Multiple imputation for non-response when estimating HIV prevalence using survey data

Amos Chinomona, Henry Mwambi

Missing data are a common feature in many areas of research especially those involving survey data in biological, health and social sciences research. Most of the analyses of the survey data are done taking a complete-case approach, that is taking a list-wise deletion of all cases with missing values assuming that missing values are missing completely at random (MCAR). Methods that are based on substituting the missing values with single values such as the last value carried forward, the mean and regression predictions (single imputations) are also used. These methods often result in potential bias in estimates, in loss of statistical information and in loss of distributional relationships between variables. In addition, the strong MCAR assumption is not tenable in most practical instances. Since missing data are a major problem in HIV research, the current research seeks to illustrate and highlight the strength of multiple imputation procedure, as a method of handling missing data, which comes from its ability to draw multiple values for the missing observations from plausible predictive distributions for them. This is particularly important in HIV research in sub-Saharan Africa where accurate collection of (complete) data is still a challenge. Furthermore the multiple imputation accounts for the uncertainty introduced by the very process of imputing values for the missing observations. In particular national and subgroup estimates of HIV prevalence in Zimbabwe were computed using multiply imputed data sets from the 2010-11 Zimbabwe Demographic and Health Surveys (2010-11 ZDHS) data. A survey logistic regression model for HIV prevalence and demographic and socio-economic variables was used as the substantive analysis model. The results for both the complete-case analysis and the multiple imputation analysis are presented and discussed. Across different subgroups of the population, the crude estimates of HIV prevalence are generally not identical but their variations are consistent between the two approaches (complete-case analysis and multiple imputation analysis). The estimates of standard errors under the multiple imputation are predominantly smaller, hence leading to narrower confidence intervals, than under the complete case analysis. Under the logistic regression adjusted odds ratios vary greatly between the two approaches. The model based confidence intervals for the adjusted odds ratios are wider under the multiple imputation which is indicative of the inclusion of a combined measure of the within and between imputation variability. There is considerable variation between estimates obtained between the two approaches. The use of multiple imputations allows the uncertainty brought about by the imputation process to be measured. This consequently yields more reliable estimates of the parameters of interest and reduce the chances of declaring significant effects unnecessarily (type I error). In addition, the utilization of the powerful and flexible statistical computing packages in R enhances the computations.