Assessing the influence of reversible disease indicators on survival

In a randomized clinical trial of the effect of prednisone versus placebo on survival in patients with liver cirrhosis, follow-up visits were scheduled after 3, 6 and 12 months of treatment and thereafter once a year. At each follow-up the prothrombin index, a measure of liver function, was recorded and scored as either low or normal. The interaction between treatment and prothrombin index was analysed using a three-state illness-death model with recovery. The continuous-time Markov process model with constant or piecewise constant intensities suggested by Kay allows inference to proceed even though the status of the disease indicator, here the prothrombin index, is only known at the time of each visit and not between visits. We compare the analysis with the theoretically incorrect, but practically rather common approximation, where the status of the disease indicator is assumed to remain constant from one visit until just before the next. Under this approximation both standard parametric methods and non-parametric approaches developed by Aalen and Johansen are available.