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Health Services Utilization by Individuals with Substance Abuse and Mental Disorders |
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Sarah Q. Duffy, Ph.D.
The Treatment Episode Data Set (TEDS) is a compilation of admissions data that State substance abuse treatment agencies collect from substance abuse treatment providers. States use these data to monitor their treatment systems. The Substance Abuse and Mental Health Services Administration (SAMHSA), which administers the Federal Government's Substance Abuse Prevention and Treatment (SAPT) block grant program, requests that States send a minimum dataset consisting of commonly defined variables on all clients admitted to treatment facilities that accept public funds earmarked for substance abuse treatment, including funds from the SAPT block grant.
Each State, however, sets its own requirements on the types of providers that must report. Some States' requirements exactly match what SAMHSA requests. Other States provide information only on admissions that are paid with public funds. Still other States require data from all licensed providers, whether for-profit or nonprofit, and whether or not they accept public funds earmarked for substance abuse treatment. Other States' requirements fall between those extremes. In some States, providers that are not required to report do so voluntarily. States typically send all of the records they collect to SAMHSA, which compiles them into TEDS.
Because admission to facilities that do or do not accept earmarked funds is unlikely to be random, results from analyses of admissions data solely from such facilities may be subject to selection bias. This chapter presents the results of an investigation into whether or not estimates from TEDS data appear to be subject to selection bias. If selection bias occurs, it may be important for States to collect data on all clients from all facilities, not just those that receive earmarked funds, to fully understand the publicly funded treatment system. If such selection bias does not occur, SAMHSA and the States can have greater confidence in analytic results using TEDS data as they are currently collected.
The substance abuse treatment system has been characterized as having two tiers (Institute of Medicine [IOM], 1990; Pauly, 1991; Wheeler & Nahra, 2000). One tier serves clients who are wealthy or insured and consists of privately run and, in many cases, for-profit firms. Providers in this tier tend to be more likely to provide care in inpatient settings, not to accept earmarked funds, and to have excess capacity. Providers in the other tier serve those who have no insurance coverage for these disorders, as well as those who cannot pay the full cost of their care, if they can pay anything at all. This tier consists of publicly or privately owned, largely nonprofit providers that accept earmarked funds and that tend to have excess demand for care.
Studies that compare or describe substance abuse treatment clients by the characteristics of the facilities to which they have been admitted, however, typically have focused on differences in facility ownership status, whether the provider is for-profit, private nonprofit, or government-owned, rather than on funding sources (Hays, Farabee, & Patel, 1999; Wheeler, Fadel, & D'Aunno, 1992; Wheeler & Nahra, 2000). Dayhoff, Pope, and Huber (1993) noted that although ownership and financing are related, they are not identical. Some private, for-profit substance abuse treatment facilities accept earmarked funds, and some government-run facilities accept private insurance. Still, findings from these studies provide evidence that there are real differences in clients based on facility ownership status, which may translate to differences based on program funding sources. Most recently, Wheeler and Nahra (2000) reported differences in variables, such as primary substance of abuse, expected source of payment, and whether or not clients pay a reduced fee.
Based on these findings of differences in clients by facility ownership status, there is reason to believe that clients in facilities receiving earmarked funding may differ in important ways from clients in facilities that do not. This raises two questions about the applicability of the inferences drawn from data from only facilities that receive earmarked funding. First, if a State only requires facilities that receive earmarked funding to report data, can the State use those data to get a good picture of the clients in treatment in that State? Second, is there a selection effect that biases coefficients estimated using data only on facilities that receive earmarked funding, so the results do not even apply to that population? To examine these issues, we first present a simple model of how selection bias may occur in analyses using data from TEDS. Then we analyze TEDS data from two States that collect sufficient data from both types of facilities to explore the effects on inferences and predictions based on data from only those who are admitted to facilities that receive earmarked funds. To focus the discussion on the estimation issues, we do not identify by name the two States whose data we use in the analysis.
Selection bias can appear in coefficients estimated using data from nonrandomly selected samples, such as the samples from the States that require reporting only by facilities that receive earmarked funds. In the substance abuse treatment field, such effects have been found, for example, in estimates of the effectiveness of Alcoholics Anonymous (AA), either as a stand-alone treatment (Humphreys, Phibbs, & Moos, 1996) or aftercare (Fortney, Booth, Zhang, Humphrey, & Weisman, 1998). As an example of how this might occur in admissions data, consider the following model along the lines of one described by O'Higgins (1994).
Suppose we are interested in estimating the effect of various client characteristics on the probability of admission to an inpatient substance abuse treatment setting, such as a hospital or long- or short-term residential facility, to explore whether treatment resources are being used according to current thinking on appropriate treatment setting. Suppose further that we begin with a single equation (univariate) probit model. Assume that the variables in the model include a dummy variable (y) indicating whether or not the admission was to a facility that accepted earmarked funds. This would lead to the following model:
D (1)
where
e* = a latent variable that represents the individual's demand for treatment intensity (if it is positive, the individual chooses inpatient treatment; otherwise, the individual chooses outpatient treatment);
y = a dummy variable set equal to 1 when the client is admitted to a treatment facility that accepts earmarked funds and 0 otherwise;
X = a vector of individual characteristics;
,
= parameters to be estimated; and
= a normally distributed error term with variance normalized (without loss of generality) to 1.
