Proportional Hazards Regression for Cancer Studies

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.

[1]  M. C. Jones.  Kernel density estimation for length biased data , 1991 .

[2]  S R Lipsitz,et al.  Jackknife estimators of variance for parameter estimates from estimating equations with applications to clustered survival data. , 1994, Biometrics.

[3]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[4]  Masoud Asgharian,et al.  Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data , 2005, math/0602239.

[5]  N. Day,et al.  Simplified models of screening for chronic disease: estimation procedures from mass screening programmes. , 1984, Biometrics.

[6]  Modelling tumour biology–progression relationships in screening trials , 2006, Statistics in medicine.

[7]  James M. Robins,et al.  Unified Methods for Censored Longitudinal Data and Causality , 2003 .

[8]  D. Cox.  Regression Models and Life-Tables , 1972 .

[9]  T Duchesne,et al.  Alternative Time Scales and Failure Time Models , 2000, Lifetime data analysis.

[10]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[11]  A Yu Yakovlev,et al.  Stochastic Models of Tumor Latency and Their Biostatistical Applications , 1996 .

[12]  M Kimmel,et al.  Nonparametric estimation of the size-metastasis relationship in solid cancers. , 1991, Biometrics.

[13]  J L Xu,et al.  Estimating a distribution function of the tumor size at metastasis. , 1998, Biometrics.

[14]  J. Robins,et al.  Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers , 1992 .

[15]  Marvin Zelen,et al.  On the theory of screening for chronic diseases , 1969 .

[16]  Zhiliang Ying,et al.  Semiparametric regression for the mean and rate functions of recurrent events , 2000 .

[17]  T. Louis,et al.  Screening for the early detection of cancer— I. The temporal natural history of a progressive disease state , 1978 .

[18]  M. Zelen,et al.  Parametric estimation procedures for screening programmes: Stable and nonstable disease models for multimodality case finding , 1999 .

[19]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[20]  Mei-Cheng Wang,et al.  Hazards regression analysis for length-biased data , 1996 .

[21]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[22]  A. Fowler,et al.  A simplified model , 1992 .

[23]  Danyu Lin,et al.  On fitting Cox's proportional hazards models to survey data , 2000 .

[24]  Estimating the cumulative risk of false positive cancer screenings , 2003, BMC medical research methodology.

[25]  C. R. Rao,et al.  Weighted distributions and size-biased sampling with applications to wildlife populations and human families , 1978 .

[26]  Y. Vardi,et al.  Nonparametric Estimation in the Presence of Length Bias , 1982 .

[27]  Nonparametric estimation of solid cancer size at metastasis and probability of presenting with metastasis at detection. , 1997, Biometrics.

[28]  N. Breslow,et al.  Statistical methods in cancer research: volume 1- The analysis of case-control studies , 1980 .

[29]  W. Barlow,et al.  Robust variance estimation for the case-cohort design. , 1994, Biometrics.

[30]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .