. Author manuscript; available in PMC: 2010 Aug 16.

Published in final edited form as: Psychiatr Ann. 2008 Dec;38(12):772–783. doi: 10.3928/00485713-20081201-10

Table 1.

Formulae for calculating without baseline covariates the ITT, AT, PP, and IV treatment effect estimates under two different clinical trial designs: 1) when adherence to the experimental treatment is not measured in the control group; and 2) when adherence is measured in the control group, e.g., adherence to treatment guidelines. We first define the character symbols used for the formulae.

Design	Estimated Treatment Effect
Design	Intention to Treat	As Treated	Per Protocol	Instrumental Variable
Adherence not measured in controls	A1−A0 = (A11+A10) − A0	A11 − (A10+A0)	A11−A0	ITT/P11 = (A1− A0)/P11
Adherence measured in controls	A1−A0 = (A11+A10) − (A01+A00)	(A11+A01) − (A10+A00)	A11−A00	ITT/(P11−P01) = (A1−A0)/ (P11−P01)

A1 = observed average for randomized to treatment group

A0 = observed average for randomized to control group

A11 = observed average for participants who receive treatment in the randomized to treatment group

A10 = observed average for participants who do not receive treatment in the randomized to treatment group

A00 = observed average for participants who do not receive the treatment in the randomized to control group

A01 = observed average for participants who do receive the treatment in the randomized to control group (e.g., take the medication in the usual care group)

P11 = Proportion receiving treatment in the randomized to treatment group

P01 = Proportion receiving treatment in the randomized to control group