Residual maximum likelihood (REML) is a technique for estimating varia
nce components in multi-classified data. In contrast to analysis of va
riance it can be routinely applied to unbalanced data and avoids some
of the problems of biased variance estimates found with standard maxim
um likelihood estimation. The full REML method is of particular value
for the analysis of unbalanced clinical trials as it allows recovery o
f all the available information on treatment effects which can lead to
significant improvements in their precision. The use of REML has unti
l recently been limited by heavy computational requirements and lack o
f readily available software. This is no longer such a restriction, ho
wever, as REML procedures are now available in several widely-used sta
tistical packages, including BMDP, Genstat and SAS. This paper describ
es the REML technique and discusses its application to three common ty
pes of clinical trial: crossover, repeated measures and multicentre.