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An Indicator of
Nonresponse Bias
Derived from Call-back
Analysis
Paul P. Biemer
RTI International and UNC
Outline
Ignorable vs. non-ignorable nonresponse
Bias in the nonresponse adjusted estimator
Call-back model for estimating non-ignorable nonresponse
Application for estimating drug use prevalence
Future research
Estimation for Population Proportions
Consider a SRS of size n
Want to estimate some proportion, 
Let
Let
yi
denote the observed dichotomous variable
ri  response indicator
i  E (ri | i )  response propensity
ˆi  estimator of response propensity
Nonresponse Adjusted Estimator
Estimator of  is
ˆ adj
n
1
1
  ri yi ˆi
n i 1
which is unbiased if nonresponse is ignorable w.r.t. ˆi
i.e., if the error in
ˆi
is uncorrelated with
yi
Bias in the Adjusted Estimator
B(ˆ adj )  E (ˆ adj   )
1  n  ˆ i  i
  E   yi 
n  i 1  ˆ i

 

 Cov( yi , ei )
ˆi  i
where ei 
 error in the estimate of i
ˆi
Cov( yi , ei )  0 if nonresponse is ignorable
Call-back Model Analysis
Goal is to estimate i when nonresponse is non-ignorable
Uses
yi and call-back patterns to predict i ; note, yi are
only observed for respondents.
For example, suppose
yi  1 for a alcohol user (positive)
 0 for non-alcohol user (negative)
Using data on call outcomes at each call-back for users and
nonusers, we can estimate response propensity as a function
of yi
Then Cov( yi , ei )  0
Call-outcomes by LOE for Alcohol
Call-back Data for Alcohol
Negative
7000
Positive
Interviewed positives
Refused
Number of Cases
6000
Other NR
5000
4000
Interviewed negatives
3000
2000
1000
0
0
5
10
15
LOE
20
25
Call-outcomes by LOE for Marijuana
Call-back Data for Marijuana
Number of Cases
Negative
9000
Positive
8000
Refused
7000
Other NR
Interviewed negatives
6000
5000
4000
Interviewed positives
3000
2000
1000
0
0
5
10
15
LOE
20
25
Call-outcomes by LOE for Cocaine
Call-back Data for Cocaine
Negative
10000
Positive
9000
Refused
Interviewed negatives
Number of Cases
8000
Other NR
7000
6000
5000
Interviewed positives
4000
3000
2000
1000
0
0
5
10
15
LOE
20
25
Call-back Notation
1 = interview
2 = non-interview
3 = noncontact
Call pattern 31111 => noncontact followed by interview
Once interviewed, stays interviewed (absorbing state)
Once non-interviewed, stays non-interviewed (absorbing state)
Call-Back Data for LOE=5
Pattern Definition
Users
Nonusers Total
11111
Interviewed at call 1
n(1,1|1) n(1,1|2)
n(1,1|+)
31111
Interviewed at call 2
n(2,1|1) n(2,1|2)
n(2,1|+)
33111
Interviewed at call 3
n(3,1|1) n(3,1|2)
n(3,1|+)
33311
Interviewed at call 4
n(4,1|1) n(4,1|2)
n(4,1|+)
33331
Interviewed at call 5
n(5,1|1) n(5,1|2)
n(5,1|+)
22222
Non-interviewed at call 1
n(1,2|+)
32222
Non-interviewed at call 2
n(2,2|+)
33222
Non-interviewed at call 3
n(3,2|+)
33322
Non-interviewed at call 4
n(4,2|+)
33332
Non-interviewed at call 5
n(5,2|+)
33333
Never contacted
n(5,3|+)
Simple Call-back Model for NI-NR
LOE-5 Log-Likelihood
log ‹ ( ) 
5
n(l ,1| g )log 
l 1
g
5
l ,1| g
Likelihood of
interview after l
calls
  n(l ,2 | )log( g l ,2| g )  n(5,3 | )log( g 5,3| g )
l 1
g
Likelihood of
non-interview
after l calls
g
Likelihood of no
contact after 5
calls
Obtain parameter estimates by maximum
likelihood
Simple LOE-5 Model Parameters
 1 (true prevalence)
 1,l|g , l  1, 2,3, 4,5, g  1, 2 (interview probabilities)
 2,l|g , l  1, 2,3, 4,5, g  1, 2 (non-interview probabilities)
11 parameters and 10 degrees of freedom
Over-parameterized; requires constraints
These constraints reduces parameters to 7:
1,2|g  1,3|g  1,4|g , g  1, 2
 2,2|g   2,3|g   2,4|g , g  1, 2
Application – Drug Use Survey
Compared estimates of alcohol, marijuana and cocaine past
year use prevalence for
 unadjusted
 current (traditional) adjustment
 call-back model adjustment
Current adjustment incorporates 13 grouping variables and
their interactions including a number of state specific
components
Call-back model incorporated call-back data (for up to 15
call-backs) and the drug use variable of interest
Estimated Response Propensities
for Simple LOE-15 Model
Positive
%
Negative
%
Overall
%
Alcohol
Marijuana
53.4
96.9
94.9
58.6
62.8
62.8
Cocaine
95.4
62.0
62.8
Prevalence Estimates
for Simple LOE-15 Model
Unadjusted
%
Alcohol
Marijuana
Cocaine
Current
%
Call-back
%
Bias Due
to NI-NR
65.86
16.98
65.15
10.58
77.92
11.00
-12.77
-0.42
3.63
2.35
2.39
-0.04
Future Work
Test feasibility of incorporating call-back data in the
nonresponse adjustment process
 Enter # call-backs into the current logistic regression
model (does not adjust for NI-NR)
 Apply the simple call-back model to the drug use data
after traditional adjustment to provide second
adjustment factor for NI-NR
Use the simple call-back model to assess NI-NR bias
following traditional adjustment approach