Effectiveness Of Rehabilitation Facilities

ABOUT: If someone has asthma, then a typical person might find it hard to ask

that asthmatic to stop using his/her inhaler because it of course aids in breathing. Certain medical professionals have even gone as far as to compare drug addiction to the dependency of someone who relies on an inhaler to breathe on the grounds that both drugs aim to relieve some sort of symptoms (recovery.org). This study was done to analyze the effectiveness of rehabilitation among substance abusers from three different perspectives. Sample data was pulled from UMASS’s statistical database and focuses on a group of 575 patients from two unknown rehab centers, from Hosmer and Lemeshow (2000) Applied Logistic Regression: Second Edition, dedicated to aids research.

VARIABLES: RESPONSE VARIABLES

◦ Remained Drug Free for 12 Months (DFREE); 1= Yes 0=No

◦ The Beck Test Depression score = beck *** (Higher= More Depressed); 0-54

PREDICTOR VARIABLES

◦ Age of patient (AGE)

◦ Drug Use History at Admission (IVHX); 1= never, 2=previous, 3= Recent

◦ Race of patient (RACE); 1=other, 0=white

◦ Number of prior drug treatments (NDRUGTX); 0-40

◦ Treatment Randomization (REAT); 1=long, 0=short

◦ Treatment Site (SITE); 1=A, 0=B

Figure 1Variable N Mean Std Dev Minimum Maximumage

beckivhxndrugtx

racereatsitedfre

e

575575575575575575575575

32.382608717.36742782.03478264.54260870.25217390.49739130.30434780.2556522

6.19314939.33296250.90035265.47542910.43463870.50042850.46053130.4366070

20.00000000

1.000000000000

56.000000054.00000003.0000000

40.00000001.00000001.00000001.00000001.0000000

Figure 2

dfree Frequency PercentCumulativeFrequency

CumulativePercent

0 428 74.43 428 74.43

1 147 25.57 575 100.00

Descriptives: The study was composed of three continuous variables and five categorical variables which were all binary except for one which fell more along the lines of a Likert scale. Minimum to maximums for the continuous variables age, beck and “ndrugtx” respectively: 20-56 {mean=32.38+-6.193}, 0-54 {mean=17.37+-9.33} and 0-40 {mean= 4.54+5.48}. The “ivhx” or Drug Use History at Admission ranged from 1-3 {mean=2.03+-.9}. All the remaining variables except for “id” ranged from 0-1 with race mean= .25+-.43, “reat” mean= .5+-.5, site mean=.3+-.46 and lastly drug free or not mean=.26+-.44. ***(1). From table above it is evident that the majority of the patients were surprisingly at a lower score on average indicating that they at the very least were not severely depressed, given there were a few exceptions. Drug history for the most part was in the middle of the two extremes of familiarity with illegal substances.7

Objectives: •Determine an equation to predict BECK (depression test) scores using a multiple regression test

•Find out whether the amount of time spent at the facility and which of the two facilities affect the odds of remaining drug free for 12 moths after rehabilitation using 2x2 Chi-Sq. Tests•Find out, using the amount of time spent at the facility, being at one of the two facilities, age and The Beck’s Depression Test score to see their effects on the odds of remaining drug-free for 12 months using Logistic Regression.

1) Determine an equation to predict BECK (depression test) scores using a multiple regression test ***(USED BACKWARDS SELECTION)

VariableParameter

EstimateStandard

Error Type II SS F Value Pr > FIntercept 18.36143 2.05505 6766.16553 79.83 <.0001age -0.14858 0.06598 429.84617 5.07 0.0247ivhx 1.87614 0.45384 1448.44092 17.09 <.0001

