ACORN Toolkit Case Mix Model

ACORN Toolkit Case Mix Model

Question: Are KP norms for change different from ACORN norms?

This document contains the SAS output for a series of GLM procedures modeling the Toolkit case mix model. In its simplest form, the model uses the GDS score at the first assessment for each episode of care to predict subsequent GDS scores.

The GLM to predict the final score in treatment was performed first using the first score to predict the final score in the episode, regardless of assessment count. The GLM used to predict scores at each session used the first GDS in the episode to predict the score at assessment number (up to 10 assessments). Separate GLM procedures were performed for each of the 3 classes of questionnaires: adults, youth/child self report, and youth/child caregiver report.

The output for each GLM procedure includes an estimate of the % pf variance explained (R-square) and the values of the slope and intercept for the linear model. (See Parameters: gds_assess_num1 = slope; intercept=intercept)

The first set of analyses utilized all available data in the Toolkit, in order to produce estimates bases on the largest sample possible. A second set of analyses utilizes KP data only. There were not a sufficient number of cases to calculate the slope and intercept for KP youth measures beyond assessment number 3.

Answer: The KP slope and intercept values at each assessment appear to differ from the results of combining all data in the toolkit. However, the sample sizes used to calculate the KP values are significantly smaller that than the sample as a whole. The raises the possibility that the differences observed are due to measurement error, and that as sample sizes increased the results would converge. This is evidenced by the slope and intercept values for all pre-post KP adults compared to the entire sample.

All Adults:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 11744

Number of Observations Used 11744

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 3466.598095 3466.598095 8273.46 <.0001

Error 11742 4919.923170 0.419002

Corrected Total 11743 8386.521265

R-Square Coeff Var Root MSE gds Mean

0.413354 37.09575 0.647304 1.744954

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 3466.598095 3466.598095 8273.46 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 3466.598095 3466.598095 8273.46 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.3966947661 0.01598102 24.82 <.0001

gds_assess_num1 0.6421021648 0.00705928 90.96 <.0001

All Youth/Child self report:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 1574

Number of Observations Used 1574

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 237.9712752 237.9712752 719.60 <.0001

Error 1572 519.8584068 0.3306987

Corrected Total 1573 757.8296820

R-Square Coeff Var Root MSE gds Mean

0.314017 47.94936 0.575064 1.199315

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 237.9712752 237.9712752 719.60 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 237.9712752 237.9712752 719.60 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.3012958204 0.03647980 8.26 <.0001

gds_assess_num1 0.5643439551 0.02103768 26.83 <.0001

All Youth/Child caregiver report:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 1314

Number of Observations Used 1314

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 152.6740023 152.6740023 484.12 <.0001

Error 1312 413.7540549 0.3153613

Corrected Total 1313 566.4280572

R-Square Coeff Var Root MSE gds Mean

0.269538 38.63692 0.561570 1.453455

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 152.6740023 152.6740023 484.12 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 152.6740023 152.6740023 484.12 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.5586676120 0.04351784 12.84 <.0001

gds_assess_num1 0.5223986740 0.02374235 22.00 <.0001

KP Adults:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 2768

Number of Observations Used 2768

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 728.150607 728.150607 1532.98 <.0001

Error 2766 1313.821268 0.474990

Corrected Total 2767 2041.971875

R-Square Coeff Var Root MSE gds Mean

0.356592 35.92319 0.689195 1.918523

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 728.1506070 728.1506070 1532.98 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 728.1506070 728.1506070 1532.98 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.4415406896 0.03993281 11.06 <.0001

gds_assess_num1 0.6326823590 0.01615910 39.15 <.0001

KP Youth/Child self report:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 69

Number of Observations Used 69

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 10.33401064 10.33401064 38.87 <.0001

Error 67 17.81325024 0.26586941

Corrected Total 68 28.14726088

R-Square Coeff Var Root MSE gds Mean

0.367141 50.18247 0.515625 1.027501

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 10.33401064 10.33401064 38.87 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 10.33401064 10.33401064 38.87 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.1629862448 0.15192636 1.07 0.2872

gds_assess_num1 0.6118775117 0.09814411 6.23 <.0001

KP Youth/Child caregiver report:

GDS_Assess_num1 predicts final GDS

The GLM Procedure

Number of Observations Read 116

Number of Observations Used 116

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 14.59927962 14.59927962 40.62 <.0001

Error 114 40.97291666 0.35941155

Corrected Total 115 55.57219627

R-Square Coeff Var Root MSE gds Mean

0.262708 41.93704 0.599509 1.429546

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 14.59927962 14.59927962 40.62 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 14.59927962 14.59927962 40.62 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.4246855619 0.16720265 2.54 0.0124

gds_assess_num1 0.5557871072 0.08720447 6.37 <.0001

All Adults:

GDS_Assess_num1 predicts GDS at Assess_num_2

The GLM Procedure

Number of Observations Read 12618

Number of Observations Used 12609

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 4580.773588 4580.773588 13514.1 <.0001

Error 12607 4273.298634 0.338962

Corrected Total 12608 8854.072223

R-Square Coeff Var Root MSE gds Mean

0.517363 31.22729 0.582205 1.864410

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 4580.773588 4580.773588 13514.1 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 4580.773588 4580.773588 13514.1 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.3745769316 0.01382483 27.09 <.0001

gds_assess_num1 0.7138676641 0.00614079 116.25 <.0001

All Youth/Child self report:

GDS_Assess_num1 predicts GDS at Assess_num_2

The GLM Procedure

Number of Observations Read 1519

Number of Observations Used 1519

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 349.0582245 349.0582245 1379.09 <.0001

