In a randomized controlled trial, missing data led to biased results regarding anxiety

Abstract

Background and objective

Randomization does not protect against bias due to missing observations. In addition, different reasons for missing observations may lead to different invalid results. The purpose of this study was to illustrate how randomized intervention studies can be threatened by bias due to missing observations because of death or nonresponse.

Methods

A randomized clinical trial of the effect of psychosocial intervention on well-being after an operation for colorectal cancer was conducted in Denmark. Patients were interviewed 3, 6, 12, and 24 months after discharge from hospital.

Results

We found that the probability of nonresponse decreased with increasing anxiety score in the intervention group, but it increased with increasing anxiety score in the control group. This could lead to severe bias in an analysis of the effect of intervention on anxiety. Low physical functioning and low global health status and quality of life were related to an increased probability of dying before the next follow-up, and this association could explain the associations between anxiety and depression, respectively, and the probability of dying observed in crude analyses.

Conclusion

Our study emphasizes the importance of performing specific missing data analyses in any study of well-being variables.

Introduction

The hypothesis that psychosocial intervention could affect the well-being of cancer patients has been subject to research for some 30 years [1]. The randomization used in clinical trials protects against bias in treatment allocation, but missing values may still lead to severe bias in a randomized trial, or in any other intervention trial [2], [3], [4], [5], [6], [7].

Besides death, the main reason for missing observations is nonresponse by choice: that is, refusal to participate in one or more follow-up assessments. Given the obvious large psychosocial differences between nonresponse by choice and nonresponse by death, the associated factors are bound to differ. Insight into the mechanisms will be severely weakened if nonresponse and death are mixed. Furthermore, differential associations for the two randomization groups may be more likely for nonresponse. A low level of well-being or a high level of distress (singly or in combination) could be associated with unwillingness among all participants to take the trouble to participate in an interview. A falsely lower level of anxiety and depression will be observed in the control group if, for example, the distressed patients in the intervention group feel obliged to participate in the interview anyway, but the patients in the control group feel free to decline participation in times of distress. Such a differential association between well-being and nonresponse could diminish or even reverse the estimated effect of the intervention on the well-being variables. It is therefore important for any clinical trial of well-being to check that differential nonresponse has not occurred.

The problem of missing data has been dealt with in the statistical literature, with distinctions drawn among different missing data mechanisms: missing completely at random, missing at random, and informative missing. Several papers report different ways to distinguish among these missing data mechanisms [5], [6], [8], [9], [10], [11], [12], [13], [14], [15]. The method for dealing with missing data depends on the missing data mechanism and the missing data pattern (drop-outs or missing intermittently), as well as the type of the outcome variable (continuous, ordinal, binary, or failure time data) [10], [11], [13], [15], [16], [17], [18], [19], [20], [21], [22]. A few papers focus on quality of life data [22], [23], [24], but psychosocial intervention studies reporting on missing data usually consider sociodemographic variables only [25], [26], [27], [28]. Other aspects of well-being may, however, be very important factors in relation to the missing data mechanism.

Based on a randomized trial of psychosocial intervention, this study investigates the associations between well-being and missing observations at the next follow-up. It is hypothesized that distress increases the probability of nonresponse, but that this may be less pronounced in the intervention group. Furthermore, another study has found an association between distress and imminent death [29], and we wanted to investigate whether this association could be explained by concurrent physical health as measured by physical functioning and global health status and quality of life.