What form of analysis does this problem
represent? What texts (books) should I study to gain a better
understanding of the problem?

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