DIAGNOSING QUALITY OF TREATMENT FROM SURVIVAL TIMES

Purpose: CUSUM plots monitoring quality of treatment are not readily applicable to cancer case series with prolonged follow-up. We describe a Bayesian technique for timely detection of inferior results based on observed survival times.

Method(s): Kaplan-Meier 5-year survival curves for children with acute lymphoblastic leukemia treated on the ongoing Nordic 2008 protocol are available, showing “healthy” standard of treatment. The curves are divided in 3-month intervals, and the risk of event (hazard) in each interval calculated from the survival curves. A “sick” hazard function is specified by multiplying the failure:success ratio in each interval by 1.5, and a hypothetical Kaplan-Meier curve for poor treatment constructed by sequentially multiplying the probabilities of surviving each interval without event. For each patient the likelihood ratio of the observed survival time is determined: for event free cases the ratio of survival probabilities on the two curves, for cases with event the same ratio multiplied with the hazard ratio in the time interval. Using Bayes theorem, considering each case a test of good treatment quality, diagnostic odds are calculated by multiplying prior odds sequentially with the likelihood ratios. The accumulated weight of evidence in favour of or against good performance is determined by adding up log to base 2 of the likelihood ratios.

Result(s): We have included 35 children on the ongoing protocol; 9 have completed 5-year follow-up and can be considered cured, 2 have had events during follow-up, and 24 are still at risk with survival times 8-59 months. A Kaplan-Meier estimate of 5-year event free survival for all risk groups combined is 90.7%. Using the Bayesian approach, the weight of evidence in favor of good treatment quality is 1.43, corresponding – if prior odds are fifty:fifty – to odds 2 to the power of 1.43 = 2.70 to 1, i.e. probability 73%. Displaying the accumulation of evidence in a CUSUM plot for the sequential case mix reveals a very good run of the first 14 patients accounting for most of the favourable evidence.

Conclusion(s): The quality of treatment in small patient series with unfinished follow-up can be assessed from the observed survival times, permitting monitoring of results in a risk-adjusted CUSUM plot and detection of temporal changes that are not apparent in Kaplan-Meier curves or Cox proportional hazard models.