The probability that an individual is admitted to inpatient substance abuse treatment, then, is
D (2)
where e = an observed dummy variable that equals 1 if the client was admitted to an inpatient facility (e* > 0) and 0 otherwise. This leads to the probit likelihood function,
D (3)
where 
is the normal distribution function.
But suppose that admission to facilities across funding sources is not random. Suppose that individuals admitted to facilities that receive earmarked funds differ from individuals admitted to other facilities on some uncollected variable that affects both the facility and treatment choices. An example might be treatment readiness. Suppose that clients who enter facilities that accept earmarked funds are, on average, more "ready" for treatment than those who enter programs that do not. Then those in a facility that accepts earmarked funds might have been less likely to be admitted to inpatient treatment, according to the American Society of Addiction Medicine's Patient Placement Criteria (ASAM, 1991), even if they had not chosen a facility that accepted earmarked funds. A bias exists, in this example, because the parameter (), which is the estimated effect of having sought treatment in a facility that accepts earmarked funds on the probability of being admitted to inpatient treatment, will include the unobserved factors influencing the choice of treatment based both on funding type and treatment intensity.
The more general problem, of which the above example is one possible cause, is that may be correlated with the variables on the right-hand side of the equation. To illustrate, assume that y and in equation (2) are correlated. Assume that the choice of entering a facility that accepts earmarked funds may itself be thought of as a latent variable. We can model this as
D (4)
where
y* = an underlying continuous variable measuring some characteristic of the client's perception of treatment facilities, such as quality, convenience, location, or types of clients, that is related to program financing;
Z = a vector of client characteristics determining y*; and
= an error term that is distributed normally with a variance normalized to 1.
Let y be a dummy variable that equals 1 if y* > 0 and 0 otherwise. The probability that the individual would choose a facility that accepts public funding would be
D (5)
If and are correlated, meaning their correlation, 
, does not equal 0, then and y are correlated [E( | y) 
0]. The estimate of in equation (3) will be biased. To obtain unbiased estimates, alternative methods would have to be employed.
If the correlated error terms are individually normally distributed, then the model can be estimated consistently using a bivariate probit technique. The joint probability that the individual chooses a facility that receives public funding and is admitted to inpatient treatment is
D (6)
where 
(·) and (·) are the standardized bivariate normal density and distribution functions, respectively. The bivariate probit estimates the effect of client characteristics on the joint determination of admission to facilities that accept earmarked funds and inpatient treatment.
The conditional probability that the individual is admitted to inpatient treatment, given that he or she is admitted to a facility that accepts earmarked funds, then, is
D (7)
The model is identified (i.e., the estimates it provides will be unique) as long as Z, the vector of explanatory variables in the earmarked funding equation, contains at least one independent variable not in X, the vector in the inpatient/outpatient (IP/OP) equation (O'Higgins, 1994).
We first conducted preliminary analyses to provide evidence as to whether or not selectivity may be a problem in the TEDS data. There are two econometric issues. The first is the stability of coefficient estimates between the models run on clients from facilities with different funding sources. To address this issue, we ran separate IP/OP probits on the samples from facilities that received earmarked funds and those in facilities that did not. We used standard likelihood ratio (LR) tests to determine whether the differences in the coefficients were significant at conventional levels (Greene, 2000).1 The second econometric issue is the correlation between the unobservable factors affecting the IP/OP decision and the unobservable factors affecting the facility choice. To address this second issue, we estimated a variant of the bivariate probit model called the "seemingly unrelated probit" (Stata Corporation, 2001). In this model, both the facility and the IP/OP decisions depend on the same set of independent variables, and the correlation between the two error terms is estimated as an auxiliary parameter. By modeling the correlation between the two decisions, we provide evidence on the significance and direction of the correlation between the two decisions. The advantage of the seemingly unrelated probit over the bivariate probit described above is that the seemingly unrelated probit is identified by distributional assumptions alone. We can investigate whether or not the correlation, , is significantly different from zero, without making a priori identifying restrictions, as would be preferable when using the standard bivariate probit (Powell, Czart Ciecierski, Chaloupka, & Wechsler, 2002). We report the results of these preliminary investigations and of our final models in the following section.
We used data from the 1996 TEDS, which is maintained by SAMHSA's Office of Applied Studies (OAS, 1998; also see Chapter 4 in the present compendium). We used data on adult males with alcohol as a primary substance of abuse from two States that collect data both from both types of facilities. We refer to these States as "State A" and "State B."
