= Symmetric treatment crossover attenuates a risk difference
{title2=$\Delta_{\rm assignment}=(1-2c)\Delta_{\rm receipt}$}
Assume treatment receipt gives event risk $p_1$, nonreceipt gives risk $p_0$, and a fraction $c$ in each equally sized randomized arm crosses to the opposite treatment. The two assignment risks are $(1-c)p_1+cp_0$ and $cp_1+(1-c)p_0$. Subtracting yields the displayed attenuation, with $\Delta_{\rm receipt}=p_0-p_1$. It depends on the stated equal crossover fractions and unchanged receipt-specific risks; it is not a universal formula for every form of <treatment contamination>.
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