Sensitivity analysis for the estimation of rates of change with non-ignorable drop-out: an application to a randomized clinical trial of the vitamin D3.

The vitamin D(3) trial was a repeated measures randomized clinical trial for secondary hyperparathyroidism in haemodialysis patients where the efficacy of the vitamin D(3) infusions for suppressing the secretion of parathyroid hormone (PTH) was compared among four dose groups over 12 weeks. In this trial, patients terminated the study before the scheduled end of the study due to their elevated serum calcium (Ca) level, that is, the administration of the vitamin D(3) was expected to cause hypercalcaemia as an adverse event. In this setting of monotone missingness, there is a potential for bias in estimation of mean rates of decline in PTH for each treatment group using the standard methods such as the generalized estimating equations (GEE) which ignore the observed past Ca histories. We estimated the treatment-group-specific mean rates of decline in PTH by the inverse probability of censoring weighted (IPCW) methods which account for the observed past histories of time-dependent factors that are both a predictor of drop-out and are correlated with the outcomes. The IPCW estimator can be viewed as an extension of the GEE estimator that allows for the data to be MAR but not MCAR. With missing data, it is rarely appropriate to analyse the data solely under the assumption that the missing data process is ignorable, because the assumption of ignorable missingness cannot be guaranteed to hold and is untestable from the observed data. We proposed a sensitivity analysis that examines how inference about the IPCW estimates of the treatment-group-specific mean rates of decline in PTH changes as we vary the non-ignorable selection bias parameter over a range of plausible values.