We used two methods to determine which facilities received earmarked funding. First, we identified facilities in the TEDS file that reported to another OAS data file, the Uniform Facility Data Set (UFDS). UFDS data come from a survey of facility administrators that collects information on a variety of facility characteristics, including information on ownership and funding sources, such as whether they accept earmarked funds (OAS, 1997). Using this method, we were able to identify funding status for 88 percent of the facilities and 93 percent of the admissions in State A and 74 percent of both the facilities and admissions in State B. Second, for those facilities that did not report funding information to UFDS, we used expected payer information from the TEDS files to identify which facilities received earmarked funds and which did not. Unfortunately, this latter method is not exact, as the field in which earmarked funding is reported, "other government funds," also includes funding from other government sources, such as the Department of Veterans Affairs (VA) and CHAMPUS.2 However, we expect the proportions of those payment sources to be small enough not to affect the findings materially.
Seemingly Unrelated Probit Specification
As mentioned earlier, the seemingly unrelated probit model does not require exclusion restrictions to provide meaningful estimates, particularly of . Based on the model developed in earlier work (see Chapter 4), we include several variables in both the IP/OP and earmarked funding equations measuring client characteristics at the time of admission to explain these decisions. Measures of client severity include a set of dummy variables indicating (a) frequency of use (daily use, use three to six times in the past week, use one to two times in the past week, and use one to three times in the past month, with no use in the past month as the reference category), (b) intoxication before age 15, (c) secondary substance use (marijuana/hashish, cocaine, and other, with no secondary substance use as the reference category), (d) one or two prior treatments (with no prior treatment as the reference category), (e) co-occurring mental disorders, and (f) homelessness.
We also include socioeconomic characteristics in the form of dummy variables indicating (a) part-time or full-time employment (not employed as the reference cell), (b) the client's race/ethnicity (Hispanic, non-Hispanic white, and non-Hispanic black, with "other" as the reference category), (c) marital status, and (d) education status (no high school, which equals 1 if the client did not complete high school and 0 otherwise, and high school, which equals 1 if the client completed high school, with some college as the reference category). We include season of admission variables (summer, fall, winter, with spring as the reference cell) to capture differences among seasons, due to such things as the weather or the client's obligations, in a client's probability of entering inpatient treatment. We include indicator variables for referral source (self, alcohol or drug abuse services provider, other health care provider, other sector provider, with criminal justice system as the reference cell) and expected payer (self-pay, Medicare, Medicaid, private, other [e.g., worker's compensation], and other government funding/no charge as the reference category) to control for any differences that might be caused by these factors. Government funding and no charge are combined in the reference category because no charge is a relatively small category, especially in State A, and because we believe clients who are not charged likely are more similar to those who receive government funding for their care than those who have insurance coverage that pays for care.
Bivariate Probit
Although it also is technically acceptable to rely on functional form to identify the bivariate probit (Greene, 2000), we follow Powell et al. (2002) in choosing to impose exclusion restrictions to increase our confidence in the model. Our bivariate probit model is identical to our seemingly unrelated probit model except that, in addition to including a dummy variable in the IP/OP equation identifying whether or not the admission was to a facility that received earmarked funding, we exclude the education variables from the IP/OP equation. This specification passed standard overidentification and instrument validity tests applied to a two-stage least squares version of the model (Davidson & MacKinnon, 1993), following Powell et al. (2002). However, although the education variables were highly significant in the earmarked funding equation for State B, they were not significant in the earmarked funding equation for State A. Because the excluded variables should be correlated with the dependent variable in the earmarked funding equation to ensure consistent estimates, and given that we had no other good candidates for exclusion, we present the bivariate probit results only for State B.
Descriptive Statistics
Table 8.1 shows that, in these two States, there were several differences between clients who entered facilities that accepted earmarked funds compared with those who entered other facilities, and that, for some variables, the differences varied by State. For example, in State A, clients admitted to facilities that accepted earmarked funds were significantly less likely to be admitted to inpatient treatment, while in State B they were significantly more likely to be admitted to inpatient treatment. In State B, clients admitted to facilities that accepted earmarked funds were more likely to use alcohol daily at admission than were those in other facilities, while in State A, the opposite was true. In State B, clients in programs that accepted earmarked funds were more likely to have first used alcohol prior to age 15, while in State A the difference between clients admitted to different types of facilities was insignificant. However, in both States, clients admitted to facilities that received earmarked funds were more likely to have a secondary substance of abuse, less likely to have co-occurring mental disorders, and more likely to have had two or more prior treatment episodes than were clients admitted to facilities that did not accept earmarked funds.
