MINISTERIO DE SALUD

Survival analyses were used to answer the research questions associated with Aim 4 (e.g., examine longitudinal patterns of post-detention treatment service utilization). First, two separate Kaplan-Meier survival analyses were run to examine the following outcomes: 1) connection to care, or time to first post-detention treatment utilization and 2) retention in outpatient services, or time to termination from outpatient treatment services. For the first outcome, the origin of time was defined as the date of release from first detention stay and the endpoint was defined as date of first treatment service (or end of study time frame). Since the origin of time differed across DAs, follow-up times ranged from 0 years (i.e. released in 2011 at the end of data collection) to 14 years (i.e. released from detention in 1998 at the beginning of data collection). The metric of time was continuous, measured in days since release from detention. Participants who did not utilize treatment were deemed non-users and treated as censored cases (Cloyes, Wong, Latimer, Abarca, 2010; Corning & Malofeeva, 2004). For the second survival analysis, the origin of time was defined as the date of first outpatient treatment session and the endpoint was the date of final outpatient session. The metric of time for these analyses was also continuous, measured in days since participation in first outpatient session. Again, participants who did not utilize outpatient treatment were treated as non-users and censored cases (Corning & Malofeeva, 2004).

Descriptive statistics for the survival analysis models were generated and examined via life tables, which show the event histories of participants from the beginning to the end of data collection (Bewick, Cheek, & Ball, 2004). Given the

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extended length of follow-up (i.e., 14 years), time for the life tables were divided into 6- month time intervals. For each time interval, the following statistics were generated: number of treatment users during time interval, censored cases (i.e., non-users), risk set (i.e., number of adolescents eligible to experience the outcome), probability of outcome (i.e., treatment utilization, treatment termination), and hazard rate (Bewick et al., 2004; Corning & Malofeeva, 2004).

To address question two of Aim 4, analyses were re-run to examine group differences. Specifically, Kaplan-Meier survival analyses were conducted to determine whether the two main outcomes significantly differed (p < .01) for the following

independent variables: male gender (yes/no), Black race (yes/no), age cohorts (younger age [≤13 years], mid-age [14-15 years], and older age [≥16 years]), MAYSI-2 (did not take the MAYSI-2, positive screen, non-positive screen), disorder type (mental disorder, substance-related disorder, comorbid), violent offender (yes/no), repeat offender (yes/no), repeat detention/incarceration (yes/no), pre-detention treatment (yes/no), treatment type (mental health, substance-related either/both), and setting (outpatient, non-outpatient). The median time to event (i.e., treatment utilization, dropout) for each group was calculated (Willie, 2012).

Survival curves for each group were directly compared using several chi-square tests, including the Log Rank, Breslow/Wilcoxon, and Tarone-Ware (Bewick et al., 2004; Bouliotis & Billingham, 2011). The Log Rank chi-square represents the most common and frequently used test for identifying differences in survival analysis outcomes (Willie, 2012), with significant results indicating that survival curves differ significantly across groups in the long-term. This test can be limited in examining survival curves that intersect over time, which typically yield non-significant results, even though curves may be significantly different at other follow-up time points (Bouliotis & Billingham, 2011). Thus, alternative chi-square tests include weighted log-rank tests, such as the

Breslow/Wilcoxon test and Tarone-Ware test. The Breslow/Wilcoxon test is more sensitive to differences in early follow-up periods, with significant results indicating survival curves differ significantly across groups in the short-term (Willie, 2012). The Tarone-Ware chi-square test considers the overall survival curve and has been shown to

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be superior to the Log Rank test because it can better compare variables with more than two levels (Willie, 2012). Significant results for the Tarone-Ware tests indicate that survival curves differ significantly across groups in the middle portion of the follow-up time, with the magnitude of results typically falling in between the results for the Log Rank test and Breslow/Wilcoxon test. In addition to examining the chi-square tests, the survival curves for different groups for each independent variable were generated and displayed via graphs to visually examine longitudinal patterns of treatment utilization.

To identify significant predictors of treatment utilization over time, Cox

proportional hazards regression models with time-dependent variables were conducted. Cox proportional hazards regression analyses can be interpreted like other regression analyses, in that multiple variables can be entered into the model in stages to determine whether they significantly impact the risk of an outcome (Bewick et al., 2004). Similar to the logistic regression analyses, the following variables were entered via three separate stages: male gender (yes/no), Black race (yes/no), age, number of pre-detention arrests, number of charges upon detention entry, charge severity (1 to 5), length of detention stay, violent offender (yes/no), conduct-related disorder (yes/no), non-conduct mental disorder (yes/no), substance-related disorder (yes/no), pre-detention outpatient treatment (yes/no), and pre-detention non-outpatient treatment (yes/no). In addition, being re-

detained/incarcerated (yes/no) was included as a criminal history variable in stage two. Since this event occurred after release from detention and possibly after treatment

utilization, the variable was not included as a predictor in the logistic regression analyses. However, Cox proportional hazards regression models are able to control for timing effects by treating such variables as time-dependent, in which the value of the variable is expected to change (i.e., from no [0] to yes [1]) within the same time frame as the

occurrence of the outcome (Corning & Malofeeva, 2004). The model handles time- dependent variables by excluding participants via pairwise deletion who experience the independent variable after the dependent variable (i.e., re-detained after treatment utilization), while still retaining participants for the other components of the Cox regression analyses pertaining to the other independent variables (i.e., hazard ratios for independent variables like age, race, charge severity) (Corning & Malofeeva, 2004).

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Similar to logistic regression analyses, additional analyses were conducted to examine differences between DAs within cohort one versus cohort two. Analyses for cohort one included the same predictors; analyses for cohort two included the addition of RAI scores in stage two and MAYSI-2 positive screen (yes/no) in stage three. Several goodness-of-fit statistics were examined to determine model fit, including -2 Log

Likelihood and chi-square tests (Corning & Malofeeva, 2004). Finally, the hazard ratios, standard errors, and significant values for each predictor variable were calculated to identify significant variables (p ≤ .05) associated main outcomes. Hazard ratios are interpreted like odds ratio, with the exception that hazard ratios indicate the risk of an outcome at any time during the 14-year follow-up period for one group compared to another group, whereas odds ratios indicate the likelihood of an outcome by the endpoint of a follow-up period (Bewick et al., 2004). Hazard ratios are considered to remain constant over time (Corning & Malofeeva, 2004), so that the risk of an outcome like dropping out of treatment is the same within two years of detention release as it is within ten years of detention release. All data analyses were conducted using the software program SPSS0-Version 22.0 and all study procedures were approved by the institutional review board at Indiana University-Purdue University Indianapolis.