Multiple Imputation of Missing Values Using the Response Function Method Based on a Data Set of the Health Assessment Questionnaire Disability Index

Objectives: This study aims to investigate how imputing missing values in data obtained from the Health Assessment Questionnaire Disability Index (HAQ-DI) influences the bias and precision of patient disability measurements.

Patients and methods: Hypothetical missing data sets were created by deleting item responses completely at random from the original data set with three missingness proportions (0.10, 0.30 and 0.50). Multiple imputation was carried out using the response function method for each hypothetical data set containing the missing values. The Rasch model was used to estimate the patients' latent trait levels for the original data, the hypothetical incomplete data sets, and the multiple imputed data sets. Then the estimates from the hypothetical missing data sets and the multiple imputed data sets were compared with those of the original data set.

Results: A bias in disability estimates was observed, particularly as the missingness proportion increased for both the incomplete and imputed data; however, this bias was indiscernible even for the 0.50 proportion of missingness. In terms of the uncertainty of the disability estimates, the imputed data had a higher precision of estimates than the incomplete data.

Conclusion: When researchers encounter missingness in data collected with the HAQ-DI, the response function imputation could be a convenient approach to impute missing values in order to improve the precision of the patient disability level estimates.