I am trying to estimate a duration model based on two data sets, let's say A and B. A and B are identical, except that (a) A only contains data for subjects that are older than X years, and B covers their entire life span (b) A covers all subjects, while B covers only part of them. Whether a subject is covered by data set B depends on criteria that imply that B is a biased sample. I can consider the following options (a) estimating the model using data set A only, but then I lose all the information for subjects who do not survive beyond X (b) estimating the model using data set B only, but then I lose all the information contained in set A, using a non-representative data set (c) using both data sets - this contains more information than any individual data set, but it does not solve the problem that all my data before year X are part of a biased sample. Does anyone know of statistical techniques that deal with this type of questions?
I tried to follow a to c scenarios. I think that probably...
Cox C, Chu H, Schneider MF, Muñoz A. Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine. 15 de octubre de 2007;26(23):4352-74.
Shen P. Nonparametric estimation with left-truncated and right-censored data when the sample size before truncation is known. Statistics [serial on the Internet]. (2014, Feb), [cited February 10, 2018]; 48(2): 315-326. Available from: Academic Search Ultimate.
... and related work could help.
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