Imputation strategies for blood pressure data nonignorably missing due to medication use

Abstract

Underlying or untreated blood pressure (BP) is often an outcome of interest, but is unobservable when study participants are on anti-hypertensive medications. Untreated levels are not missing at random but would be higher among those on such medication. In such cases, standard methods of analysis may lead to bias. BPs obtained at the private physician's office (out-of-study BPs) at the time of prescription of anti-hypertensive medications were available from Phase II of the Trials of Hypertension Prevention (TOHP) and were used to adjust for the potential bias. Observed out-of-study BPs were used to estimate the conditional expectation and variance of the unobserved unmedicated study BPs. For those with no physician data, imputation from bootstrap samples of out-of-study BPs was used. An iterative method based on the EM algorithm was used to estimate the unknown study parameters in a random-effects model using multiple imputations. This was compared to an alternative model for the out-of-study BPs based on a theoretical truncated normal distribution, and to standard analyses, including both multivariate repeated measures and last-observation-carried-forward (LOCF) analyses, using data from Phase II of TOHP. Differences between methods were seen in the decline in BP over time in the reference group, where the changes from baseline to 36 months were 3.0 in univariate analyses, 2.4 using LOCF, and 2.6 in the multivariate analysis, compared to 2.0 or 1.7 in the imputation analyses, depending on the number of physician visits. Estimated intervention effects tended to be slightly larger using the imputation methods. out-of-study measures may not be available for other studies. Because the proposed strategy was based on an empirically observed distribution for out-of-study BP, fewer assumptions about the missing data were made. These data may be useful in suggesting imputation strategies for other studies.