Differences across facility funding source in demographic and socioeconomic variables were more similar between the two States. In both States, clients admitted to facilities that received earmarked funds were younger, less likely to be employed, less likely to be married, less likely to have any postsecondary education, and less likely to have had private insurance pay for their substance abuse treatment. The only major difference between the two States in socioeconomic variables was in the race/ethnicity variable. In State B, clients in facilities that received earmarked funds were less likely to be white than those in other facilities, while in State A the proportions were approximately the same.
| Variable | State A | State B | ||
|---|---|---|---|---|
| Earmarked Funds (n = 15,317) |
No Earmarked Funds (n = 2,274) |
Earmarked Funds (n = 7,560) |
No Earmarked Funds (n = 2,854) |
|
| Percent Inpatient* | 0.12 | 0.19 | 0.23 | 0.18 |
| Referral Source** | ||||
| Self | 0.16 | 0.27 | 0.19 | 0.19 |
| Alcohol/drug treatment provider | 0.07 | 0.11 | 0.21 | 0.06 |
| Other health care provider | 0.06 | 0.12 | 0.10 | 0.11 |
| Other sector | 0.04 | 0.12 | 0.08 | 0.06 |
| Criminal justice | 0.67 | 0.38 | 0.52 | 0.58 |
| Frequency of Use** | ||||
| None | 0.41 | 0.26 | 0.23 | 0.19 |
| 1–3 times in past month | 0.24 | 0.14 | 0.11 | 0.14 |
| 1–2 times in past week | 0.12 | 0.14 | 0.17 | 0.24 |
| 3–6 times in past week | 0.10 | 0.17 | 0.14 | 0.14 |
| Daily | 0.13 | 0.30 | 0.35 | 0.29 |
| Used Alcohol Prior to Age 15*** | 0.34 | 0.36 | 0.35 | 0.31 |
| Secondary Substance** | ||||
| None | 0.58 | 0.66 | 0.56 | 0.65 |
| Marijuana | 0.31 | 0.23 | 0.18 | 0.15 |
| Cocaine/crack | 0.03 | 0.05 | 0.20 | 0.15 |
| Other | 0.07 | 0.06 | 0.06 | 0.05 |
| Prior Treatment Episode** | ||||
| None | 0.41 | 0.44 | 0.50 | 0.52 |
| One | 0.29 | 0.30 | 0.25 | 0.26 |
| Two or more | 0.30 | 0.26 | 0.26 | 0.22 |
| Mental Disorder* | 0.15 | 0.21 | 0.07 | 0.13 |
| Homeless | 0.01 | 0.02 | 0.05 | 0.05 |
| Age* | 33.84 | 37.32 | 35.87 | 36.89 |
| Employed* | 0.64 | 0.70 | 0.53 | 0.64 |
| Married* | 0.33 | 0.40 | 0.25 | 0.27 |
| Education** | ||||
| No high school | 0.21 | 0.17 | 0.28 | 0.23 |
| High school | 0.57 | 0.55 | 0.51 | 0.49 |
| Postsecondary | 0.22 | 0.28 | 0.21 | 0.29 |
| Race/Ethnicity** | ||||
| Non-Hispanic white | 0.90 | 0.91 | 0.67 | 0.74 |
| Non-Hispanic black | 0.04 | 0.05 | 0.20 | 0.17 |
| Hispanic | 0.04 | 0.03 | 0.12 | 0.07 |
| Other | 0.12 | 0.14 | 0.01 | 0.02 |
| Season of Admission**** | ||||
| Winter | 0.30 | 0.29 | 0.26 | 0.25 |
| Spring | 0.32 | 0.28 | 0.26 | 0.27 |
| Summer | 0.19 | 0.21 | 0.25 | 0.26 |
| Fall | 0.19 | 0.22 | 0.23 | 0.22 |
| Payment Source** | ||||
| Self | 0.06 | 0.09 | 0.29 | 0.41 |
| Private insurance | 0.11 | 0.49 | 0.17 | 0.23 |
| Medicare | 0.01 | 0.06 | 0.03 | 0.04 |
| Medicaid | 0.05 | 0.05 | 0.03 | 0.06 |
| Other government and no charge | 0.76 | 0.30 | 0.44 | 0.24 |
| Other | 0.00 | 0.02 | 0.05 | 0.03 |
| *Differences by funding source significant at better than the 5 percent level for both States. **Differences in distributions significant at better than the 5 percent level for both States. ***Difference significant at better than the 5 percent level for State B only. ****Difference significant at better than the 5 percent level for State A only. Source: SAMHSA, Office of Applied Studies, Treatment Episode Data Set, 1996. |
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Multivariate Analyses
Table 8.2 displays, for each State, the marginal effects3 and standard errors for three equations: Model 1, univariate probit IP/OP model estimated on observations from programs that received earmarked funds; Model 2, a univariate probit IP/OP model estimated on observations from programs that did not receive earmarked funds; and Model 3, a seemingly unrelated (SUR) probit of the IP/OP and earmarked funding equations. In addition, Table 8.2 displays results from the bivariate probit model (Model 4) for State B.
Comparing Models 1 and 2 in Table 8.2 shows that, for both States, there are many differences in magnitude and significance levels of the effects of client characteristics on the probability of inpatient admission across facility funding type. Consider, for example, the referral source variables. In State A, self-referred clients in the earmarked funding sample were more likely to be admitted to inpatient treatment than those in the reference cell (those referred by the criminal justice system). In contrast, self-referred individuals in the non-earmarked funding sample were no more or less likely to be admitted to inpatient treatment than those referred by the criminal justice system. In State B, although self-referred clients were significantly more likely to be admitted to inpatient treatment than those referred by the criminal justice system, the marginal effect in the earmarked funding sample was more than twice as large as that in the other sample. In both States, those referred by alcohol or drug abuse treatment providers were more likely to be admitted to inpatient treatment in both samples, but the magnitude of the marginal effect differed. In State A, the effect was larger among those admitted to facilities that did not receive earmarked funds, while in State B, the effect was larger among those who were admitted to facilities that did not receive earmarked funds.
