Model Parameters

Parameter Mean Std k 0.44/hr 0.074/hr km 0.097/hr 0.020/hr f 0.30/hr 0.072/hr V 60 ml/hr

d 200 mg 600 mg

0.5 mg 1.5 mg

From Li et al, based on 10 subjects

Assume all parameters are independently and normally distributed

Mean dose = 200 mg IV

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0

0.2

0.4

0.6

0.8

1.0

Pro

babili

ty

Days since most recent use

Mean dose = 200 mg IV

Variability due to lumping all 14-day histories having most recent use 3 days ago (plus error of simulation).

Line shows log-normal approximation * based only on most recent dose.

Pr(+ urine on day 0) versus days since most recent dose, for all possible 14-day histories

tp, fp, tn, and fn rates of X-test as function of p, the daily probability of use

Rate

p

Assuming a positive test, when was the most recent use?• Bayes theorem

– Pr(most recent use = k | + urine)• = Pr(+|k) Pr(k) / [Pr(+|1)Pr(1) + Pr(+|2)Pr(2) + …

• = xk zk / [x1z1 + x2z2 + …]

• Similarly– Pr(k|-)=(1-xk)zk/[(1-x1)z1 + (1-x2)z2 + …]

Theoretical Error Rates of Qualitative UDS Tests for StimulantsNeal Oden, PhD, Paul VanVeldhuisen, PhD, NIDA Data and Statistics Center 2, The EMMES Corporation

Second SimulationFirst Simulation

Clinical trials in cocaine abuse and addiction often use a urine drug screen (UDS) as part of the primary outcome. Operationally, a popular approach is to consider a positive qualitative UDS (BE concentration > 300 ng/ml) on day 0 as indicating that there must have been drug use at least once during days -1 to -3, while a negative qualitative UDS is interpreted as indicating that there cannot have been drug use on those days. Call this the X-test. How unrealistic are the assumptions of the X-test?

There are at least two potential sources of error. The first, which involves the laboratory analysis, concerns the accuracy with which the UDS determines BE concentration. The second, which is more concerned with human behavior, hinges on whether a high BE concentration day 0 is reliably associated with drug-taking behavior on days -3 to -1. We ignore the first source, and attempt to determine theoretical error rates associated with the second source.

Li et al. express BE concentration in urine as a function of initial dose and time since dose. An implication is that, because BE clears so quickly, test outcomes depend mostly on time since most recent dose. We use Li’s expression in conjunction with assumptions about normality and behavior of participants in addiction trials to derive theoretical curves showing sensitivity, specificity, positive predictive value, and negative predictive value of the X-test as a function of probability of daily drug use. Under these assumptions, the probabilities of false negative and false positive are not likely to be more than 0.20.

Abstract

Background

• Urine Drug Screen (UDS) results are often outcomes of clinical trials for cocaine use

• Operationally, one way to use UDS is to:– Measure urinary concentration of

benzoylecgonine (BE), a cocaine metabolite

– Consider urine positive if BE concentration exceeds 300 ng/ml

– Take positive urine on day 0 to indicate drug use some time between day -3 and day -1, while negative urine indicates no use on those days

• Call this “the X test”

How accurate is the X test?

• Two sub-questions:– How accurately can a lab test

determine whether BE concentration exceeds 300?

– What does BE > 300 tell us about past cocaine use?

• We use simulation to begin to answer the second question

Research supported by the National Institute on Drug Abuse, National Drug Abuse Treatment Clinical Trials Network, National Institutes of Health, through Contract No. HHSN271200900034C.

Acknowledgement

Source: Li SH, Chiang N, Tai B, Marschke CK, Hawks RL: NIDA Research Monograph 175, 1997

One-compartment Pharmacokinetic Model for IV Cocaine Disposition

Summary of Simulation Conclusions

• In a population of IV cocaine users who use not more than once a day:

– Probability of positive urine depends mostly on time since most recent use

• Log-normal approximation is fairly accurate

– If probability of drug-taking is about 0.3 to 0.4 per day,

• X-test accuracy is as follows:

– sensitivity 0.8-0.9

– specificity > 0.95

– positive predictive value ~1

– negative predictive value 0.6-0.8

• Time since most recent use:

– If urine positive, probably yesterday

– If urine negative, probably 3-4 days ago