Estimating Drug Use Prevalence Using Latent Class Models with Item Count

Response as One Indicator

Paul Biemer

RTI International and

University of North Carolina

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

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

Illustration – One Pair of Lists

Random sample

Subsample A Subsample Brandom split

ICQ (short list)

ICQ (long list)

Long list = short list + sensitive item

Illustration – One Pair of Lists

Shortx

Random sample

Subsample A Subsample Brandom split

ICQ (short list)

ICQ (long list)

Long list = short list + sensitive item

Longx

Prevalence Estimate for Single Pair Design

ˆ Long Shortp x x

Prevalence = avg count for long list – avg count for short list

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

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

Results Using the Standard IC Estimator

Item Count Estimates by Age and Gender

Age Gender Item Count NSDUH

12-17 Total 0.73% 1.5%

Male 0.19% 1.4%

Female 1.28% 1.5%

18+ Total -0.08% 1.9%

Male 0.42% 2.8%

Female -0.55% 1.1%

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

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

Pseudo-IC Response

Short-List IC Response

0 1 2 3 4

0 51,015 1,641 286 49 47

1 4,392 6,333 447 48 19

2 718 607 622 53 9

3 263 114 48 44 7

4 1,393 96 37 9 8

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

Central Idea for the Modeling Approach

ˆ ICp D A

ˆIC Z X

Let A = short form responseD = long form responseA 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

A B

X Y Z

C D

G

Path Model for One IC Pair of Questions

Short IC Question

Pseudo Short IC Question

Cocaine Long IC Question

Grouping variable

A B

X Y Z

C D

G

Path Model for One IC Pair of Questions

Short IC Question

Pseudo Short IC Question

Cocaine Long IC Question

Grouping variable

A B

X Y Z

C D

G

Path Model for One IC Pair of Questions

Short IC Question

Pseudo Short IC Question

Cocaine Long IC Question

Grouping variable

Data Likelihood

( , )GABC GCDL ( ) ( )GABC GCD L L

Random split half-sample

Subsample I Subsample II

MAR

where

| |log ( ) log( )gabc g xyz g abc xyzxyz gabc

GABC n L

| |log ( ) loggcd g xyz g cd xyzxyz gcd

GCD n L

xyzN denotes summation over x, y and z = x+y.

Estimation of Cocaine Use Prevalence

|[ ]c i y j c|yπ ˆ c|yπ

( ) 1 0ˆ ˆ ˆ=[ , ] NSDUH c c cπ1 0[ , ]y y yπ

Parameters Estimators

from LCA

Cocaine prevalence

Corrected Estimator of Cocaine Prevalence

1( )ˆ ˆ ˆ= NSDUH

y c|y cπ π π

Corrected cocaine use prevalence

Correction estimated from LCM

NSDUH Estimate

Results Using the LCM-based Estimator

Pair 1 s.e. Pair 2 s.e. Average s.e.

.6953 .1961 .7065 .2835 .7009 .1724

.9988 .0012 .9993 .0012 .9991 .0004

Estimates of Classification Accuracy from LCM

1| 1ˆc y

0| 0ˆc y

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

NSDUH s.e. LCM s.e.

Total 1.90 0.08 2.71 0.36

Male 2.600.14

3.710.44

Female 1.10 0.08 1.57 0.28

12-17 1.50 0.10 2.14 0.33

18+ 1.90 0.09 2.71 0.36

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

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