Pearson Correlation Coefficients, N = 575Prob > |r| under H0: Rho=0

age beck ivhx ndrugtx race reat site dfreeage 1.00000 -0.03705

0.37520.34004

<.00010.19752

<.00010.01393

0.7389-0.04465

0.2852-0.02868

0.49240.04945

0.2364beck -0.03705

0.37521.00000 0.14746

0.00040.05925

0.15590.00111

0.97880.00965

0.8175-0.08749

0.0360-0.03318

0.4271ivhx 0.34004

<.00010.14746

0.00041.00000 0.30821

<.0001-0.20498

<.0001-0.05393

0.1966-0.18103

<.0001-0.15118

0.0003ndrugtx 0.19752

<.00010.05925

0.15590.30821

<.00011.00000 -0.09859

0.0180-0.00203

0.9613-0.09808

0.0187-0.13027

0.0017race 0.01393

0.73890.00111

0.9788-0.20498

<.0001-0.09859

0.01801.00000 0.07912

0.0579-0.07947

0.05690.09117

0.0288reat -0.04465

0.28520.00965

0.8175-0.05393

0.1966-0.00203

0.96130.07912

0.05791.00000 -0.02301

0.58190.09475

0.0231site -0.02868

0.4924-0.08749

0.0360-0.18103

<.0001-0.09808

0.0187-0.07947

0.0569-0.02301

0.58191.00000 0.05425

0.1940dfree 0.04945

0.2364-0.03318

0.4271-0.15118

0.0003-0.13027

0.00170.09117

0.02880.09475

0.02310.05425

0.19401.00000

Root MSE 9.20633 R-Square 0.0303Dependent Mean 17.36743 Adj R-Sq 0.0270Coeff Var 53.00917

Source DFSum of

Squares Mean Square F Value Pr > FModel 3 26.4024713 8.8008238 11.45 <.0001Error 571 438.9018765 0.7686548 Corrected Total 574 465.3043478

•2) Find out, using the amount of time spent at the facility, being at one of the two facilities, age and The Beck’s Depression Test score to see their effects on the odds of remaining drug-free for 12 months using Logistic Regression.◦ A Logistic Regression test in which the event occurring would be for the

patient to remain drug-free for 12 months after their treatment and of course the non-event would be for the patient to relapse before the 12 month sobriety mark. At a 0.7 Probability cutoff level there is a corresponding 65.6 correct percentage, 78% sensitivity and 27.9 specificity.

Analysis of Maximum Likelihood Estimates

Parameter DF EstimateStandard

ErrorWald

Chi-Square Pr > ChiSqIntercept 1 1.9251 0.5711 11.3619 0.0007

age 1 -0.0199 0.0154 1.6763 0.1954

beck 1 0.00687 0.0105 0.4298 0.5121

site 1 -0.2721 0.2059 1.7470 0.1863

reat 1 -0.4569 0.1941 5.5431 0.0186

Odds Ratio Estimates and Wald Confidence IntervalsEffect Unit Estimate 95% Confidence Limitsage 1.0000 0.980 0.951 1.010beck 1.0000 1.007 0.986 1.028site 1.0000 0.762 0.509 1.140reat 1.0000 0.633 0.433 0.926

Hosmer and Lemeshow Goodness-of-Fit Test

Chi-Square DF Pr > ChiSq15.5261 8 0.0497

Conclusion: The predictor equation in which I used age and drug-use

history levels to estimate a Beck’s Test Depression score ranging from 0-54. Residuals look as they should ideally although the coefficient of determination, R-squared indicates that around 3.03% of the variation about the line could be explained by using age and past drug history to explain the depression test scores. Another test was ran on the same data using Logistic Regression to determine the odds of a patient remaining sober for 12 months after being released from rehab. Results indicated that the older one was the less likely they were to make it 12 months sober. Similarly, those who stayed at site A for the longer time period greatly decreased their odds of making it a year without drug abuse.

Limitations/Recommendations

While I was limited to only being able to utilize 3 continuous variables the overstock in categorical variables allowed for more odds-based tests. As a result the R-square value for my predictive equation model was low due to the lack of continuous variables.