CSAT Publications -- TAP 25, The Impact of Substance Abuse Treatment on Employment Outcomes Among AFDC Clients in Washington State

This appendix provides additional information regarding the multivariate analyses presented in the body of the report. The findings of these analyses were presented in Figures III-10 through III-13 in Chapter III. Shown in Tables A-1 through A-4 below are the estimated regression coefficients generated by each of the multivariate analyses, along with the 95 percent confidence intervals and p-values.

Two type of multivariate analyses were conducted: (1) logistic regression, and (2) ordinary least squares (OLS) regression. To examine the effect of treatment on the likelihood of becoming employed, logistic regression was used. The general estimation model for the logistic regression is shown below:

Logit Model:

Log [P_i ) (1 - P_i)] = " + $₁X_1i + $₂X_2i + ,_i where " is a constant term, X₁ is a variable denoting some treatment group (outpatient, inpatient or methadone treatment), X₂ is a vector of control variables and , is an error term. Figures III-10 and III-11 show the adjusted odds ratios generated from the $₁ logistic regression estimates. These estimates provide information about the likelihood of some employment outcome occurring holding other factors constant. The estimates generated are in the form of log odds and are exponentiated to obtain the estimated adjusted odds ratios (shown in the tables below).In addition to examining the effect of treatment on the likelihood of becoming employed, the study assessed the effect of treatment on earnings among those clients who became employed during the followup period (Figures III-12 and III-13). OLS regression was used to estimate the effect of treatment on the level of earnings. The general OLS model is shown below:

OLS Model:

Y _i = " + $₁X_1i + $₂X_2i + ,_i where " is a constant term, X₁ is a variable denoting some treatment group (outpatient, inpatient or methadone treatment), X₂ is a vector of control variables and , is an error term. Figure III-12 shows the $₁ OLS regression estimates. Figure III-13 presents the results of the interaction model constructed to estimate the effects of outpatient treatment for clients with differing amounts of time on AFDC prior to treatment. This model is the same as the model depicted above, except that it includes an interaction term. The estimated OLS coefficients indicate the difference in earnings between the treatment and comparison groups holding other factors constant.

A. Logistic Regression Estimates

Tables A-1 and A-2 below show the estimated odds ratios depicted in Figures III-10 and III-11, respectively. The effects of other independent (control) variables and the statistical properties of the models are also described.

Table A-1. Likelihood of Any Employment
Treatment Group	Adjusted Odds  Ratio	95% Confidence  Interval	P-Value (one-tailed test)
Intensive Inpatient	1.64	1.17 - 2.29	.001
Outpatient	1.26	1.03 - 1.53	.013
Methadone	1.50	1.01 - 2.27	.05

The -2LL values for the intensive inpatient, outpatient and methadone treatment logistic models were, respectively, 1614, 2478 and 467. The associated P² values were 229, 245 and 57. The significance levels for the models overall were < .001. There was no clear pattern of findings with regard to the effects of other variables on the odds of achieving any employment.

The inpatient and outpatient treatment models had greater statistical power than the methadone model due to the greater numbers of observations. In the inpatient model, years of education, baseline earnings, Asian ethnicity and male gender were positively associated (p < .05) with the odds of achieving employment in the followup period. Native Americans were less likely to obtain employment compared to whites. Clients who used needles as the mode of drug taking and clients receiving mental health treatment at time of treatment intake were also less likely (p < .05) to obtain employment.

In the outpatient model, older clients, Native Americans, clients with chronic disease and clients with previous outpatient treatment in the past 12 months were less likely (p < .05) to become employed during the followup period. Baseline earnings were a strong (positive) predictor of post-treatment employment. Asian clients were more likely than white clients to achieve employment.
The adjusted odds ratios, along with 95 percent confidence intervals and p-values, for Figure III-11 are presented in Table A-2. 

 The -2LL values for the intensive inpatient, outpatient and methadone treatment logistic models were, respectively, 1519, 2273 and 379. The associated P² values were 219, 335 and 49. The significance levels for the models overall were < .005. The same general pattern of effects as discussed above for the initial logistic regression analysis was observed for this analysis. Compared to white clients, Native American clients were less likely to achieve earnings of $1,500 or more in 1 of the 8 followup quarters, while Asian clients were more likely than white clients to obtain this level of employment. Higher baseline earnings and male gender were associatedwith a greater likelihood of achieving employment at the specified earnings level. Outpatient and inpatient clients who used needles as their mode of drug taking were less likely (p < .05) to achieve employment than clients who did not use needles.

B. OLS Regression Estimates

Tables A-3 and A-4 below show the OLS results depicted in Figures III-12 and III-13, respectively. 

The F statistics and adjusted R² for the three OLS models summarized in Table A-3 were as follows: Intensive Inpatient Treatment-F = 20.8 _(22,854), adjusted R² = .33; Outpatient Treatment-F = 24.0 _(22,1,147), adjusted R² = .30; and Methadone Treatment-F = 2.2 _(16,150), adjusted R² = .11. Among the control variables, baseline earnings was the strongest and most consistent predictor of post-treatment earnings. For every $1 in the pretreatment baseline period, clients earned from approximately $1.65 to $4.60 more in the followup period, other things equal. Years of education was also a strong and consistent predictor of post-treatment earnings. Other than these two variables there were no other control variables consistently associated with post-treatment earnings. In the inpatient treatment equation, needle use was associated (p = .03) with lower earnings. Variables representing race/ethnic group were not related to post-treatment earnings.The explanatory power of the outpatient treatment interaction model (Table A-4 and Figure III-13) was modest: F = 4.6_(24,1282), R² = .09. The estimated treatment, time-on-welfare, and interaction coefficients are shown in the Table A-4. 

Table A-4. Differences in Post-Treatment Aggregate Earnings Among Outpatient  Clients Having Different Amounts of Time on Welfare
Measure	Estimated  Coefficient	95% Confidence  Interval	P-Value (one-tailed test)
Outpatient Treatment	$2,378	$18 - $3,428	.004
Time on Welfare	-$968	-$1,918 - -$16	.041
Interaction Term	-$1,232	-$2,442 - -$22	.048

Few control variables were found to be associated with post-treatment earnings in the interaction model. Male gender was positively associated with earnings, as was years of education. Daily use of alcohol/drugs and previous mental health treatment were negatively associated with earnings.

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