= Randomized controlled trial
{wiki}
= Randomised controlled trial
{synonym}
A <randomized controlled trial> assigns experimental units to competing <treatments> by a specified random mechanism and compares their outcomes. Under <complete randomization> of $N$ units, exactly $n_1$ receive assignment one and $n_0=N-n_1$ assignment zero. With fixed <potential outcomes>, each unit has assignment <probability> $n_1/N$. Therefore
$$
\mathbb E_A\left[\frac1{n_1}\sum_i A_iY_i(1)-\frac1{n_0}\sum_i(1-A_i)Y_i(0)\right]
=\frac1N\sum_i[Y_i(1)-Y_i(0)].
$$
This proves design-unbiasedness of the mean difference for the finite-population <average treatment effect>, assuming <consistency in causal inference> and no <interference in causal inference>.
<Randomization> controls the assignment distribution; it does not force every realized baseline <covariate> difference to be zero. Equal assignment <probabilities> yield unconditional exchangeability in the design, whereas covariate-dependent randomization can require <conditional exchangeability> and an analysis respecting that design.<Estimating causal effects from epidemiological data by Miguel A. Hernán and James M. Robins>[Computation of causal effects via (conditional) randomisation: designs 1 and 2]{ref}
When assigned and received <treatments> differ, an <intention-to-treat analysis> estimates an assignment-policy effect. A treatment-receipt effect needs additional assumptions. <Allocation concealment>, <blinded outcome assessment> and handling of missing follow-up address other sources of distortion beyond random assignment itself.
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