As another example, consider the effect of having a co-occurring mental disorder. In State A, having a co-occurring mental disorder had a very small, only marginally significant effect on inpatient admission in facilities that received earmarked funds. It had a much larger and more strongly significant effect among those in facilities that received no earmarked funds. In State B, having a mental disorder was positively associated with inpatient admission in both types of facilities, but the effect was almost 3 times as large in facilities that receive earmarked funds compared with those that did not. The likelihood ratio test provided support for what is apparent from casual observation: The relationship between the covariates and the IP/OP decision is influenced by the facility choice decision.4 Therefore, a single model run on the pooled sample would not be appropriate.
Table 8.2 also displays the seemingly unrelated results (SUR) for both States. As suspected, the 's in both equations were statistically significantly different from zero. However, they were of opposite signs. The negative estimated value of in State A suggests that the unobserved characteristics that led to entry into a facility that received earmarked funds made it less likely that an individual would be admitted to inpatient treatment. In State B, the positive estimated value of suggests that the unobserved characteristics that led to entry into a facility that received earmarked funds made it more likely that the individual would be admitted to inpatient treatment. The results from these preliminary analyses suggest that a bivariate probit analysis jointly estimating the facility and treatment location choices would be appropriate.
| State A | State B | ||||||
|---|---|---|---|---|---|---|---|
| Model 1 Univariate Probit IP/OP Model Obs. from Facilities w/Earmarked Funds (standard error) |
Model 2 Univariate Probit IP/OP Model Obs. from Facilities w/o Earmarked Funds (standard error) |
Model 3 SUR Probit IP/OP and Earmarked Funds, Full Sample (standard error) |
Model 1 Univariate Probit IP/OP Model Obs. from Facilities w/Earmarked Funds (standard error) |
Model 2 Univariate Probit IP/OP Model Obs. from Facilities w/o Earmarked Funds (standard error) |
Model 3 SUR Probit IP/OP and Earmarked Funds, Full Sample (standard error) |
Model 4 Bivariate Probit, Full Sample (standard error) |
|
| Number of Observations | 15,317 | 2,274 | 17,591 | 7,560 | 2,854 | 10,414 | 10,414 |
| Referral Status | |||||||
| Self-referred | 0.017*** | 0.011 | -0.016*** | 0.121*** | 0.056*** | 0.133*** | 0.178*** |
| (0.006) | (0.021) | (0.005) | (0.012) | (0.011) | (0.010) | (0.014) | |
| Alcohol/drug abuse treatment provider |
0.107*** | 0.151*** | 0.116*** | 0.213*** | 0.026*** | 0.176*** | 0.300*** |
| (0.007) | (0.025) | (0.007) | (0.014) | (0.009) | (0.012) | (0.020) | |
| Other health care provider | 0.033*** | 0.055** | 0.037*** | 0.121*** | 0.039*** | 0.114*** | 0.161*** |
| (0.008) | (0.025) | (0.007) | (0.015) | (0.009) | (0.012) | (0.018) | |
| School, employer, and other community |
-0.035*** | -0.035 | -0.035*** | 0.037** | 0.010 | 0.03** | 0.076*** |
| (0.013) | (0.029) | (0.006) | (0.017) | (0.009) | (0.013) | (0.019) | |
| Drug Use in the Month Prior to Admission | |||||||
| 0.018*** | 0.210*** | 0.033*** | -0.077*** | 0.035** | -0.055*** | ||
| (0.006) | (0.027) | (0.006) | (0.022) | (0.014) | (0.019) | (0.017) | |
| 1–2 times in the past week | 0.064*** | 0.163*** | 0.071*** | -0.035** | 0.035*** | -0.022 | -0.042*** |
| (0.007) | (0.030) | (0.007) | (0.018) | (0.013) | (0.019) | (0.015) | |
| 3–6 times in the past week | 0.121*** | 0.230*** | 0.128*** | 0.086*** | 0.044*** | 0.073*** | 0.075*** |
| (0.007) | (0.028) | (0.002) | (0.015) | (0.013) | (0.013) | (0.017) | |
| Daily use | 0.179*** | 0.298*** | 0.187*** | 0.159*** | 0.083*** | 0.164*** | 0.181*** |
| (0.007) | (0.025) | (0.006) | (0.013) | (0.017) | (0.012) | (0.015) | |
| Used Alcohol Prior to Age 15 | 0.016*** | -0.026 | 0.010** | 0.005 | -0.003 | 0.318 | 0.003 |
