Journal of Environmental and Public Health 2.2.4. Program and Patient Residence ZIP Code Areas. Both sizes of the ZIP code in which the patient resided and in which the program was located were indicated by area in square miles. For statistical modeling, the natural logarithm of square miles (with a constant of 1 added to all areas) was used. 2.2.5. Bodily Pain a Reason for Enrolling. Patients were asked “Other than drug withdrawal pain, is bodily pain a reason for enrolling in methadone treatment? ” with responses of “Yes” or “No.” 2.2.6. First Methadone Treatment. Patients were asked “Before coming to this program, when were you last in a methadone treatment program?” with a response of “Never” indicating ﬁrst methadone treatment (Yes/No). 2.2.7. Withdrawal Severity. Patients were asked “Which word best describes your drug withdrawal pain in the past week? ” with ﬁve responses ranging from “None” to “Very Severe.” 2.2.8. Urge to Use. Patients were asked “Which word best describes your urge to use your primary drug in the past week? ” with ﬁve responses ranging from “None” to “Very Strong.” 2.2.9. Recent Heroin Use. Patients were asked whether they had used heroin in the 30-day period before admission (Yes/No). 2.2.10. Recent Prescription Opioid Use. Patients were asked whether they had used a prescription opioid to get high in the 30-day period before admission (Yes/No). 2.3. Data Analysis. A total of 5,349 respondents were not included in a multivariable mixed model analysis due to missing data on gender, race/ethnicity, source of income, urge to use, withdrawal severity, past methadone treatment, or pain as a reason for enrolling in treatment, resulting in a sample for multivariable analysis of 17,792 and a total sample of 23,141 OTP enrollees. To account for clustering of the 17,792 patients in 84 OTPs, a linear mixed model analysis with a random intercept [13] was used to predict distance traveled to the treatment program by individual patients. The nlme package [14, 15] of the freely available, open-source R program [16] was used to ﬁt linear mixed models. Program-level predictors included population density and the natural logarithm of the square miles of each OTP’s ZIP code. Patient-level predictors included age, gender, race/ethnicity, employment, pain as a reason for enrolling in treatment, ﬁrst methadone treatment, urge to use, withdrawal severity, use of prescription opioids in the past 30 days, and use of heroin in the past 30 days. Predictors were entered in conceptually related blocks of variables. The ﬁrst block included the program-level variables of urbanicity. The second block included the area of both the program ZIP code and the ZIP code of the patient’s residence. The third block included the following demographic variables: age; gender; race/ethnicity; employment as the major source of income. The ﬁnal 3 block included the following characteristics related to each patient’s opioid use: pain as a reason for enrolling in treat- ment; ﬁrst methadone treatment; urge to use; withdrawal severity; prescription opioid use in the past 30 days; heroin use in the past 30 days. Each variable’s relation to travel distance was estimated controlling for other variables on the same block and for all variables entered in previous blocks. The use of a natural logarithm transformation eﬀectively reduced positive skew in travel distance. To convey the eﬀect of predictors in the mixed model analysis, ﬁxed- eﬀects regression coeﬃcients were exponentiated (i.e., the Eulerian number, e, which is the base of the natural logarithm and approximately equal to 2.718282, was raised to the power of each regression coeﬃcient). These exponentiated regression coeﬃcients indicate how a one-unit change in the predictor multiplies travel distance. For example, a regression coeﬃcient of .70 is interpreted as roughly a doubling (e.70 = 2.014) of travel distance for a one-unit change in the predictor (or for a coeﬃcient representing the contrast between a particular level of a categorical predictor and the reference category of that categorical variable). In a separate analysis we used a multilevel logistic regression model to identify covariates among patients who crossed a state border to attend an OTP. 2.4. Mapping OTPs. We prepared a map of study and non- study OTPs to represent their location in the U.S. Location data for OTPs was obtained from the USA Substance Abuse and Mental Health Services Administration (SAMHSA) [17] including an updated report that there are no OTPs in South Dakota (Nick Reuter, SAMHSA, e-mail communication, Oct. 13, 2010). A map can immediately display spatial associations and patterns, otherwise impossible to identify in a tabular format. Data were imported into MapPoint (Microsoft Corp., Redmond, WA) to map the locations of OTPs and patient 3DZ code level data throughout the USA on a national map. Maps are traditionally a way of visualizing tabular data. 3. Results Table 1 presents data on the characteristics of patients and treatment programs. The area of the ZIP codes in which the 84 programs were located ranged from less than one square mile to more than one thousand squares miles, with a median of ten square miles. The number of patients responding to the survey in each program ranged from two to more than a thousand, with a median of 155 patients per program. More than half of all programs (54%) were located in densely populated urban areas, and at least fourteen programs were sampled from each USA region. Table 1 presents characteristics of patients and programs in the full sample (n = 23,141). Patient age ranged from 18 to 81 years with a median age of 32 years. Most patients were male and non-Hispanic white. Thirty percent of patients used both prescription opioids and heroin in the month before treatment. The comparably higher rate of prescription opioid use (73%) compared with heroin use