University of Wisconsin Madison Department of Biostatistics and

University of Wisconsin – Madison Department of Biostatistics and Medical Informatics HOW TO BIAS A KAPLAN-MEIER CURVE AND WHY MANY PROSTATE CANCER TRIALS ARE IN DANGER Rick Chappell, Ph. D. Department of Biostatistics and Medical Informatics Depart of Statistics University of Wisconsin Madison 1 R. Chappell - Stat 642, Spring 2016

Outline I. II. Obviously Dependent Censoring “Retiring to Arizona” or “Going back to the farm” Dependent Administrative Censoring Induced by time trends III. The ASTRO Definition of Biochemical Recurrence in Prostate Cancer 2 R. Chappell - Stat 642, Spring 2016

I. Obviously Dependent Censoring Consider a simple situation without censoring: x x Time 3 R. Chappell - Stat 642, Spring 2016

The K-M curve is the empirical CDF: 1 x x 0 Time 4 R. Chappell - Stat 642, Spring 2016

If the healthiest in terms of remaining life are selectively censored (negatively dependent censoring) then the K-M curve is biased downward: 1 x x 0 O O x Time 5 x R. Chappell - Stat 642, Spring 2016

If the sickest are selectively censored (positively dependent censoring) then the K-M curve is biased upward: 1 ox x x ox 0 Time 6 R. Chappell - Stat 642, Spring 2016

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”. 7 R. Chappell - Stat 642, Spring 2016

“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: 1990 200 accrued 50% failure in 1991 1993 2000 accrued 50% failure in 1996 The rest are cured. An analysis is performed in 1995.

1 K-M estimate for 1990 cohort of 200 analyzed in 1995 . 5 0 0 years 5 1 + K-M estimate for 1993 cohort of 2000 analyzed in 1995 . 5 0 0 years 5 = 1 K-M estimate for combined sample of 2200 analyzed in 1995 . 5 0 0 years 5

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. 10 R. Chappell - Stat 642, Spring 2016

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. ” 11 R. Chappell - Stat 642, Spring 2016

A hypothetical PSA curve after radiation treatment PSA level PSA assay times treatment observed backdated BF nadir “at call” BF Time 12 R. Chappell - Stat 642, Spring 2016

Why Backdating is a 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. 13 R. Chappell - Stat 642, Spring 2016

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: 553 -561.

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 and the frail patient population. 15 R. Chappell - Stat 642, Spring 2016