| (0.004) | (0.016) | (0.004) | (0.009) | (0.004) | (0.074) | (0.008) | |
| Secondary Drug of Abuse | |||||||
| Marijuana | -0.020*** | -0.011 | -0.020*** | -0.018 | 0.002 | -0.014 | -0.002 |
| (0.005) | (0.020) | (0.005) | (0.013) | (0.006) | (0.011) | (0.012) | |
| Cocaine | 0.028*** | 0.043 | 0.040*** | 0.061*** | 0.008 | 0.048*** | 0.059*** |
| (0.010) | (0.031) | (0.009) | (0.011) | (0.006) | (0.009) | (0.012) | |
| Other substance | 0.006 | 0.070** | 0.012 | 0.076*** | 0.019** | 0.064*** | 0.082*** |
| (0.008) | (0.031) | (0.008) | (0.016) | (0.009) | (0.013) | (0.019) | |
| Prior Number of Treatment Episodes | |||||||
| One prior treatment episode |
0.018*** | 0.005 | 0.017*** | 0.021* | 0.014** | 0.023** | 0.019* |
| (0.005) | (0.019) | (0.005) | (0.011) | (0.006) | (0.009) | (0.010) | |
| 2 or more prior treatment episodes |
0.030*** | 0.047** | 0.032*** | 0.000 | 0.009* | 0.009 | 0.021** |
| (0.005) | (0.019) | (0.005) | (0.011) | (0.006) | (0.009) | (0.011) | |
| Age | |||||||
| Age of respondent | 0.003** | 0.007** | 0.003*** | -0.003 | 0.000 | -0.003 | -0.003 |
| (0.001) | (0.003) | (0.001) | (0.002) | (0.001) | (0.002) | (0.002) | |
| Age-squared | 0.000*** | 0.000** | 0.000*** | 0.000 | 0.000 | 0.000 | 0.000 |
| (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | (0.000) | |
| Education/Employment | |||||||
| Non-high school graduate | 0.016** | 0.040* | 0.018*** | 0.028** | -0.002 | 0.023** | |
| (0.007) | (0.024) | (0.006) | (0.013) | (0.006) | (0.011) | ||
| High school graduate | 0.006 | 0.013 | 0.009 | 0.002 | 0.001 | 0.005 | |
| (0.005) | (0.018) | (0.005) | (0.012) | (0.005) | (0.009) | ||
| Employed prior to admission |
-0.075*** | -0.067*** | -0.076*** | -0.116*** | -0.017*** | -0.101*** | -0.129*** |
| (0.004) | (0.018) | (0.005) | (0.010) | (0.006) | (0.009) | (0.010) | |
| Race/Other Demographics | |||||||
| Non-Hispanic white | -0.054*** | -0.150*** | -0.064*** | -0.038 | 0.003 | -0.028 | -0.009 |
| (0.012) | (0.054) | (0.013) | (0.039) | (0.021) | (0.033) | (0.036) | |
| Non-Hispanic black | -0.034** | -0.185*** | -0.048*** | -0.083** | 0.002 | -0.065* | -0.039 |
| (0.015) | (0.063) | (0.015) | (0.040) | (0.021) | (0.033) | (0.033) | |
| Hispanic | -0.057*** | -0.122* | -0.062*** | -0.035 | 0.003 | -0.024 | 0.026 |
| (0.017) | (0.071) | (0.017) | (0.041) | (0.023) | (0.035) | (0.040) | |
| Homeless at Time of Admission | 0.120*** | 0.285*** | 0.143*** | 0.182*** | 0.101*** | 0.200*** | 0.126*** |
| (0.015) | (0.049) | (0.014) | (0.020) | (0.023) | (0.017) | (0.022) | |
| Existing Mental Disorder | 0.009* | 0.061*** | -0.015*** | 0.147*** | 0.048*** | 0.158*** | 0.101*** |
| (0.005) | (0.018) | (0.005) | (0.015) | (0.011) | (0.012) | (0.016) | |
| Married | -0.031*** | -0.051*** | -0.033** | -0.009 | -0.010* | 0.014 | -0.012 |
| (0.005) | (0.016) | (0.004) | (0.011) | (0.005) | (0.009) | (0.010) | |
| Time of Admission | |||||||
| Summer | 0.017*** | -0.002 | 0.015*** | 0.028** | -0.009* | 0.012 | 0.016 |
| (0.006) | (0.021) | (0.006) | (0.012) | (0.006) | (0.010) | (0.011) | |
| Fall | 0.011* | -0.038* | 0.006 | 0.039*** | -0.030*** | 0.006 | 0.015 |
| (0.006) | (0.022) | (0.006) | (0.013) | (0.009) | (0.011) | (0.012) | |
| Winter | 0.019*** | 0.007 | 0.019*** | 0.028** | -0.012** | 0.003 | 0.008 |
| (0.005) | (0.020) | (0.005) | (0.012) | (0.006) | (0.011) | (0.011) | |
| Expected Form of Payment | |||||||
| Self-pay | 0.026*** | -0.153*** | 0.014 | -0.137*** | -0.040*** | -0.138*** | -0.172*** |
| (0.008) | (0.032) | (0.008) | (0.013) | (0.009) | (0.011) | (0.009) | |
| BCBS or other health insurance co-pay |
0.014** | -0.154*** | -0.011 | -0.038*** | 0.022*** | -0.009 | -0.071*** |
| (0.007) | (0.021) | (0.006) | (0.014) | (0.008) | (0.001) | (0.011) | |
| Medicare | 0.011 | -0.061* | 0.001 | -0.121*** | 0.035*** | -0.034* | -0.103*** |
| (0.016) | (0.033) | (0.013) | (0.027) | (0.012) | (0.021) | (0.013) | |
| Medicaid | -0.028*** | -0.057 | -0.027*** | -0.254*** | 0.017** | -0.106*** | -0.152*** |
| (0.009) | (0.035) | (0.008) | (0.033) | (0.009) | (0.021) | (0.009) | |
| Other payment or worker's compensation |
