Count regression models for novel NIDA process

Transcription

1 Count regression models for novel NIDA process phenotypes CPDD Methods Workshop Sunday, 10 June 2012 Palm Springs, California Jim Anthony Professor of Epidemiology & Biostatistics College of Human Medicine Michigan State University East Lansing, Michigan Ask me about our open postdoctoral (and predoctoral) NIDA research training fellowships for US citizens and green card holders.

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3 As shown in Figure 2, we focus on an epidemiological sample of newly incident drug users (i.e., those who just started to use the drug in a relatively l short interval just prior to the date of being sampled, recruited for participation, and assessed). We ask about what happens next. Figure 2. Some try once and only once; never try it again (1). In effect, zero future uses, and no drug dependence process. Some move rapidly into a process of repetitive occasions of use (2). For some, this process includes initial formation of clinical lfeatures of dependence such as subjectively felt tolerance, or time to first drug use soon after waking (3). Figure 3 (next slide) shows evidence of very rapid onset of the tobacco dependence process, within six months after onset of smoking initiation, with respect to the Fagerstrom TTFC construct. Fagerstrom TTFC construct: How soon after waking do you smoke your first cigarette? (TTFC=1 if onset within 0 30 minutes)

4 Figure 3. Epidemiological Evidence of Very Rapid Onset of the Dependence Process: Newly Incident Tobacco Smokers See Poster #51 (Wue et al.) at Wednesday noon CPDD poster session.

5 But we trace the initial features of the drug dependence process back to earlier steps manifest in a count process such that some try the drug for the first time, and never try again, while for others, drug use persists and the rate of use accelerates. Figure 4. In ordinary count process models, we might turn to the Poisson count distribution, which originated in a time trend study of the number of deaths by horse kick observed each year in a military population. Nonetheless, in our epidemiological research on newly incident drug users, we typically find an excess of zero count values, perhaps reflecting the fact that for most individuals the initial drug use experience serves no special reinforcing function. Assuch, there isno further repetition of the behavior. For other users, the drug user persists, and the occasions of drug taking behavior mount up concurrent with an accelerating rate of use of the drug. The observed over dispersion of the count distribution, and the excess of zeroes, motivate a two part mixture model approach, with one part focused on whether use persists, and the second part focused on rate of use, conditional on persistence.

6 In our research group at Michigan State University, David Barondess has been the leader of our work to study this count process soon after onset of tobacco cigarettesmoking smoking, which follows a chance to try tobacco. I ll present some of the group s work to illustrate our conceptualization of a novel phenotype that can be observed early in the process of drug involvement. This count process phenotype has two facets. One facet involves persistence versus non persistence of drug use. The other facet involves estimation of the rate of drug use, conditional i on persistence of use.

7 Figure 5. Newly incident tobacco cigarette smokers, all qualifying as Recent Onset Cigarette Smokers (ROCUs) From: Barondess et al. (2010). Epidemiological evidence on count processes in the formation of tobacco dependence. Nicotine & Tobacco Research, 12(7):

8 Among newly incident tobacco smokers: Members of the Hispanic subgroup differed: (1) Were more likely to have not persisted (as compared to non Hispanic Whites), (2) Had manifest a lower rate of smoking, conditional on persistence Covariate adjusted estimates were not appreciably different: (From: Barondess et al., 2010)

9 Among newly incident tobacco smokers: Members of the year old subgroup differed: (1) Were more likely to have persisted (as compared to yr old ROCUs), (2) Had developed a greater rate of smoking, conditional on persistence Covariate adjusted estimates were negligibly different (essentially the same). (From: Barondess et al., 2010)

10 Looking across psychoactive drug compounds: Members of the Asian American subgroup differed only in relation to alcohol: (1) Were less likely to have persisted in drinking (as compared to all other subgroups), but (2) Had no different rate of smoking, conditional on persistence of drinking. From: Anthony J.C. (2010). Novel Phenotype Issues Raised in Cross National Epidemiological Research on Drug Dependence. Annals New York Acad of Science. 1187:

11 Many software options for zero inflated modeling of count process outcomes, and a few accommodate departures from simple random sampling. We use either Stata or MPlus for complex study data (e.g., multi stage area probability samples; multi center clinical research samples). Here is Stata example as might be used with a simple random sample of newly incident drug users recruited at a single site trial in a multi site trial (site==1), and the question is whether a brief intervention (briefint==1) alters persistence of cocaine use, or rate of use, conditional on persistence, as measured by the number of cocaine using days during the 30 days prior to the final trial followup assessment (yvar = count ): xi: svy,subpop(if site==1): zip count i.briefint, /// inflate(i.briefint) i fi t)

12 A more complex situation is faced when the newly incident users are recruited from multiple sites, with individual and site level variation in sampling probabilities, similar to what we face in our work on newly incident id tdrug users in the complex samples of the World Mental Health Surveys or the United States National Surveys on Drug Use & Health: Here is Stata example as might be used with complex sample of newly incident drug users recruited for a multi site trial of this type, with city as a primary sample unit, and clinics as strata, with an analysis weight equal to the inverse of the probability of selection. Here again the question is whether a brief intervention (briefint==1) alters persistence of cocaine use, or rate of use, conditional on persistence, as measured by the number of cocaine using days during the 30 days prior to the final trial followup assessment (yvar= count ): svyset city [pw=analysiswt], strata(clinic) svy: zip count briefint, inflate(briefint)

13 You might wish to have one set of hypothesized explanatory variables for the zero inflation (persistence versus non persistence) part of the model, and another set for the conditional rate ratio estimation part of the model as shown below, reflecting your conceptual model about what might account for persistence, and what might account for variation in rate of use, conditional on persistence. Here, the model stipulates that the rate ratios might vary with intervention status, malesex, and age. svy: zip count briefint malesex age, /// inflate(briefint malesex eastasian) As for the zero inflation part of the model (for persistence), two covariates overlap, but one covariate (eastasian) does not.

14 Here is Stata example for newly incident cocaine users (nicu==1), based on Brian Fairman s CPDD 2012 work to be presented as Poster 171, Thursday AM session. (The svyset command already has been issued dfor the complex sample design and analysis weights for his data.) nicu = 1 for newly incident cocaine users count = number of cocaine using days per 30 days cigcoc= indicatorfor nicotine pre treatment svy,subpop(if nicu==1): /// zip count cigcoc, /// inflate(cigcoc)

15 The log rate ratios are estimated in the top part (i.e., the estimated rate ratios conditional on persistence). The zero inflation persistence it parameters are estimated t as log odds of non persistence in the inflate part of the model output: As you can see, Brian has found some interesting variation in the conditional rates, but no subgroup variation in the log odds for (non ) persistence. Visit Brian s poster #171 on Thursday AM poster session for the rest of the story. (And as Paul Harvey always said: Good day! )

16 Here are citations for Lambert s pioneering ZIP work on soldering defects in a manufacturing context, and some later work on high risk heterosexual behavior, as well as motor vehicle crash rates: (1) Lambert (1992) Soldering defects on print wiring boards: Lambert, D., Zero inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34, (2) Estimated covariate effect on high risk heterosexual behavior: Heilbron, D. (1994). Zero alteredand and other regression models for count data with added zeros. Biometrical J. 36, (3) Motor vehicle crash frequencies: Shankar, V., Milton, J., Mannering, F. (1997). Modelling accident frequencies as zero altered probability process: an empirical inquiry. Accid. Anal. Prev. 29,

17 THANK YOU!! (ALMOST TIME FOR SWIMMING!!!)