1Statistics 741, Chappell - Spring 2012 Rick Chappell, Ph.D. Professor, Department of Biostatistics and Medical Informatics Department of Statistics University of Wisconsin Madison University of Wisconsin – Madison Department of Biostatistics and Medical Informatics Defining Biochemical Recurrence in Prostate Cancer

2Statistics 741, Chappell - Spring 2012 I. Obviously Dependent Censoring “Retiring to Arizona” or “Going back to the farm” II.Dependent Administrative Censoring Induced by time trends III.The ASTRO Definition of Biochemical Recurrence in Prostate Cancer IV.Why Backdating is a Problem And many comments on it IV.Conclusions Outline

3Statistics 741, Chappell - Spring 2012 I. Obviously Dependent Censoring Consider a simple situation without censoring: x x x x Time

4Statistics 741, Chappell - Spring 2012 The K-M curve is the empirical CDF: x x x x 1 0 Time

5Statistics 741, Chappell - Spring 2012 If the healthiest in terms of remaining life are selectively censored (negatively dependent censoring) then the K-M curve is biased downward: x x O O 1 0 x x Time

6Statistics 741, Chappell - Spring 2012 If the sickest are selectively censored (positively dependent censoring) then the K-M curve is biased upward: x x x x 1 0 o o Time

7Statistics 741, Chappell - Spring 2012 II. Dependent Administrative Censoring  Even when the sole source of censoring is administrative (event hasn’t yet occurred at the time of analysis), it can be dependent with failure time.  Pointed out by Kaplan & Meier (1958), credited to Sartwell and Merrell (1952), Am. J. Pub. Health 42, “Influence of the dynamic character of chronic disease on the interpretation of morbidity rates”.

“For example, in a study of survival after an operation, a change in surgical technique five years before the data are analyzed will affect the survival times only of those with observation limit less than five years [p. 470].” Consider an extreme example: accrued50% failure in accrued50% failure in 1986 The rest are cured. An analysis is performed in 1995.

0 years 5 K-M estimate for 1980 cohort of 200 analyzed in 1985 K-M estimate for 1983 cohort of 2000 analyzed in 1985 K-M estimate for combined sample of 2200 analyzed in =

10Statistics 741, Chappell - Spring 2012  Thus, even though the long-term failure rate in both cohorts is 50%, the K-M curve remains near 100%.  This is not a sample-size issue: the confidence intervals for the previous example are narrow (and can be made arbitrarily narrower by choosing higher sample sizes).  Note that censoring is solely administrative.

11Statistics 741, Chappell - Spring 2012 III. The ASTRO Definition of Biochemical Failure (BF) in Prostate Cancer The American Society for Therapeutic Radiology and Oncology consensus statement on guidelines for PSA following radiation therapy (1997): “Three consecutive rises in prostate-specific antigen (PSA) after reaching the PSA nadir constitute BF. The date of failure is the midpoint between the nadir and the first of the three consecutive rises in PSA.”

12Statistics 741, Chappell - Spring 2012 A hypothetical PSA curve after radiation treatment PSA level PSA assay times treatment observednadir backdated BF “at call” BF Time

13Statistics 741, Chappell - Spring 2012 IV. Why Backdating is a Problem  Problems with definition quickly noticed by Vicini et al., attributed to inadequate followup.  They examined a series of prostate cancer patients treated with radiation and followed for up to 12 years.  They artificially censored patients at a range of followups, recalculated backdated BF times, and plotted K-M curves.

Vicini, F.A., Kestin, L.L., and Martinez, A.A. The importance of adequate follow-up in defining treatment success after external beam irradiation for prostate cancer. IJROBP 1999; 45:

15Statistics 741, Chappell - Spring 2012  Their conclusion: need more followup – at least 5, preferably 10 years.  Vicini and others recommended that most or all patients be followed “at least beyond the time point at which actuarial results are examined”.  This is problematic considering the lengthy progress of the disease, frail patient population.  Also, even in Vicini’s results, the actuarial curves start to be biased even before attempted followup (see plot).

16Statistics 741, Chappell - Spring 2012 Subsequent comments:  One proposed solution was to also back-date the censoring times.  But if there were no rises in PSA, to when would the censoring be backdated?  How would this curve be comparable to others, which are usually “at call”?

17Statistics 741, Chappell - Spring 2012 Subsequent comments (cont.):  The backdated definition is said to have high sensitivity.  But backdating can move the BF date from after the CF to before if CF occurs between the nadir and the third rise.  Thus the “sensitivity” is to CF events which occur before the BF is determined (see slide 12).  Even so, Thames (2003) found on-call definitions with superior sensitivity.

18Statistics 741, Chappell - Spring 2012 Subsequent comments (cont.):  The fundamental statistical problem:  When, for a failure to be observed at time t, followup to about t + 2 years is required, we know that followup and failure are dependent; usually, given failure at t, we know nothing of further followup.  As with the previous two examples, dependent censoring biases the K-M curve.

19Statistics 741, Chappell - Spring 2012 Other remarks:  Two purposes for predicting CF: 1) To determine in a clinical trial whether a patient relapsed; and 2) To plan therapy for a patient. For the first, the entire patient history is relevant. E.g., suppose a patient had 3 rises in PSA then a decrease, followed by 10 years all clear? He shouldn’t be said to relapse. For the second, only current information can be used. A patient with 3 rises might well be given salvage therapy.

20Statistics 741, Chappell - Spring 2012 Other remarks (cont.):  For each purpose, timing is important (but presently ignored). E.g.,  Is it useful to detect a CF in two months? Not very, because CF would have been detected anyway and treatment not delayed much.  Is it useful to detect a CF in ten years? Perhaps not, because that CF might not be important to the patient. Its prevention may not be worth additional treatment.  When is it useful to predict a CF?

21Statistics 741, Chappell - Spring 2012 Subsequent comments (cont.):  Taylor (see Wang and Taylor, 2001 for an application to AIDS) has jointly modeled PSA and CF in order to obtain the best prediction possible at any given time in a patient’s history.  For treatment purposes, a complex model yielding a probability of CF by (say) 3 years seems best, but results in a “black box” definition of biochemical failure.

22Statistics 741, Chappell - Spring 2012 V. Conclusions  Prognostic methods for prostate cancer can be improved upon and may depend upon their purpose.  Dependent censoring produces bias, avoidable only by complete  Even a large sample size can’t correct the problem.

23Statistics 741, Chappell - Spring 2012 V. Conclusions  Prognostic methods for prostate cancer can be improved upon and may depend upon their purpose.  Dependent censoring produces bias, avoidable only by complete  Even a large sample size can’t correct the problem.  If this is so obvious, why have thousands of patients been enrolled on trials with backdated endpoints?