Proportional Hazards Regression for Cancer Studies

Abstract

There has been some recent work in the statistical literature for modeling the relationship between the size of cancers and probability of detecting metastasis, i.e., aggressive disease. Methods for assessing covariate effects in these studies are limited. In this article, we formulate the problem as assessing covariate effects on a right-censored variable subject to two types of sampling bias. The first is the length-biased sampling that is inherent in screening studies; the second is the two-phase design in which a fraction of tumors are measured. We construct estimation procedures for the proportional hazards model that account for these two sampling issues. In addition, a Nelson-Aalen type estimator is proposed as a summary statistic. Asymptotic results for the regression methodology are provided. The methods are illustrated by application to data from an observational cancer study as well as to simulated data.

A maximum pseudo-profile likelihood estimator for the Cox model under length-biased sampling

“…Thus, a consistent estimator of the regression parameters can be easily derived by maximizing the pseudo-profile likelihood. Unlike other bias-adjusted risk-set methods, including Ghosh (2008), Tsai (2009) and Qin & Shen (2010), the proposed estimation procedure does not involve estimation of the censoring distribution, so it is expected to be more stable when the censoring proportion is high.…”

Proportional hazards regression for cancer screening data

“…Provided one can consistently estimate the growth function of a tumour and correctly parameterize the distribution of left-truncation time, Ghosh [6]'s approach can be extended to the case when each subject has a specific growth function. Simulation results show that given a growth curve is correctly specified, the estimation procedures perform well for proportional hazards model.…”

“…Note that our approach differs from what is proposed by Ghosh [6], where it is assumed that V is independent of C and φ(x|Z) = φ(x). Under these two assumptions, models (1) and (2) are equivalent, and we have the Kaplan-Meier estimator, sayŜ W (y), and it is not necessary to estimate φ(x).…”

Linear transformation models for survival analysis with tumor growth information in cancer screening study

“…Under the assumption that all subjects have the same tumor growth function, i.e. φ(•|L) ≡ φ(•), Ghosh (2008) developed estimation procedures for the Cox proportional hazards model. In medical practice, the tumor growth function can vary among individuals, e.g.…”