We consider the problem of variable selection for logistic regression when the dependent variable is measured imperfectly, under both differential and non-differential misclassification. An MCMC sampling scheme is designed, incorporating uncertainty about which explanatory variables affect the dependent variable and which affect the probability of misclassification. We assume that a small gold standard perfectly measured sample is available to augment the imperfectly measured sample, under the differential misclassification framework. A simulation study illustrates favourable results both in terms of variable selection and parameter estimation. Examples analysing the risk of violence against young women by their partner and the risk of injury in highway motor accidents are considered.
Cheng KF
and
Hsueh HM
(2003)
Estimation of a logistic regression model with mismeasured observations
. Statistica Sinica, 13,
111–27
.
2.
Cheng KF
,
Hsueh HM
and
Chien TH
(1998)
Goodness of fit tests with misclassified data
. Communications in Statistics A: Theory and Methods, 27,
1379–93
.
3.
Gaba A
and
Winkler RL
(1992)
Implications of errors in survey data: a Bayesian model
. Management Science, 38(7),
913–25
.
4.
Gelman A
(2006)
Prior distributions for variance parameters in hierarchical models
. Bayesian Analysis, 1(3),
515–33
.
5.
Gerlach R
,
Bird R
and
Hall A
(2002)
Bayesian variable selection in logistic regression: predicting company earnings direction
. Australian and New Zealand Journal of Statistics, 44(2),
155–68
.
6.
Gerlach R
and
Eyre T
(2004) Bayesian variable selection in discrete regression models. School of Mathematical and Physical Sciences Working Paper Series No. 003,
University of Newcastle, Australia
.
7.
Gustafson P
(2003) Measurement error and misclassification in statistics and epidemiology: impacts and Bayesian adjustments.
New York
:
Chapman and Hall/CRC Press
.
8.
Gustafson P
,
Le ND
and
Saskin R
(2001)
Case-control analysis with partial knowledge of exposure misclassification probabilities
. Biometrics, 57(2),
598–609
.
9.
Hochberg Y
(1977)
On the use of double sampling schemes in analyzing categorical data with misclassification errors
. Journal of the American Statistical Association, 72(360),
914–21
.
10.
Howard D
and
Wang M
(2003)
Risk profiles of adolescent girls who were victims of dating violence
. Adolescence, 38,
1–14
.
11.
Joseph L
,
Gyorkos TW
and
Coupal L
(1995)
Bayesian estimation of disease prevalence and parameters of diagnostic tests in the absence of a gold standard
. American Journal of Epidemiology, 141(3),
263–72
.
12.
Magder L
and
Hughes J
(1997)
Logistic regression when the outcome is measured with uncertainty
. American Journal of Epidemiology, 146(2),
195–203
.
13.
McInturff P
,
Johnson W
,
Cowling D
and
Gardner I
(2004)
Modeling risk when binary outcomes are subject to error
. Statistics in Medicine, 23(7),
1095–109
.
14.
Paulino C
,
Soares P
and
Neuhaus J
(2003)
Binomial regression with misclassification
. Biometrics, 59(3),
670–75
.
15.
Prescott G
and
Garthwaite P
(2005)
Bayesian analysis of misclassified binary data from a matched case-control study with a validation sub-study
. Statistics in Medicine, 24(3),
379–401
.
16.
Raats VA
and
Moors JJA
(2003)
Double-checking auditors: a Bayesian approach
. Journal of the Royal Statistical Society: D, 52,
351–66
.
17.
Roy S
,
Banergee T
and
Maiti T
(2005)
Measurement error model for misclassified binary responses
. Statistics in Medicine, 24(2),
269–83
.
18.
Smith M
and
Kohn R
(1996)
Nonparametric regression using Bayesian variable selection
. Journal of Econometrics, 75,
317–44
.
19.
Tenenbein A
(1970)
A double sampling scheme for estimating from binomial data with misclassification
. Journal of the American Statistical Association, 65(331),
1350–61
.
20.
Viana M
,
Ramakrishnan V
and
Levy P
(1993)
Bayesian analysis of prevalence from the results of small screening samples
. Communications in Statistics-Theory and Methods, 22(2),
575–85
.
21.
Whittemore AS
and
Gong G
(1991)
Poisson regression with misclassified counts: application to cervical cancer mortality rates
. Applied Statistics, 40,
81–93
.
