Instrument variable analysis using randomized data

[Emily Parker]

I am analyzing the effect of two randomized interventions on 1) first-time and, 2) second-time event attendance. All variables are binary (0 vs. 1). Second attendance was conditional on first attendance. A large percentage (~50%) of people did not show up for first attendance; an even smaller percentage of first-time attendees (~50%*~20% = 10%) showed up the second time.

Intervention one was designed to increase both attendances; intervention two, just second attendance. Neither increased the probability of first or second attendance, but the interaction between second attendance and intervention was significant for both. The probability of second attendance was greater for both interventions relative to first.

The issue is that we are trying to test the effect of both interventions on second attendance given first attendance. We are also controlling for household using a random intercept.

I was advised an instrumental variable (IV) analysis would adjust for first attendance (Sussman BJ, Hayward, RA, BMJ, 2010). I regressed first attendance on intervention controlling for household, and then regressed second attendance on the predicted probability of first attendance (the instrument variable). I did this separately for both interventions, and the instrument variable was significant for both. My questions are:

1. Is IV appropriate given both interventions have a non-significant association to first attendance? I've read the instrument variable (randomized intervention), should be related to the treatment/biomarker (first attendance).

2. If appropriate, how do I interpret the instrument variable coefficients?

3. Are there better analyses which measure second attendance for first-time attendees only?

[Clyde Schechter]

The issue is that we are trying to test the effect of both interventions on second attendance given first attendance. We are also controlling for household using a random intercept.

I was advised an instrumental variable (IV) analysis would adjust for first attendance (Sussman BJ, Hayward, RA, BMJ, 2010). I regressed first attendance on intervention controlling for household, and then regressed second attendance on the predicted probability of first attendance (the instrument variable). I did this separately for both interventions, and the instrument variable was significant for both.

This sounds perverse to me.

If the goal is to test the effect of both interventions on second attendance given first attendance, the first thing to do is restrict the data to those who attended the first time. You don't "control" or adjust for first attendance, because everybody in the analysis has first attendance. The assignments to the two interventions are still randomized--the selection on first attendance may make the assignments somewhat less balanced than they were, but the randomization is not broken. So just analyze this directly as a randomized trial of the two interventions on second attendance in the data restricted to first attendees.

Am I missing or misunderstanding something?

[Emily Parker]

Hi Clyde,

Thank you for response. This simple solution also occured to me, and I have since run the analysis restricting first-time attendees only.