Box 97 Options for imputation of missing values adapted from Ref [18

♦ If any one item is missing, call the scale missing, although this results in a much-reduced sample.

♦ Estimate scale score from the mean of those items that are available. This assumes missing items would have had a score equal to the average of the non-missing items. This is usually restricted to cases where the respondent has completed at least half of the items in the scale. One disadvantage is that imputing may result in numbers between the expected discrete numbers. This might affect summarizing data using presentations such as histograms, although an alternative is to estimate the score to the nearest 'real' score.

♦ Use general model-based imputation methods. The object here is to replace missing data by estimated values which preserve the relationship between items and which reflect as far as possible the most likely true value.

It is unlikely that patients who complete all QL forms will be truly representative of the whole group of patients, for example they will have to be survivors. This need not effect the comparison between treatments, as in many trials the reasons for non-completion of QL forms will be the same across treatment arms. Any differences between arms in compliance should be investigated and, if possible, explained.

If properly carried out, imputation can reduce the bias that results from ignoring non-response, can restore balance to the data and permit simpler analysis. Hence imputation is an attractive procedure, provided one can be sure that the conditions are appropriate and that unintended bias is not being introduced. Although there are increasingly complex methods of imputation, in QL analysis the aim should always be to reduce the need for imputation and, when it is necessary, to explain exactly what has been done and why. It is important to remember that any inferences in the presence of incomplete data are not as convincing as inferences based on a complete data set. It should be emphasized that if there is a bias in the amount of missing data in the arms being compared, imputation of data can magnify this bias.

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