ITT vs Weighted Per-protocol API Comparisons

Compared below is the ITT vs. Weighted Per-protocol API Comparisons.

Ratio of ratios for all outcomes

This analysis was a weighted and replicated GEE with treatment weights, stage 1 and stage 2 weights. So a heavy drinker who participated in both stages had three weights multipled (treatment, stage 1 and stage 2). A light drinker who participated at stage 1 had two weights multiplied (treatment and stage 1). Then I ran the exact ITT analysis (weighted and replicated GEE) with these new weights.

  • Light drinker weights: \(\frac{I(C_1=1)}{Pr(C_{1}|A_1,\textbf{X})*.5}\)

  • Heavy drinker weights: \(\frac {I(C_1=1,C_2=1)}{Pr(C_2=1|\textbf{X},C_1=1)Pr(C_1=1|A_1,\textbf{X})*.25}\)

where \(C_1,C_2\), \(A_1, A_2\) and \(\textbf{X}\) are the compliance/“participation” indicators, variablas for the stage 1 and stage 2 interventions and the baseline variables included in the propensity for participation models. The baseline variables I used were from stepwise regression models - Sex and pre-college drinking for stage 2 and parent education status, pre-college binge drinking, intention for greek life and the stage 1 treatment group for stage 1.
Ratio of follow-up 1 to baseline (SE)
Ratio of follow-up 2 to baseline (SE)
Early/Coach Early/Email Late/Coach Late/Email P-value Early/Coach Early/Email Late/Coach Late/Email P-value
Binge drinking
ITT 2.05 (0.28) 1.65 (0.25) 1.57 (0.23) 1.59 (0.24) 0.422 3.19 (0.47) 2.58 (0.36) 2.01 (0.30) 2.21 (0.30) 0.148
Weighted Per-protocol 2.10 (0.46) 1.67 (0.41) 1.40 (0.40) 1.23 (0.33) 0.446 2.96 (0.67) 2.50 (0.52) 1.84 (0.51) 2.14 (0.47) 0.595
Alcohol consequences
ITT 1.61 (0.15) 1.64 (0.16) 1.68 (0.16) 1.63 (0.17) 0.987 0.83 (0.12) 0.95 (0.14) 0.99 (0.15) 0.79 (0.14) 0.530
Weighted Per-protocol 1.61 (0.26) 1.46 (0.19) 1.66 (0.28) 1.62 (0.33) 0.927 0.74 (0.18) 0.81 (0.19) 0.94 (0.29) 0.87 (0.24) 0.946

ITT vs. Per-protocol: Main effect of Stage 1 (Timing)

This analysis used the same model (weighted and replicated GEE) as above except without the stage 2 weight. So heavy drinkers who participated at stage 1 but not stage 2 were included in the analysis.
Ratio of follow-up 1 to baseline
Ratio of follow-up 2 to baseline
Early (SE) Late (SE) Ratio of ratios (95% CI) P-value Early (SE) Late (SE) Ratio of ratios (95% CI) P-value
Binge drinking
ITT 1.84 (0.21) 1.58 (0.19) 1.17 (0.84, 1.61) 0.347 2.87 (0.35) 2.10 (0.24) 1.36 (0.99, 1.88) 0.059
Weighted Per-protocol 1.87 (0.33) 1.32 (0.27) 1.42 (0.83, 2.43) 0.198 2.72 (0.47) 1.99 (0.36) 1.37 (0.84, 2.23) 0.209
Alcohol consequences
ITT 1.62 (0.13) 1.65 (0.13) 0.98 (0.79, 1.23) 0.876 0.89 (0.10) 0.89 (0.12) 1.00 (0.70, 1.43) 1.000
Weighted Per-protocol 1.53 (0.17) 1.64 (0.23) 0.94 (0.66, 1.33) 0.709 0.77 (0.14) 0.90 (0.20) 0.86 (0.49, 1.51) 0.597

Binge drinking frequency

I did another analysis for stage 1 which was not a replicated GEE. For the students randomized to an API, I ran a geeglm model with log link and a exhangeable correlation structure with only stage 1 weights, since technically I don’t need treatment weights to compare the timing interventions. I was looking at significannce of the time1:A1 and time2:A1 interactions. I did this for binge drinking frequency and alcohol consequences as the outcome.

Alc Consequences

ITT vs Per-protocol: Main effect of Stage 2 (Bridging)

This analysis used the exact same model (weighted and replicated GEE with the same weights) as the analysis comparing the four adaptive interventions.

I also looked at the subset of heavy drinkers and did a geeglm with a log link and exchangeable correlation structure with stage 2 weights. I was looking at significannce of the time1:A2 and time2:A2 interactions. I did this for binge drinking frequency and alcohol consequences as the outcome.

Binge drinking frequency

Alc Consequences

API vs. Control

I did not do a replicated GEE for this analysis. I took all the subjects, gave a weight of 1 to the control subjects and used the following weights for students in the API. - Light drinker weights: \(\frac{I(C_1=1)}{Pr(C_{1}|A_1,\textbf{X})}\) - Heavy drinker weights: \(\frac {I(C_1=1,C_2=1)}{Pr(C_2=1|\textbf{X},C_1=1)Pr(C_1=1|A_1,\textbf{X})}\)

I decided to model the probabilities of compliance at Stage 1 and Stage 2 separately because there could be time-varying confounding. Then I ran a gee with exchangeable correlation and a log link. I looked at the API*time interactions.