Table 2.

Interpretation of the coefficients in Equation 1 and Equation 2 along with the relationships between the coefficeints of the two models

	Equation 1	Equation 2	Relationships
Baseline level: E(Yt|T = 0)	β0	β′0	β0 = β′0
Pre-intervention slope: E(Yt+1 − Yt | T ≤ Ti)	[β0 + β1(T+1)] − (β0 + β1T) = β1	[β′0 + β′1(T + 1)] − (β′0 + β′1T) = β′1	β1 = β′1
Post-intervention slope: E(Yt+1 − Yt | T>Ti)	[β0 +β1(T+1)+β2+β3(T + 1 − Ti)] − [β0 +β1T+β2+β3(T − Ti)] = β1+β3	[β′0 +β′1 (T + 1) + β′2 + β′3 (T + 1 − Ti)] − [β′0 +β′1 T + β′2 + β′3 (T − Ti)] = β′1+β′3	β3 = β′3
Slope change: E(Yt+1 − Yt | T>Ti) – E(Yt+1 − Yt | T≤Ti)	(β1+β3) − β1 = β3	(β′1+β′3) − β′1 = β′3
Immediate/level change: E(Yt |T = Ti & Xt = 1 ) − E(Yt | T=Ti & Xt = 0)	[β0 +β1T+(β2+β3Ti)]-[β0 +β1T] = β2+β3Ti	(β′0 + β′1T + β′2) − [β′0 + β′1T] = β′2	β2 + β3Ti = β′2

Where Y_t is the outcome at time t, T is the time elapsed since the start of the study, X_t is a dummy variable indicating the pre-intervention period (coded 0) or the post-intervention period (coded 1). T_i represents the time point when the intervention starts (X_t = 1 for T ≥ T_i). β₀ or β′₀ represents the baseline level of Y at T = 0, β₁ or β′₁ represents the underlying pre-intervention trend (the change in Y associated with a single-unit increase in time before the intervention), (β₂ + β₃T_i) or β′₂ both purport in the peer-reviewed literature to represent the immediate level (or intercept) change following the intervention, and β₃ or β′₃ is interpreted as the change in the slope of the trend following the intervention, compared with the pre-intervention trend