0.007 | -0.170** | -0.027 | 0.005 | -0.009 | -0.003 | -0.009 |
| (0.047) | (0.070) | (0.028) | (0.018) | (0.012) | (0.015) | (0.017) | |
| Publicly Funded Treatment | -0.494*** | ||||||
| (0.019) | |||||||
| Constant | -0.223*** | -0.298*** | -0.234*** | -0.178*** | -0.134*** | -0.196*** | |
| (0.024) | (0.093) | (0.024) | (0.061) | (0.039) | (0.051) | ||
|
-0.082*** | 0.10*** | 0.920*** | ||||
| (0.023) | (0.03) | (0.015) | |||||
| ***Significant at the 0.01 level. ** Significant at the 0.05 level. *Significant at the 0.10 level. BCBS = Blue Cross/Blue Shield. IP/OP = inpatient/outpatient. Obs. = observation. SUR = seemingly unrelated. Source: SAMHSA, Office of Applied Studies, Treatment Episode Data Set, 1996. |
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Bivariate Probit Results Compared with Univariate Probit Results
As mentioned earlier, we could specify the bivariate probit model only for State B because we could not satisfy the exclusion restriction in the State A equations. Table 8.2 reveals that in State B the bivariate probit estimate of suggests that the unobservables in the IP/OP equation were positively associated with those in the facility choice equation, as did the SUR probit equation, although the magnitude of the effect (0.92) was much larger.
For most variables, the bivariate probit (Model 4) estimates were similar in sign and level of significance to the univariate probit model estimates run on the sample of clients admitted to facilities with earmarked funds (Model 1), which is not surprising given the relative sizes of the earmarked-funding and no earmarked-funding samples. The magnitude of some of the marginal effects, however, did differ substantially across specifications. For example, although both specifications revealed that referral status was associated with inpatient treatment, those associations estimated using the bivariate probit model were much larger, ranging from 1.33 times for the other health care provider category to 2.05 times for the school, employer, and other community category than those estimated using the SUR probit. The marginal effect of homelessness at the time of admission, again positive and significant in both equations, was only 70 percent as large in the bivariate probit equation as in the univariate probit equation. Similarly, the presence of a co-occurring mental disorder was positive in both equations, but only 70 percent as large in the bivariate probit equation as it was in the univariate probit equation.
For other variables, substantive differences existed in the level of significance of the estimated coefficient. For example, having had two or more prior treatments increased the probability of inpatient admission in the bivariate probit model, but was insignificant in the univariate probit model. Conversely, non-Hispanic blacks were significantly less likely than those in the reference cell, other race, to be admitted to inpatient treatment according to the univariate probit, but were no more or less likely in the bivariate probit model. Finally, the effects of season of admission were significant in the univariate probit equation, but insignificant in the bivariate probit equation. The bivariate probit model also revealed that individuals admitted to facilities that received earmarked funding were less likely to be admitted to inpatient treatment, holding other factors constant.
Policy Simulations
Aside from providing substantively different marginal effects estimates, potentially leading to invalid inferences, these different specifications can affect the resulting predictions about the effect of changes in client characteristics on the probability of admission to inpatient treatment in facilities in the earmarked funding sector. To illustrate, we simulated the effects on the number of inpatient admissions to facilities that received earmarked funds of the following changes in client characteristics:
Table 8.3 displays the simulation results for Models 1 and 3 for State A, and Table 8.4 displays those from Models 1, 3, and 4 for State B.
