Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 5: Assessing the Fit of the Model

page 150 Table 5.1 Observed (obs) and estimated expected (exp) frequencies within each decile of risk, defined by fitted value (prob.) for dfree = 1 and dfree = 0 using the fitted logistic regression model in Table 4.9.

NOTE: The values in the printout do not match those in the text exactly because Stata and SPSS use different methods of handling ties between values.

Get file='uis.sav'.

compute ndrgfp1=1/((ndrugtx+1)/10).
compute ndrgfp2=ndrgfp1*ln((ndrugtx+1)/10).
compute nage=ndrgfp1*age.
compute racesite=race*site.
execute.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
  /PRINT=GOODFIT.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	575	100.0
	Missing Cases	0	.0
	Total	575	100.0
Unselected Cases		0	.0
Total		575	100.0
a If weight is in effect, see classification table for the total number of cases.

**Dependent Variable Encoding**
Original Value	Internal Value
.00	0
1.00	1

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	1.00	147	0	.0
	Overall Percentage				74.4
a Constant is included in the model.
b The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.069	.096	124.967	1	.000	.343

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	1.406	1	.236
		NDRGFP1	6.074	1	.014
		NDRGFP2	4.115	1	.043
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		RACE	4.779	1	.029
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
		NAGE	5.573	1	.018
		RACESITE	.144	1	.705
	Overall Statistics		52.071	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	55.766	10	.000
	Block	55.766	10	.000
	Model	55.766	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	597.963	.092	.136

**Hosmer and Lemeshow Test**
Step	Chi-square	df	Sig.
1	4.419	8	.818

**Contingency Table for Hosmer and Lemeshow Test**
		DFREE = .00		DFREE = 1.00		Total
		Observed	Expected	Observed	Expected	Total
Step 1	1	54	53.900	4	4.100	58
	2	52	51.644	6	6.356	58
	3	51	49.425	7	8.575	58
	4	47	47.353	11	10.647	58
	5	42	45.235	16	12.765	58
	6	46	43.163	12	14.837	58
	7	40	40.357	18	17.643	58
	8	33	37.672	25	20.328	58
	9	37	34.282	22	24.718	59
	10	26	24.970	26	27.030	52

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	417	11	97.4
	DFREE	1.00	131	16	10.9
	Overall Percentage				75.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.117	.029	16.317	1	.000	1.124
	NDRGFP1	1.669	.407	16.804	1	.000	5.307
	NDRGFP2	.434	.117	13.762	1	.000	1.543
	IVHX2	-.635	.299	4.514	1	.034	.530
	IVHX3	-.705	.262	7.263	1	.007	.494
	RACE	.684	.264	6.708	1	.010	1.982
	TREAT	.435	.204	4.556	1	.033	1.545
	SITE	.516	.255	4.101	1	.043	1.676
	NAGE	-.015	.006	6.419	1	.011	.985
	RACESITE	-1.429	.530	7.280	1	.007	.239
	Constant	-6.844	1.219	31.504	1	.000	.001
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

page 157 Table 5.2 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.5.

NOTE: The above code gives this table (at step 1).

page 159 Table 5.3 Classification table based on the logistic regression . model in Table 4.9 using a cutpoint of 0.5, but all probabilities pi-hat < 0.5 are replaced with pi-hat = 0.05 and all probabilities pi-hat >= 0.50 are . replaced with pi-hat = 0.95.

NOTE: We were unable to reproduce this table.

page 160 Table 5.4 Classification table based on the logistic regression . model in Table 4.9 using a cutpoint of 0.5, but all probabilities pi-hat < 0.50 are replaced with pi-hat = 0.45 and all probabilities pi-hat >= 0.50 are replaced with pi-hat = 0.55.

NOTE: We were unable to reproduce this table.

page 161 Table 5.5 Classification table based on the logistic regression model in Table 4.9 using a cutpoint of 0.6.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
  /CRITERTIA CUT(.6).

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	575	100.0
	Missing Cases	0	.0
	Total	575	100.0
Unselected Cases		0	.0
Total		575	100.0
a If weight is in effect, see classification table for the total number of cases.

