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 denote the observed dichotomous variable + Let

Nonresponse Adjusted Estimator Estimator of is which is unbiased if nonresponse is ignorable w.r.t. i.e., if the error in is uncorrelated with

Bias in the Adjusted Estimator if nonresponse is ignorable

Call-back Model Analysis + Goal is to estimate when nonresponse is non-ignorable + Uses and call-back patterns to predict ; note, are only observed for respondents. + For example, suppose + Using data on call outcomes at each call-back for users and nonusers, we can estimate response propensity as a function of + Then

Call-outcomes by LOE for Alcohol Interviewed positives Interviewed negatives

Call-outcomes by LOE for Marijuana Interviewed negatives Interviewed positives

Call-outcomes by LOE for Cocaine Interviewed negatives Interviewed positives

1 = interview 2 = non-interview 3 = noncontact Call pattern => noncontact followed by interview Once interviewed, stays interviewed (absorbing state) Once non-interviewed, stays non-interviewed (absorbing state) Call-back Notation

Call-Back Data for LOE=5 PatternDefinitionUsersNonusersTotal 11111Interviewed at call 1n(1,1|1)n(1,1|2)n(1,1|+) 31111Interviewed at call 2n(2,1|1)n(2,1|2)n(2,1|+) 33111Interviewed at call 3n(3,1|1)n(3,1|2)n(3,1|+) 33311Interviewed at call 4n(4,1|1)n(4,1|2)n(4,1|+) 33331Interviewed at call 5n(5,1|1)n(5,1|2)n(5,1|+) 22222Non-interviewed at call 1n(1,2|+) 32222Non-interviewed at call 2n(2,2|+) 33222Non-interviewed at call 3n(3,2|+) 33322Non-interviewed at call 4n(4,2|+) 33332Non-interviewed at call 5n(5,2|+) 33333Never contactedn(5,3|+)

Simple Call-back Model for NI-NR LOE-5 Log-Likelihood Likelihood of interview after l calls Likelihood of no contact after 5 calls Likelihood of non-interview after l calls Obtain parameter estimates by maximum likelihood

Simple LOE-5 Model Parameters 11 parameters and 10 degrees of freedom Over-parameterized; requires constraints These constraints reduces parameters to 7:

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 Cocaine

Prevalence Estimates for Simple LOE-15 Model Unadjusted % Current % Call-back % Bias Due to NI-NR Alcohol Marijuana Cocaine

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