The Problem

Experience reported for a variety of clinical trials suggests that, for most single items, between 0.5% and 2.0% of values will be missing from returned questionnaires. Thus, overall, the problem of missing items might seem relatively unimportant. However, for a questionnaire that contains about 30 questions, a 1% missing rate for items would, if it occurred at random, imply that about a quarter of patients could have a missing item on their initial QoL assessment. Even a missing rate of 0.5% could result in 14% of patients with items missing. Furthermore, at each subsequent assessment there may be additional missing data and many patients are likely to have some degree of missing QoL data.

Example

A review of 7000 forms in six UK Medical Research Council randomised trials in cancer described by Fayers, Curran and Machin (1998a) indicates that 92% of forms contained complete information with regard to 29 out of the 30 questions in the first section of the RSCL. However, one question "(to what extent you have been bothered by) Decreased sexual interest" presented particular problems. The proportion of forms with missing data varied considerably from trial to trial, ranging from 4% to 14%.

Thus even when there is only a small proportion of missing values for each item, a substantial proportion of patients may have at least one or more missing items during their follow-up period. Analyses based solely upon those patients for whom complete data are available may find that the cumulative exclusion of patients results in too few patients remaining in the final analyses, and hence a severe loss of statistical power. In addition, there is a process of selection of patients into the analysis since only those with complete data are retained. The subsequent subset of patients who have complete data may not be representative of all the patients in the trial.

Analysis of the patterns of missing QoL items suggests that they do often occur at random. Thus although those patients who, perhaps through carelessness, omit answers to one question are more likely to omit answers to other questions, the reason for their so doing may be unrelated to the (unrecorded) level of the particular QoL item. Also, although missing items within forms may take the pattern of a run of adjacent questions, often the questions are unrelated, implying oversight rather than intentional omission. In both these circumstances it is reasonable to assume the data are Missing Completely At Random (MCAR). In formal terms, an item is MCAR if the probability of having a missing item is independent of scores on previous observed questionnaires and independent of the current and future scores had they been observed.

In contrast, as already indicated, some QoL items may present particular difficulties; for example, the question concerning "sexual interest" on the RSCL. This question is frequently unanswered. One plausible assumption is that patients experiencing problems are likely to be more reticent concerning this question, and that therefore missing items occur more frequently when there are indeed sexual problems. Thus missing might imply "very much a problem". Alternatively, for those patients who are no longer sexually active, failure to respond may imply "not applicable". In either case imputation should take this into account, as simply ignoring the presence of missing scores for these patients can result in misleading conclusions about the severity of problems. Such data are classified as Not Missing At Random (NMAR), because the missing data depend on the value of the unobserved scores and so the missing data mechanism cannot be ignored.

In QoL studies it is likely that there are a number of non-ignorable mechanisms responsible for NMAR data. If sufficient data are collected concerning why QoL questionnaires have not been completed, one may be able to distinguish the missing data mechanisms. In some cases it may be possible to retrieve the QoL scores of a random sample of patients by using alternative modes of administration such as telephone interview or by obtaining proxy scores from members of the patient's family or the responsible medical team. Then the reasons for missing items can be explored.

In some situations, the likelihood of having a missing score may depend on known factors and scores recorded at an earlier QoL assessment, but is independent of the current (not recorded) score. Such data are termed Missing At Random (MAR). An example might be age group; older people are more likely to have a higher rate of missing items, and are also likely to have poorer physical functioning scores. Within any particular age group the data are MCAR, but when considering all patients together the data are MAR because those with missing values are likely to have lower true levels of PF than those with complete data.

232 QUALITY OF LIFE: ASSESSMENT, ANALYSIS AND INTERPRETATION

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