Error 1517 383.9636082 0.2531072

Corrected Total 1518 733.0218327

R-Square Coeff Var Root MSE gds Mean

0.476191 37.17864 0.503098 1.353190

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 349.0582245 349.0582245 1379.09 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 349.0582245 349.0582245 1379.09 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.2423918265 0.03257801 7.44 <.0001

gds_assess_num1 0.6969447449 0.01876729 37.14 <.0001

All Youth/Child caregiver report:

GDS_Assess_num1 predicts GDS at Assess_num_2

The GLM Procedure

Number of Observations Read 1366

Number of Observations Used 1366

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 210.1673372 210.1673372 767.74 <.0001

Error 1364 373.3947364 0.2737498

Corrected Total 1365 583.5620736

R-Square Coeff Var Root MSE gds Mean

0.360146 33.41837 0.523211 1.565639

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 210.1673372 210.1673372 767.74 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 210.1673372 210.1673372 767.74 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.5470356604 0.03939352 13.89 <.0001

gds_assess_num1 0.5975697175 0.02156666 27.71 <.0001

All Adults:

GDS_Assess_num1 predicts GDS at Assess_num_3

The GLM Procedure

Number of Observations Read 7555

Number of Observations Used 7546

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 2629.205007 2629.205007 7276.66 <.0001

Error 7544 2725.799091 0.361320

Corrected Total 7545 5355.004098

R-Square Coeff Var Root MSE gds Mean

0.490981 34.03453 0.601099 1.766145

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 2629.205007 2629.205007 7276.66 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 2629.205007 2629.205007 7276.66 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.3509799084 0.01797508 19.53 <.0001

gds_assess_num1 0.6869858340 0.00805344 85.30 <.0001

All Youth/Child self report:

GDS_Assess_num1 predicts GDS at Assess_num_3

The GLM Procedure

Number of Observations Read 925

Number of Observations Used 925

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 181.9604976 181.9604976 646.73 <.0001

Error 923 259.6902589 0.2813546

Corrected Total 924 441.6507564

R-Square Coeff Var Root MSE gds Mean

0.412001 41.13781 0.530429 1.289394

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 181.9604976 181.9604976 646.73 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 181.9604976 181.9604976 646.73 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.2367440085 0.04491674 5.27 <.0001

gds_assess_num1 0.6503128502 0.02557177 25.43 <.0001

All Youth/Child caregiver report:

GDS_Assess_num1 predicts GDS at Assess_num_3

The GLM Procedure

Number of Observations Read 800

Number of Observations Used 800

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 113.3556219 113.3556219 362.33 <.0001

Error 798 249.6550332 0.3128509

Corrected Total 799 363.0106551

R-Square Coeff Var Root MSE gds Mean

0.312265 37.37641 0.559331 1.496481

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 113.3556219 113.3556219 362.33 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 113.3556219 113.3556219 362.33 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.4984638510 0.05603601 8.90 <.0001

gds_assess_num1 0.5769458960 0.03030974 19.03 <.0001

All Adults:

GDS_Assess_num1 predicts GDS at Assess_num_4

The GLM Procedure

Number of Observations Read 5138

Number of Observations Used 5129

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 1851.539946 1851.539946 4701.14 <.0001

Error 5127 2019.264890 0.393849

Corrected Total 5128 3870.804836

R-Square Coeff Var Root MSE gds Mean

0.478335 36.80025 0.627574 1.705353

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 1851.539946 1851.539946 4701.14 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 1851.539946 1851.539946 4701.14 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.3224056856 0.02199123 14.66 <.0001

gds_assess_num1 0.6833904550 0.00996707 68.56 <.0001

All Youth/Child self report:

GDS_Assess_num1 predicts GDS at Assess_num_4

The GLM Procedure

Number of Observations Read 619

Number of Observations Used 619

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 115.5155637 115.5155637 352.51 <.0001

Error 617 202.1849492 0.3276904

Corrected Total 618 317.7005128

R-Square Coeff Var Root MSE gds Mean

0.363599 46.07444 0.572442 1.242430

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 115.5155637 115.5155637 352.51 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 115.5155637 115.5155637 352.51 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.2294803973 0.05865231 3.91 0.0001

gds_assess_num1 0.6215350016 0.03310375 18.78 <.0001

The SAS System 12:21 Sunday, May 3, 2009 335

All Youth/Child caregiver report:

GDS_Assess_num1 predicts GDS at Assess_num_4

The GLM Procedure

Number of Observations Read 539

Number of Observations Used 539

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 62.8640268 62.8640268 226.91 <.0001

Error 537 148.7710733 0.2770411

Corrected Total 538 211.6351001

R-Square Coeff Var Root MSE gds Mean

0.297040 34.91949 0.526347 1.507315

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 62.86402684 62.86402684 226.91 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 62.86402684 62.86402684 226.91 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 0.5499490701 0.06747754 8.15 <.0001

gds_assess_num1 0.5384909083 0.03574781 15.06 <.0001

All Adults:

GDS_Assess_num1 predicts GDS at Assess_num_5

The GLM Procedure

Number of Observations Read 3766

Number of Observations Used 3761

The GLM Procedure

Dependent Variable: gds gds

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 1 1400.659949 1400.659949 3504.76 <.0001

Error 3759 1502.266063 0.399645

Corrected Total 3760 2902.926012

R-Square Coeff Var Root MSE gds Mean

0.482499 38.14030 0.632175 1.657498

Source DF Type I SS Mean Square F Value Pr > F

gds_assess_num1 1 1400.659949 1400.659949 3504.76 <.0001

Source DF Type III SS Mean Square F Value Pr > F

gds_assess_num1 1 1400.659949 1400.659949 3504.76 <.0001