Estimating Drug Use Prevalence Using Latent Class Models with Item Count Response as One Indicator

1. Estimating Drug Use Prevalence Using Latent Class Models with Item Count Response as One Indicator Paul Biemer RTI International and University of North Carolina

2. Presentation Outline • Describe the item count (IC) method • Present standard IC estimates of cocaine use and compare them with direct estimates • Describe a method for adjusting the standard estimates for measurement bias • Present the bias corrected estimates • Implications for future applications of IC

3. What is the item count method? • Used for estimating the prevalence of sensitive behaviors • Sensitive behavior is one of a small number of behaviors in a list • Respondents indicate only how many behaviors in the list apply, not which ones • If the average number of “other” behaviors is known, prevalence of the sensitive behavior can be estimated

4. Random sample Subsample A Subsample B random split Illustration – One Pair of Lists ICQ (short list) ICQ (long list) Long list = short list + sensitive item

5. Random sample Subsample A Subsample B random split Illustration – One Pair of Lists ICQ (short list) ICQ (long list) Long list = short list + sensitive item

6. Prevalence Estimate for Single Pair Design Prevalence = avg count for long list – avg count for short list

7. Example of Youth ICQ: ICQ1 – Short Next is a list of things that you may or may not have done in the past 12 months. How many of the things on this list did you do in the past 12 months, that is since [DATE 12 MONTHS AGO]. • Rode with a drunk driver • Walked alone after dark through a dangerous neighborhood • Rode a bicycle without a helmet • Went swimming or played outdoor sports when it was lightning

8. Example of Youth ICQ: ICQ1 – Long Next is a list of things that you may or may not have done in the past 12 months. How many of the things on this list did you do in the past 12 months, that is since [DATE 12 MONTHS AGO]. • Rode with a drunk driver • Walked alone after dark through a dangerous neighborhood • Rode a bicycle without a helmet • Went swimming or played outdoor sports when it was lightning • Used cocaine, in any form, one or more times

9. Results Using the Standard IC Estimator

10. Item Count Estimates by Age and Gender

11. Pseudo IC Variable • Recall each of the 4 IC short-list item was asked separately • Form a “pseudo-” IC variable corresponding to the IC short-list response where Pseudo-IC = number of positive responses to the 4 IC short-list questions asked separately

12. Item Count Response by Pseudo-Item Count Response for Both Short IC Questions

13. Objective of the Modeling Approach • Combine all data on cocaine use including – • Direct question • Item count pair of questions • Pseudo-item count data • Apply latent class models to predict cocaine use • Why latent class models? • Accounts for measurement error in all the observations • Model assumptions are plausible for the current application

14. Central Idea for the Modeling Approach Let A = short form response D = long form response A is an indicator of X (latent variable) D is an indicator of Z (latent variable) Standard IC estimator is Use LCA to estimate Z and X and form Repeat this for each of the two IC pairs

15. X Y Z A B G C D Path Model for One IC Pair of Questions Grouping variable Short IC Question Pseudo Short IC Question Cocaine Long IC Question

16. X Y Z A B G C D Path Model for One IC Pair of Questions Grouping variable Short IC Question Pseudo Short IC Question Cocaine Long IC Question

17. X Y Z A B G C D Path Model for One IC Pair of Questions Grouping variable Short IC Question Pseudo Short IC Question Cocaine Long IC Question

18. Data Likelihood Random split half-sample MAR Subsample I Subsample II

19. where denotes summation over x, y and z = x+y.

20. Estimation of Cocaine Use Prevalence Parameters Estimators from LCA Cocaine prevalence

21. Corrected Estimator of Cocaine Prevalence Corrected cocaine use prevalence NSDUH Estimate Correction estimated from LCM

22. Results Using the LCM-based Estimator

23. Estimates of Classification Accuracy from LCM

24. NSDUH and Model-based IC Estimates of Past Year Cocaine Use Prevalence by Gender and Age

25. Summary • Despite careful design and large sample size, the standard item count method failed • Estimates of cocaine use prevalence were less than direct estimates from NSDUH • Major cause appeared to be measurement error • Difficult response task • IC masking may be ineffective for eliciting truthful counts • IC direct questions may be interpreted differently • Latent class model corrections were successful at reducing downward bias • NSDUH estimates were increased by ~40% on average • Standard errors were much larger

26. Further reading - Biemer, P. and Brown, G. (2005). “Model-based Estimation of Drug Use Prevalence with Item Count Data,” Journal of Official Statistics, Vol. 21, No. 3. Biemer, P., B.K. Jordan, M. Hubbard, and D. Wright (2005). A Test of the Item Count Methodology for Estimating Cocaine Use Prevalence. In Kennet, J., and J. Gfroerer (Eds.), Evaluating and Improving Methods Used in the National Survey on Drug Use and Health. Rockville, MD: SAMHSA