An index approach for the Cox model with left censored covariates

Medical studies frequently collect biological markers in which many subjects have values below the detectable limits of the assay, resulting in heavily censored data. We develop a modification of the Rigobon and Stoker index method for application to a Cox regression model with censored covariates. The index approach is compared with a complete case method and various fill-in methods. Our simulation results demonstrated that the index approach is an improvement over the other methods. We illustrated the usefulness of this approach with an example for the GenIMS study examining the relationship between two inflammatory markers and survival.

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

[2]  A. Cohen.  RESTRICTION AND SELECTION IN MULTINORMAL DISTRIBUTIONS , 1957 .

[3]  Thomas M. Stoker,et al.  Censored Regressors and Expansion Bias , 2003 .

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[5]  Frank C Curriero,et al.  Mixture models for quantitative HIV RNA data , 2002, Statistical methods in medical research.

[6]  Survival analysis with coarsely observed covariates , 2003 .

[7]  R. Lyles,et al.  Correlating Two Viral Load Assays with Known Detection Limits , 2001, Biometrics.

[8]  H. Chu,et al.  Correlating two continuous variables subject to detection limits in the context of mixture distributions , 2005 .

[9]  J. Tobin.  Estimation of Relationships for Limited Dependent Variables , 1958 .

[10]  L H Moulton,et al.  A mixture model with detection limits for regression analyses of antibody response to vaccine. , 1995, Biometrics.

[11]  S. Lipsitz,et al.  Likelihood Methods for Incomplete Longitudinal Binary Responses with Incomplete Categorical Covariates , 1999, Biometrics.

[12]  John A Kellum,et al.  Understanding the inflammatory cytokine response in pneumonia and sepsis: results of the Genetic and Inflammatory Markers of Sepsis (GenIMS) Study. , 2007, Archives of internal medicine.

[13]  Whitney K. Newey,et al.  Consistency of two-step sample selection estimators despite misspecification of distribution , 1999 .

[14]  Thomas M. Stoker,et al.  Estimation with Censored Regressors: Basic Issues , 2007 .

[15]  Hélène Jacqmin-Gadda,et al.  Joint modelling of bivariate longitudinal data with informative dropout and left‐censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection , 2005, Statistics in medicine.

[16]  Robert H. Lyles,et al.  Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop‐outs , 2000 .

[17]  R H Lyles,et al.  Correlation coefficient estimation involving a left censored laboratory assay variable , 2001, Statistics in medicine.

[18]  H. Lynn,et al.  Maximum likelihood inference for left-censored HIV RNA data. , 2001, Statistics in medicine.

[19]  J G Ibrahim,et al.  Estimating equations with incomplete categorical covariates in the Cox model. , 1998, Biometrics.

[20]  F. Vella.  Estimating Models with Sample Selection Bias: A Survey , 1998 .

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

[22]  V. De Gruttola,et al.  Modelling progression of CD4-lymphocyte count and its relationship to survival time. , 1994, Biometrics.