Validation of a longitudinally measured surrogate marker for a time-to-event endpoint

The objective of this paper is to extend the surrogate endpoint validation methodology proposed by Buyse et al. (2000) to the case of a longitudinally measured surrogate marker when the endpoint of interest is time to some key clinical event. A joint model for longitudinal and event time data is required. To this end, the model formulation of Henderson et al. (2000) is adopted. The methodology is applied to a set of two randomized clinical trials in advanced prostate cancer to evaluate the usefulness of prostate-specific antigen (PSA) level as a surrogate for survival.

[1]  K. Pienta,et al.  Change in serum prostate-specific antigen as a marker of response to cytotoxic therapy for hormone-refractory prostate cancer. , 1998, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[2]  M. Egorin,et al.  Evaluation of prostate-specific antigen as a surrogate marker for response of hormone-refractory prostate cancer to suramin therapy. , 1995, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[3]  Yudi Pawitan,et al.  Modeling Disease Marker Processes in AIDS , 1993 .

[4]  G. Molenberghs,et al.  The validation of surrogate endpoints in meta-analyses of randomized experiments. , 2000, Biostatistics.

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

[6]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[7]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[8]  M Mazumdar,et al.  Prostate-specific antigen as a measure of disease outcome in metastatic hormone-refractory prostate cancer. , 1993, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[9]  R. Prentice Surrogate endpoints in clinical trials: definition and operational criteria. , 1989, Statistics in medicine.

[10]  D. Thomas,et al.  Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. , 1996, Statistics in medicine.

[11]  W. Cleveland Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[12]  R Henderson,et al.  Joint modelling of longitudinal measurements and event time data. , 2000, Biostatistics.

[13]  S. Zeger,et al.  Joint analysis of longitudinal data comprising repeated measures and times to events , 2001 .

[14]  P. Royston,et al.  Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling. , 1994 .

[15]  M. Wulfsohn,et al.  A joint model for survival and longitudinal data measured with error. , 1997, Biometrics.

[16]  A Comparison of Methods for Constructing Confidence Intervals for the Squared Multiple Correlation Coefficient. , 1999, Multivariate behavioral research.

[17]  Jeremy M. G. Taylor,et al.  A Stochastic Model for Analysis of Longitudinal AIDS Data , 1994 .

[18]  N M Laird,et al.  Mixture models for the joint distribution of repeated measures and event times. , 1997, Statistics in medicine.

[19]  V. DeGruttola,et al.  Models for empirical Bayes estimators of longitudinal CD4 counts. , 1996, Statistics in medicine.

[20]  B. Graubard,et al.  Statistical validation of intermediate endpoints for chronic diseases. , 1992, Statistics in medicine.

[21]  H. Ramlau-Hansen Smoothing Counting Process Intensities by Means of Kernel Functions , 1983 .

[22]  J. Johansson,et al.  Liarozole--a novel treatment approach for advanced prostate cancer: results of a large randomized trial versus cyproterone acetate. Liarozole Study Group. , 1998, Urology.