(LOCF) method. In this method, the last available
value is substituted for all missed measurements.
The problem with this approach is that it assumes
that had the subject not dropped out, he or she would
continue to respond exactly the same way they did
on their last visit before dropping out. This assump-
tion is never verifiable and often unreasonable.
Another approach is to substitute the worse possible
value for the missing data. The rationale for this
approach is that the results of the analysis will show
‘worst case scenario’ and if the drug passes this test
and can be labelled safe and effective, it would still
be so had subjects not dropped out. This rationale is
certainly plausible. The trouble is that efficacy of
important and moderately efficacious drugs may be
missed, or mildly toxic drugs may end up with
unnecessarily serious safety warnings on their
labels. There are other methods of statistical ‘impu-
tation’ where a value is calculated using some algo-
rithm and is substituted for the missing value. The
reasonableness of these procedures must be judged
onacase-by-casebasisbyexaminingtheunderlying
assumptions and judging their appropriateness in
the given situation.
Missing data
Dropouts present one type of missing data; namely,
data are not available from a certain time point
onward. Data could be missing in many other
ways. A subject may miss a visit, a sample could
be invalid or a subject may fail to fill out a form or a
questionnaire. When data are missing at random,
the effect is generally some loss in the power of the
statistical analysis. When data are missing accord-
ing to some pattern, bias can be introduced in
addition. Some statistical study designs are parti-
cularly sensitive to missing data. Crossover
designs are such designs. In crossover designs,
each subject is randomly assigned to a sequence
of treatments administered at certain time interval
apart. The reason for using these designs is that
each subject serves as his own control, and the
comparisons between treatments are donewithin
subjects. When the within-subject variability is
substantially smaller than the between or inter-
subject variability, the crossover design may be
quite powerful and offer great savings in the utili-
zation of subject resources. The loss of onevalue in
a crossover study may result in a loss of the entire
sequence. Some designs require certain balances
among the treatments and schedules of treatment.
Missing data can destroy such balances, seriously
handicapping the statistician’s ability to analyze
the data. Here too, imputation, with all the caveats
going along with it, is the method of ‘correcting’
for the missing data. When much data are missing,
say 20% or more, one should seriously question the
validity of the conclusions drawn from the study, as
they might be over-influenced by the assumptions
made how to handle the missing data than by the
data themselves.Intent-to-treat analysis
One possible way of handling protocol violations,
noncompliance, missing data, dropouts and so on is
to remove all subjects whose violations are con-
sidered to be serious from the analysis and analyze
only the data obtained from the subjects who rea-
sonably complied with all the requirements stated
in theprotocol.Suchanalysis is sometimes referred
to asper-protocol analysis(PP). The problem with
this approach is that the effectiveness of the rando-
mization process as a mechanism to bestow bal-
ances among latent on non-latent prognostic
factors, and set the stage for making causal rela-
tionship inferences, is disturbed. Also, if the rea-
sons for these violations are not independent of
treatment or the subject’s condition, the removal
of these subjects for the analysis may introduce a
bias in the analysis. Therefore, it is customary to
always perform anintent-to-treat-analysis(ITT) in
which all subjects randomized, or all subjects ran-
domized who received at least one dose of study
medication, are included. The proponents of this
approach argue that in addition to the preservation
of the randomizationprocess, the ITTreflects ‘real-
life’ results. They argue that in ‘real-life’, as
opposed to the artificial setup of the clinical
study, neither patients not their physicians follow
a specific rigorous protocol. So, if the outcome of
noncompliance, for example, is reduced efficacy,
this is what one should expect to see when the drug340 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH