Estimation of Lag Time Between Onset of and Death from an Occult Tumor

Abstract

A new statistical method for estimating the lag time between onset of and death from an occult tumor is proposed for data without cause-of-death information. In this method, the survival function for time to tumor onset, tumor-specific survival function, and competing risks survival function are estimated using the maximum likelihood estimates of the parameters. The proposed method utilizes the estimated survival functions and statistically imputed fatal tumors to estimate the lag time. This approach is developed for rodent tumorigenicity assays that have at least one interim sacrifice and a terminal sacrifice. If the data contain cause-of-death information given by pathologists and it is believed to be reliable, it may be used for estimating the lag time. The proposed method is illustrated using a real data set. The accuracy of the estimation of lag time is evaluated via a Monte Carlo simulation study. This study shows that the estimated lag time is quite reliable.

Key Words:

• Bioassay
• Cause of death
• Likelihood
• Sacrifice
• Tumor lethality

ACKNOWLEDGMENTS

Hongshik Ahn's research was partially supported by the Faculty Research Participation Program at the National Center for Toxicological Research (NCTR) administered by the Oak Ridge Institute for Science and Education through an interagency agreement between US Department of Energy (USDOE) and US Food and Drug Administration (USFDA). Hojin Moon's research was partially supported by the Scholarly and Creative Activities Committee (SCAC) Award from California State University, Long Beach (CSULB).

Notes

¹Time intervals 1–3 represent, respectively, 0–40, 41–60, 61–80 weeks.

²With tumor

³Without tumor

⁴Insufficient data

F1F: F1 female; F1M: F1 male; F2F: F2 female; F2M: F2 male; F1 and F2 are strain names. ¹Time intervals 1–3 represent, respectively, 0–40, 41–60, 61–80 weeks. ² a _1j  + d _j . ³Estimated number of fatal tumors. ⁴Number of fatal tumors assigned by pathologists.

^aTime intervals 1–3 represent, respectively, 0–40, 41–60, 61–80 weeks.

¹Estimated lag time using the method by Kodell and Nelson (1980)

²Insufficient data to obtain estimates

Standard error estimates are given in parentheses. For each configuration, the average is taken from 5000 trials. The competing risks survival rate is 0.5.