MULTIPLE IMPUTATION FOR THRESHOLD-CROSSING DATA WITH INTERVAL CENSORING

Medical statistics often involve measurements of the time when a varia ble crosses a threshold value. The time to threshold crossing may be t he outcome variable in a survival analysis, or a time-dependent covari ate in the analysis of a subsequent event. This paper presents new met hods for analysing threshold-crossing data that are interval censored in that the time of threshold crossing is known only within a specifie d interval. Such data typically arise in event-history studies when th e threshold is crossed at some time between data-collection points, su ch as visits to a clinic. We propose methods based on multiple imputat ion of the threshold-crossing time with use of models that take into a ccount values recorded at the times of visits. We apply the methods to two real data sets, one involving hip replacements and the other on t he prostate specific antigen (PSA) assay for prostate cancer. In addit ion, we compare our methods with the common practice of imputing the t hreshold-crossing time as the right endpoint of the interval. The two examples require different imputation models, but both lead to simple analyses of the multiply imputed data that automatically take into acc ount variability due to imputation.