  Response-biased sampling, in which samples are drawn from a popula- tion
according to the values of the response variable, is common in biomedical,
epidemiological, economic and social studies. In particular, the complete
obser- vations in data with censoring, truncation or missing covariates can be
regarded as response-biased sampling under certain conditions. This paper
proposes to use transformation models, known as the generalized accelerated
failure time model in econometrics, for regression analysis with
response-biased sampling. With unknown error distribution, the transformation
models are broad enough to cover linear re- gression models, the Cox's model
and the proportional odds model as special cases. To the best of our knowledge,
except for the case-control logistic regression, there is no report in the
literature that a prospective estimation approach can work for biased sampling
without any modification. We prove that the maximum rank corre- lation
estimation is valid for response-biased sampling and establish its consistency
and asymptotic normality. Unlike the inverse probability methods, the proposed
method of estimation does not involve the sampling probabilities, which are
often difficult to obtain in practice. Without the need of estimating the
unknown trans- formation function or the error distribution, the proposed
method is numerically easy to implement with the Nelder-Mead simplex algorithm,
which does not require convexity or continuity. We propose an inference
procedure using random weight- ing to avoid the complication of density
estimation when using the plug-in rule for variance estimation. Numerical
studies with supportive evidence are presented. Applications are illustrated
with the Forbes Global 2000 data and the Stanford heart transplant data.