**Dependent Variable Encoding**
Original Value	Internal Value
.00	0
1.00	1

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	1.00	147	0	.0
	Overall Percentage				74.4
a Constant is included in the model.
b The cut value is .600

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.069	.096	124.967	1	.000	.343

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	1.406	1	.236
		NDRGFP1	6.074	1	.014
		NDRGFP2	4.115	1	.043
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		RACE	4.779	1	.029
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
		NAGE	5.573	1	.018
		RACESITE	.144	1	.705
	Overall Statistics		52.071	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	55.766	10	.000
	Block	55.766	10	.000
	Model	55.766	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	597.963	.092	.136

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	428	0	100.0
	DFREE	1.00	142	5	3.4
	Overall Percentage				75.3
a The cut value is .600

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.117	.029	16.317	1	.000	1.124
	NDRGFP1	1.669	.407	16.804	1	.000	5.307
	NDRGFP2	.434	.117	13.762	1	.000	1.543
	IVHX2	-.635	.299	4.514	1	.034	.530
	IVHX3	-.705	.262	7.263	1	.007	.494
	RACE	.684	.264	6.708	1	.010	1.982
	TREAT	.435	.204	4.556	1	.033	1.545
	SITE	.516	.255	4.101	1	.043	1.676
	NAGE	-.015	.006	6.419	1	.011	.985
	RACESITE	-1.429	.530	7.280	1	.007	.239
	Constant	-6.844	1.219	31.504	1	.000	.001
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

page 161 Table 5.6 Summary of sensitivity, specificity, and 1-specificity for classification tables based on the logistic regression model in Table 4.9 using a cutpoint of 0.05 to 0.60 in increments of 0.05.

NOTE: We were unable to reproduce this table.

page 162 Figure 5.1 Plot of sensitivity and specificity versus all . possible cutpoints in the UIS.

NOTE: We were unable to reproduce this graph.

page 163 Figure 5.2 Plot of sensitivity versus 1-specificity for all . possible cutpoints in the UIS. The resulting curve is called a ROC curve.

NOTE: We were unable to reproduce this graph.

page 171 Figure 5.3 Plot of leverage (h) versus the estimated logistic probability (pi-hat) for a hypothetical univariable logistic regression model.

NOTE: We cannot recreate this figure because we do not have the hypothetical data that were used.

page 172 Figure 5.4 Plot of the distance portion of leverage (b) versus the estimated logistic probability (pi-hat) for a hypothetical univariable logistic regression model.

NOTE: We cannot recreate this figure because we do not have the hypothetical data that were used.

page 177 Figure 5.5 Plot of delta-chi-square versus the estimated probability from the fitted model in Table 4.9, UIS J = 521 covariate patterns.

NOTE: We have skipped this for now.

page 178 Figure 5.6 Plot of delta-D versus the estimated probability from the fitted model in Table 4.9, UIS J = 521 covariate patterns.

NOTE: We have skipped this for now.

page 179 Figure 5.7 Plot of delta-beta-hat versus the estimated probability from the fitted model in Table 4.9, UIS J = 521 covariate patterns.

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
  /SAVE COOK PRED LEV.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	575	100.0
	Missing Cases	0	.0
	Total	575	100.0
Unselected Cases		0	.0
Total		575	100.0
a If weight is in effect, see classification table for the total number of cases.

**Dependent Variable Encoding**
Original Value	Internal Value
.00	0
1.00	1

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	1.00	147	0	.0
	Overall Percentage				74.4
a Constant is included in the model.
b The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.069	.096	124.967	1	.000	.343

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	1.406	1	.236
		NDRGFP1	6.074	1	.014
		NDRGFP2	4.115	1	.043
		IVHX2	.207	1	.649
		IVHX3	9.737	1	.002
		RACE	4.779	1	.029
		TREAT	5.163	1	.023
		SITE	1.692	1	.193
		NAGE	5.573	1	.018
		RACESITE	.144	1	.705
	Overall Statistics		52.071	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	55.766	10	.000
	Block	55.766	10	.000
	Model	55.766	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	597.963	.092	.136

