Survival analysis of microarray expression data by transformation models

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Abstract

Many microarray experiments involve examining the time elapsed prior to the occurrence of a specific event. One purpose of these studies is to relate the gene expressions to the survival times. The Cox proportional hazards model has been the major tool for analyzing such data. The transformation model provides a viable alternative to the classical Cox's model. We investigate the use of transformation models in microarray survival data in this paper. The transformation model, which can be viewed as a generalization of proportional hazards model and the proportional odds model, is more robust than the proportional hazards model, because it is not susceptible to erroneous results for cases when the assumption of proportional hazards is violated. We analyze a gene expression dataset from Beer et al. [Beer, D.G., Kardia, S.L., Huang, C.C., Giordano, T.J., Levin, A.M., Misek, D.E., Lin, L., Chen, G., Gharib, T.G., Thomas, D.G., Lizyness, M.L., Kuick, R., Hayasaka, S., Taylor, J.M., Iannettoni, M.D., Orringer, M.B., Hanash, S., 2002. Gene-expression profiles predict survival of patients with lung adenocarcinoma. Nat. Med. 8 (8), 816–824] and show that the transformation model provides higher prediction precision than the proportional hazards model.

Section snippets

Background

A major goal of many microarray studies is to relate gene expressions to biological conditions such as disease status, tumor types, drug treatment effects and time to events of interest. Survival analysis is concerned with the relationship of covariates and the time to events of interest. Since event times or survival times that are often incomplete or censored are available for the biological samples in microarray studies, the data requires more sophisticated methods of analysis. For example,

Transformation models

Suppose T is the survival time, which is possibly censored. Cox proportional hazards model is widely used in survival analysis. It assumes that the hazard rate at time t, given covariate z, has the following form:λtz=λ0(t)ezβwhich implies that the hazard rate changes proportionally when the covariate z or its components changes. However, the PH assumption may be violated in practice. As an illustration, the Cox–Snell residual plot for proportional hazards model fitting is shown in Fig. 1 for

Example: methods and results

We illustrate the benefits of transformation model in analyzing microarray data by the lung cancer dataset from Beer et al. (2002). The data consists of gene expressions of 4966 genes for 83 patients (we do not include those patients with missing values). The patients were classified according to the progression of the disease. Sixty four patients were classified as stage I. Nineteen patients were classified as stage III. For each of the 83 patients, the survival time as well as the censoring

Discussion

We have applied the transformation regression models to microarray survival data. Our preliminary exploration shows that microarray data may not have the property of proportionality in hazards. Therefore, proportional hazards modelling approaches may not be valid in analyzing such microarray data. Our results indicate that analyses based on transformation models have better prediction capabilities than those based on Cox proportional hazards model alone for the microarray dataset we analyzed.

Acknowledgements

The second author is sponsored by NIH grant HG00008 and by China Bairen funding. We gratefully acknowledge the encouragement and many helps from Dr. Zhiliang Ying and Dr. Zhezhen Jin. We also thank the anonymous referees for their helpful comments.

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