Regression Analysis of Censored Data with Applications in Perimetry
Anna Lindgren
Centre for Mathematical Sciences
Mathematical Statistics
Lund University,
1999
ISBN 9162834991
LUNFMS10081999

Abstract:

This thesis treats regression analysis when either the dependent or the
independent variable is censored. We deal with quantile regression when the
dependent variable is censored. Using the independence between the true values
and the censoring limits the quantile function for the true values can be
rewritten as another quantile function of the observed, censored values,
where the quantile value itself is a function of the censoring distribution.
The quantile value is estimated nonparametrically and the properties of
the resulting quantile function estimate studied by simulations. We also
apply this technique in practice to the problem of finding limits for the
normal variability in stable glaucomatous visual fields.


When the independent variable is censored it is possible to achieve estimates
by throwing away the censored data and estimate the mean function by ordinary
least squares using only the noncensored data. We try to improve on these
estimates by redistribution the censored values to positions based on the
value of the dependent variable and the estimated distribution of the independent
variable conditional on the fact that it is censored. The distributions are
estimated in three different ways, parametrically, assuming, e.g. a
twodimensional normal distribution, semiparametrically, assuming a normal
distribution for the dependent variable given the independent one while
estimating the distribution of the independent variable nonparametrically,
and nonparametrically estimating the distribution of the independent variable
locally in a band around the value of the dependent variable.

Key words:

Quantile regression, L_1 minimization, rightcensoring, censored covariate