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	417	11	97.4
	DFREE	1.00	131	16	10.9
	Overall Percentage				75.3
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.117	.029	16.317	1	.000	1.124
	NDRGFP1	1.669	.407	16.804	1	.000	5.307
	NDRGFP2	.434	.117	13.762	1	.000	1.543
	IVHX2	-.635	.299	4.514	1	.034	.530
	IVHX3	-.705	.262	7.263	1	.007	.494
	RACE	.684	.264	6.708	1	.010	1.982
	TREAT	.435	.204	4.556	1	.033	1.545
	SITE	.516	.255	4.101	1	.043	1.676
	NAGE	-.015	.006	6.419	1	.011	.985
	RACESITE	-1.429	.530	7.280	1	.007	.239
	Constant	-6.844	1.219	31.504	1	.000	.001
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

GRAPH
  /SCATTERPLOT(BIVAR)=pre_1 WITH coo_1.

page 180 Figure 5.8 Plot of delta-x-square versus the probability from the fitted model in Table 4.9 with size of the plotting symbol proportional to delta-beta-hat, UIS J = 521 covariate patterns.

NOTE: We have skipped this for now.

page 182 Table 5.8 Covariate values, observed outcome (yj), number (mj), estimated logistic probability (pi-hat), and the value of the four diagnostic statistics delta-beta-hat, delta-x-square, and leverage (h) for the four most. extreme covariate patterns (P#).

SORT CASES BY
  age (A) ndrgfp1 (A) ndrgfp2 (A) ivhx2 (A) ivhx3 (A) race (A) treat (A)
  site (A) nage (A) racesite (A) .
save outfile = 'd:uissort.sav'.

aggregate outfile=*
  /break=age ndrgfp1  ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
  /count=n.
compute covpat = $casenum.
save outfile = 'd:uiscovpat.sav'.

match files  /file='d:uissort.sav' /table='d:uiscovpat.sav'
   /by age ndrgfp1  ndrgfp2 ivhx2 ivhx3 race treat site nage racesite .
execute.

USE ALL.
COMPUTE filter_$=(covpat=31 or covpat=477 or covpat=105 or covpat=468).
VARIABLE LABEL filter_$ 'covpat=31 or covpat=477 or covpat=105 or covpat=468 '+
 '(FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FORMAT filter_$ (f1.0).
FILTER BY filter_$.
EXECUTE .

list covpat age ndrugtx ivhx race treat site count pre_1 coo_1 lev_1.

The variables are listed in the following order:

LINE   1: COVPAT AGE NDRUGTX IVHX RACE TREAT SITE

LINE   2: COUNT PRE_1 COO_1 LEV_1


  COVPAT:    31.00     24.00     20.00      2.00       .00       .00      1.00
   COUNT:       1      .03263      .27429      .00917

  COVPAT:   105.00     26.00       .00      1.00      1.00       .00       .00
   COUNT:       2      .40300      .05503      .03582

  COVPAT:   105.00     26.00       .00      1.00      1.00       .00       .00
   COUNT:       2      .40300      .05503      .03582

  COVPAT:   468.00     40.00       .00      3.00      1.00       .00       .00
   COUNT:       1      .16760      .22610      .04354

  COVPAT:   477.00     41.00       .00      3.00      1.00       .00       .00
   COUNT:       1      .16263      .25409      .04703

Number of cases read:  5    Number of cases listed:  5

page 183 Table 5.9 Estimated coefficients from all data, the percent change when the covariate pattern is deleted, and values of goodness-of-fit statistics for each model.

USE ALL.
COMPUTE filter_$=(covpat ~= 31 and covpat ~= 477 and covpat ~= 105 and covpat
  ~= 468).
VARIABLE LABEL filter_$ 'covpat ~= 31 and covpat ~= 477 and covpat ~= 105 and'+
 ' covpat ~= 468 (FILTER)'.
VALUE LABELS filter_$  0 'Not Selected' 1 'Selected'.
FORMAT filter_$ (f1.0).
FILTER BY filter_$.
EXECUTE .

NOTE: This code gives the value for C-hat. The code below gives the coefficients listed in the column labeled "all data".

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	570	100.0
	Missing Cases	0	.0
	Total	570	100.0
Unselected Cases		0	.0
Total		570	100.0
a If weight is in effect, see classification table for the total number of cases.

