Bias

The main cause for concern is that missing data may result in bias, and that the apparent results of a clinical trial will not reflect the true situation. That is, we will not know if the difference we observe between treatments is a truly reliable estimate of the real difference. If the proportion of anticipated data missing is small then, provided the data are analysed appropriately, we can be confident that little bias will result. However, if the proportion of data missing is not small then a key question is: "Are the characteristics of patients with missing data different from those for whom complete data are available?" For example, it might be that the more ill patients, or patients with more problems, are less willing or less able to complete the questionnaires satisfactorily. Then the missing QoL assessments (had we been able to receive them) might have indicated a poor outcome whereas those that were completed may reflect a better QoL.

Alternatively, perhaps patients without problems are less convinced about the need to return comprehensive information. In that case, the questionnaires that have been completed may reflect a worse QoL. In practice, there may be a mixture of these two possibilities within a particular trial. There may also be different patterns amongst patients receiving the different protocol treatments within one trial. Any analysis that ignores the presence of missing data may result in biased conclusions about both the changing QoL profiles over time and the between-treatment differences.

Consider a randomised clinical trial where we wish to estimate the overall QoL scores of patients at one time point and compare these between treatments. If we first consider one of the treatment groups, suppose that of the N patients recruited to that treatment M(< N) fail to complete the key QoL assessment. The proportion of missing data is P - M/N and the proportion of patients with complete data is therefore 1 - P. We assume that the responding and the non-responding patients do have different mean QoL values and these are ¡j. Responding an<3 nNot Responding respectively. The patients recruited to the trial comprise a mixture of those who ultimately do respond and those who do not. The combined mean, were we able to observe it, for all patients is

But here we are assuming that we do have responses from the non-responders. However, since one clearly cannot observe the non-responders, we cannot estimate ¡j, with the QoL data recorded but only ¡iResponding• Thus the bias, B, will be

The bias will be zero if the mean scores of responders and non-responders are in fact equal. However, since the non-responders do not record their QoL we have no means of knowing if this is indeed the case. If there are no missing data, P = 0 and there will be no bias.

/' (1 Responding P'ßNotResponding-

B [I f.1Responding

= (1 - P)nR esponding ^Not Responding - Vr esponding P Not Responding ~ Responding)•

In a clinical trial comparing two treatments there will be a potential bias of the form of equation (11.2) for each treatment. The aim of a clinical trial is to estimate the difference in QoL between treatments. Thus the bias of this difference, for a trial comparing a test and control therapy, will therefore be

The treatment comparison will be unbiased only if the bias happens to be the same in both treatment arms, but again we have no means of knowing this.

There can be considerable bias in the estimated treatment difference if the proportion of missing assessments differs substantially between the treatment arms. Information regarding the reason for non-response, if known, may be useful in determining whether the analysis is biased or not. Additionally, if the probability of completing the QoL assessment is associated with patient characteristics measured at entry into the trial, such as their age, performance status or clinical stage of disease, then it may be possible to reduce the bias by adjusting for these factors. It is important to note that the bias of equation (11.2), and hence (11.3), depends upon the proportion of missing data, and not the number of observations. Bias cannot be reduced by increasing the total sample size.

Example

In the example given by Curran et al. (1998b), patients completed the EORTC QLQ-C30 (see Appendix E6). Physical functioning (PF) was assessed using items Q\ to <25. In this study the QLQ-C30 (version 2) was used, and these items were scored 1 (No) or 2 (Yes). Thus the minimum sum-score is 5 and the maximum 10, which is then scaled to range from 0 to 100. There were 86 patients completing the first or baseline assessment. However, following recruitment, some patients dropped out before the next QoL assessment was made, and the remainder carried on until the next monthly assessment, following which others dropped out.

Figure 11.2 presents the mean PF score by time of dropout either by death or failure to complete the QoL assessment. Each profile was calculated from the patients completing all QoL assessments up to the specified number of months. As may be seen, those patients who provided information on all five PF assessments tended to have a higher baseline mean PF score than the other groups of patients. Thus there is an intrinsic bias that tends to include only the better patients into the QoL analysis at later time points. Care should therefore be taken in interpreting any graphs or tabular displays that include mean scores calculated from all the data available regarded as if all from one group, albeit comprising subjects for whom differing numbers of QoL assessments are available. The overall mean PF score, the bold broken line of Figure 11.2, rises steadily from 55.4 at baseline to 70.8 at the last assessment, suggesting an overall improvement in PF. This contrasts with the decline in PF that has occurred in, for example, those patient groups with three and four assessments in which the last observed mean PF dropped below previous levels. Since only a few patients dropped out at each month, the overall mean score is dominated by the patients who completed all five assessments.

Assessment

Figure 11.2 Mean physical functioning (PF) score stratified by time of dropout due to death or non-compliance in patients with metastatic breast cancer (Based on Curran et al., 1998)

Assessment

Figure 11.2 Mean physical functioning (PF) score stratified by time of dropout due to death or non-compliance in patients with metastatic breast cancer (Based on Curran et al., 1998)

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