AbstractMedical statistics often involve measurements of the time when a variable crosses a threshold value. The time to threshold crossing may be the outcome variable in a survival analysis, or a time‐dependent covariate in the analysis of a subsequent event. This paper presents new methods for analysing threshold‐crossing data that are interval censored in that the time of threshold crossing is known only within a specified interval. Such data typically arise in event‐history studies when the threshold is crossed at some time between data‐collection points, such as visits to a clinic. We propose methods based on multiple imputation of the threshold‐crossing time with use of models that take into account values recorded at the times of visits. We apply the methods to two real data sets, one involving hip replacements and the other on the prostate specific antigen )PSA( assay for prostate cancer. In addition, we compare our methods with the common practice of imputing the threshold‐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 account variability due to imputation.