The correct
answer is (b).
An adjusted
analysis provides a higher power for detection of any treatment
effects compared to an unadjusted (or "crude" analysis). With
linear models, predictor variables explain variability in the
outcome, which leads to smaller variability in the adjusted
estimate of the treatment effect. With nonlinear models, such
as logistic regression or Cox
regression, the variability in the adjusted estimate of the
treatment effect is not smaller. However, the adjusted estimate
will be more extreme (further away from the neutral value),
which causes a net increase in power to detect a treatment effect
(Robinson
and Jewell, 1991). So, in either analysis, the adjusted
model will increase the likelihood that the researcher can detect
a true difference between groups.