Here, we show that the CUL4A protein level, a component of the CRL4–CRBN complex, has predictive value in MM patients treated with thalidomide- or lenalidomide-based therapy with higher response rates (ORR ≥ PR vs. SD/PD, p = 0.007; ORR ≥ VGPR vs. <VGPR, p = 0.027), translated into a favourable PFS (HR = 0.66, 95% CI 0.44–0.99; p = 0.046). This evidence concerns the gene CRBN and Miyoshi myopathy.