[gov3009-l] 11/15 Applied Stats: Rebecca Betensky
Dana Higgins
danahiggins at fas.harvard.edu
Mon Nov 13 10:22:02 EST 2017
Hi everyone!
This week at the Applied Statistics Workshop we will be welcoming *Rebecca
Betensky*, Professor of Biostatistics at the Harvard School of Public Health.
She will be presenting work entitled *Nonidentifiability in the presence of
factorization for truncated data*. Please find the abstract below and on
the Applied Stats website here
<https://projects.iq.harvard.edu/applied.stats.workshop-gov3009>.
As usual, we will meet at noon in CGIS Knafel Room 354 and lunch will be
provided. See you all there!
-- Dana Higgins
*Title:* *Nonidentifiability in the presence of factorization for truncated
data*
*Abstract:* Truncation is a structured form of selection bias that arises
often in cohort studies. A time to event, X, is left truncated by T if X
can be observed only if T < X. This often results in over sampling of large
values of X, and necessitates adjustment of estimation procedures to avoid
bias. Simple risk-set adjustments can be made to standard risk-set based
estimators to accommodate left truncation as long as T and X are
“quasi-independent,” i.e., independent in the observable region. Through
examination of the likelihood function, we derive a weaker factorization
condition for the conditional distribution of T given X in the observable
region that likewise permits risk-set adjustment for estimation of the
distribution of X (but not T). Quasi-independence results when the
analogous factorization condition for X given T holds, as well, in which
case both distributions of X and T are easily estimated. While we can test
for factorization, if the test does not reject, we cannot identify which
factorization condition holds, or whether both (i.e., quasi-independence)
hold. Importantly, this means that we must ultimately make
an unidentifiable assumption in order to estimate the distribution of X
based on truncated data. This contrasts with common understanding that
truncation is distinct from censoring in that it does not require any
unidentifiable assumptions. We illustrate these concepts through examples
and a simulation study.
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