| Change | Model 1 Univariate Probit, Earmarked Funding Sample | Model 3 SUR Probit, Full Sample |
|---|---|---|
| 10 percent increase in secondary cocaine | No change | 0.22% |
| 10 percent increase in unemployment | 2.15% | 1.5% |
| 10 percent decrease in homelessness | -1.00% | -3.23% |
| 10 percent increase in co-occurring mental disorders | 0.57% | No change |
| 10 percent increase in the number who paid for their own care | 0.29% | No change |
| SUR = seemingly unrelated. Source: SAMHSA, Office of Applied Studies, Treatment Episode Data Set, 1996. |
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In State A, Models 1 and 3 yielded several dissimilar predictions about the magnitudes of the effects of the changes. For example, Model 1, the univariate probit model based on only the sample of clients entering programs that received earmarked funds, suggested that a 10 percent decrease in the number of homeless clients would lead to a 1 percent decrease in the number of individuals entering inpatient treatment in the sector that received earmarked funds. The SUR probit (Model 3), however, which was estimated on all clients in the sample and allowed for a correlation among the IP/OP and facility choice equations, revealed that there would be a 3.2 percent decrease in the number of clients admitted to inpatient treatment in facilities that accepted earmarked funds. Similarly, according to the univariate probit model, a 10 percent increase in the number of clients that had cocaine as a secondary substance would result in no change in the number admitted to inpatient treatment. The SUR probit suggested that there would be a small increase of 0.22 percent. Increases in the number with a co-occurring mental disorder or those who would pay for their own care would appear to increase the number of clients admitted to inpatient treatment in facilities that received earmarked funds according to the univariate probit, but not according to the SUR probit model.
There were differences in the findings among the three State B models as well, as Table 8.4 reveals. For example, while all three models revealed that an increase in unemployment would increase the number of clients admitted to inpatient treatment in facilities that received earmarked funds, the increase estimated by the bivariate probit model, 2.52 percent, was substantially larger than the increase estimated by the univariate probit model and almost twice that estimated by the SUR probit model. Likewise, the effect of a 10 percent increase in the number of clients who paid for their own care was substantially larger in the bivariate probit model than in the other two models. A 10 percent increase in the number of clients with a co-occurring mental disorder, in contrast, had a much smaller estimated effect in the bivariate probit than in the other two models.
| Change | Model 1 Univariate Probit, Earmarked Funding Sample | Model 3 SUR Probit, Full Sample | Model 4 Bivariate Probit, Full Sample |
|---|---|---|---|
| 10 percent increase in secondary cocaine | 0.59% | 1.09% | 0.42% |
| 10 percent increase in unemployment | 1.51% | 1.33% | 2.52% |
| 10 percent decrease in homelessness | -0.59% | -1.33% | -0.58% |
| 10 percent increase in co-occurring mental disorders | 0.75% | 1.25% | 0.31% |
| 10 percent increase in the number who paid for their own care | -2.76% | -1.88% | -3.31% |
| SUR = seemingly unrelated. Source: SAMHSA, Office of Applied Studies, Treatment Episode Data Set, 1996. |
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This analysis suggests that the IP/OP choice and the choice of facility are not independent, at least in the two States studied here, and that selectivity bias is a problem that should be dealt with in analyses of admissions data. If this finding extends to other States, it suggests that estimates based on data from only those facilities that receive earmarked funds may not always lead to an accurate understanding of the substance abuse treatment problem that the State faces. Use of these data may result in a misunderstanding of the influences of various characteristics on treatment setting choice, as well inaccuracy in predictions for clients the States are trying to monitor—those in facilities that receive earmarked funding. Reliance on the univariate probit model in State B, for example, would lead one to believe that having two or more prior treatments was not associated with the probability of inpatient treatment in the sector that accepts earmarked funds, while the bivariate probit model suggested that it would increase that probability. Also in State B, the effect of unemployment on the probability of inpatient treatment was much smaller in the univariate probit model than in the bivariate probit model.
These findings provide an example of the value that States may derive from collecting data on all of the facilities that clients can attend, not just those that receive earmarked funding. Some States collect these data already. New York, for example, requires reporting of client data to the State as a condition of licensure, whether or not the facility accepts earmarked funds.5 Second, when conducting analyses, States may want to consider allowing for complicated relationships among the many factors that lead clients into substance abuse treatment. These steps would improve each State's understanding of their treatment systems and their ability to monitor their treatment systems effectively.
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1 We conducted the test by first estimating the equation separately on the sample of clients from facilities with public funding and on the sample of clients from facilities with no public funding to obtain the LRs. Then, summing these LRs, we got the unrestricted LR. Next, we estimated the equation on the pooled sample of clients from all facilities in our dataset to obtain the restricted LR. Finally, by subtracting the restricted and unrestricted LRs and multiplying by 2, we derived the LR statistic.
2 CHAMPUS stands for the Civilian Health and Medical Program for the Uniform Services. It provides health care in private facilities for dependents of military personnel on active duty or retired for reasons other than disability.
3 Marginal effects are the derivative of the estimated equation as a function of the independent variable of interest. They represent the change in the probability of inpatient admission due to a small change in the independent variable. In a standard linear ordinary least squares regression, the derivative is simply the estimated coefficient. In nonlinear models, such as the bivariate probit, the derivative is more complicated. See Greene (2000, p. 852).
4 The statistic was 174.02 for State A and 355.65 for State B, significant at better than the p = 0.001 level.
5 We did not include New York in this analysis because their data do not contain "expected source of payment," which is an important control variable in the model.
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