Estimating Causal Treatment Effects in the Sequential Parallel Comparison Design (SPCD)

The high placebo responses observed in many placebo-controlled randomized clinical trials, particularly in psychiatric research, have hindered the demonstration of treatment efficacy. To address this issue, Fava proposed the Sequential Parallel Comparison Design (SPCD) in 2003, which aims to mitigate the placebo response by estimating a pooled treatment effect (denoted by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>SPCD</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{SPCD}} $$</mml:annotation></mml:semantics> </mml:math> ). This is achieved by combining the treatment effect observed in the first stage among intention-to-treat (ITT) subjects with the second-stage treatment effect among placebo non-responders through a weighted average approach. However, the challenges in interpreting this pooled treatment effect causally complicate the review of SPCD-designed studies. This paper explored the pooled SPCD treatment effect and contrasted it with two causal estimators: The causal average treatment effect among non-responders (denoted by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mi>N</mml:mi> <mml:mi>R</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{NR} $$</mml:annotation></mml:semantics> </mml:math> ) and the causal average treatment effect had all ITT subjects exhibited low responses during the study (denoted by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>Joint</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{Joint}} $$</mml:annotation></mml:semantics> </mml:math> ). These estimators reflect two opposing views of the placebo response, either as an immutable personal trait or as a manipulable feature. Through carefully designed simulation studies, we demonstrated the direction and magnitude of bias when interpreting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>SPCD</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{SPCD}} $$</mml:annotation></mml:semantics> </mml:math> as either <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mi>N</mml:mi> <mml:mi>R</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{NR} $$</mml:annotation></mml:semantics> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>Joint</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{Joint}} $$</mml:annotation></mml:semantics> </mml:math> . In these simulation studies, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>SPCD</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{SPCD}} $$</mml:annotation></mml:semantics> </mml:math> tends to underestimate the treatment benefit when compared to two causal estimators in most scenarios. Furthermore, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>Joint</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{Joint}} $$</mml:annotation></mml:semantics> </mml:math> , developed to overcome the interpretational limitations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>SPCD</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{SPCD}} $$</mml:annotation></mml:semantics> </mml:math> , exhibits statistically superior performance over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mi>N</mml:mi> <mml:mi>R</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{NR} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow> <mml:mrow><mml:mtext>SPCD</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\Delta}_{\mathrm{SPCD}} $$</mml:annotation></mml:semantics> </mml:math> in terms of bias and MSE when using the G-formula approach. As such, we recommend its adoption where applicable. The first completed trial using the SPCD design, ADAPT-A, is reanalyzed to further confirm these findings.