Effect of Berkson measurement error on parameter estimates in Cox regression models

We study the effect of additive and multiplicative Berkson
measurement error in Cox proportional hazard model. By plotting the
true and the observed Survivor function and the true and the
observed hazard function dependent on the exposure one can get
ideas about the effect of this type of error on the estimation of
the slope parameter corresponding to the variable measured with
error. As an example we analyze the measurement error in the
situation of the German Uranium Miners Study both with the
graphical methods and with a simulation study We do not see a
substantial bias in the presence of small measurement error and in
the rare disease case. Even the effect of a Berkson measurement
error with high variance, which is not unrealistic in our example,
is a negligible attenuation of the observed effect. This effect is
more pronounced for multiplicative measurement error.