**Dependent Variable Encoding**
Original Value	Internal Value
.00	0
1.00	1

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	1.00	142	0	.0
	Overall Percentage				75.1
a Constant is included in the model.
b The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.103	.097	129.790	1	.000	.332

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	1.592	1	.207
		NDRGFP1	3.827	1	.050
		NDRGFP2	2.118	1	.146
		IVHX2	.222	1	.638
		IVHX3	9.886	1	.002
		RACE	3.123	1	.077
		TREAT	7.094	1	.008
		SITE	1.957	1	.162
		NAGE	3.288	1	.070
		RACESITE	.084	1	.772
	Overall Statistics		56.859	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	61.628	10	.000
	Block	61.628	10	.000
	Model	61.628	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	578.333	.102	.152

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	417	11	97.4
	DFREE	1.00	121	21	14.8
	Overall Percentage				76.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.138	.031	20.246	1	.000	1.147
	NDRGFP1	2.042	.443	21.259	1	.000	7.709
	NDRGFP2	.525	.123	18.291	1	.000	1.691
	IVHX2	-.702	.304	5.317	1	.021	.496
	IVHX3	-.796	.268	8.839	1	.003	.451
	RACE	.545	.273	3.990	1	.046	1.725
	TREAT	.525	.208	6.352	1	.012	1.691
	SITE	.504	.258	3.807	1	.051	1.656
	NAGE	-.020	.007	9.100	1	.003	.980
	RACESITE	-1.251	.539	5.393	1	.020	.286
	Constant	-7.800	1.300	36.024	1	.000	.000
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

*Syntax for column 2 of Table 5.9.
temporary.
select if (covpat ne 31).
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
 /print= goodfit.

*Syntax for column 3 of Table 5.9.
temporary.
select if (covpat ne 477).
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
 /print= goodfit.

*Syntax for column 4 of Table 5.9.
temporary.
select if (covpat ne 105).
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
 /print= goodfit.

*Syntax for column 5 of Table 5.9.
temporary.
select if (covpat ne 468).
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
 /print= goodfit.

*Syntax for column 6 of Table 5.9.
temporary.
select if (covpat ne 31 or covpat ne 477 or covpat ne 105 or covpat ne 468 ).
LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite
 /print= goodfit.

page 189 Table 5.10 Estimated coefficients, standard errors, z-scores, two-tailed p-values and 95% confidence intervals for the final logistic regression model for the UIS (n=575).

LOGISTIC REGRESSION VAR=dfree
  /METHOD=ENTER age ndrgfp1 ndrgfp2 ivhx2 ivhx3 race treat site nage racesite.

**Case Processing Summary**
Unweighted Cases(a)		N	Percent
Selected Cases	Included in Analysis	570	100.0
	Missing Cases	0	.0
	Total	570	100.0
Unselected Cases		0	.0
Total		570	100.0
a If weight is in effect, see classification table for the total number of cases.

**Dependent Variable Encoding**
Original Value	Internal Value
.00	0
1.00	1

**Classification Table(a,b)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 0	DFREE	.00	428	0	100.0
	DFREE	1.00	142	0	.0
	Overall Percentage				75.1
a Constant is included in the model.
b The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.103	.097	129.790	1	.000	.332

**Variables not in the Equation**
			Score	df	Sig.
Step 0	Variables	AGE	1.592	1	.207
		NDRGFP1	3.827	1	.050
		NDRGFP2	2.118	1	.146
		IVHX2	.222	1	.638
		IVHX3	9.886	1	.002
		RACE	3.123	1	.077
		TREAT	7.094	1	.008
		SITE	1.957	1	.162
		NAGE	3.288	1	.070
		RACESITE	.084	1	.772
	Overall Statistics		56.859	10	.000

**Omnibus Tests of Model Coefficients**
		Chi-square	df	Sig.
Step 1	Step	61.628	10	.000
	Block	61.628	10	.000
	Model	61.628	10	.000

**Model Summary**
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	578.333	.102	.152

**Classification Table(a)**
			Predicted
			DFREE		Percentage Correct
	Observed		.00	1.00	Percentage Correct
Step 1	DFREE	.00	417	11	97.4
	DFREE	1.00	121	21	14.8
	Overall Percentage				76.8
a The cut value is .500

**Variables in the Equation**
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1(a)	AGE	.138	.031	20.246	1	.000	1.147
	NDRGFP1	2.042	.443	21.259	1	.000	7.709
	NDRGFP2	.525	.123	18.291	1	.000	1.691
	IVHX2	-.702	.304	5.317	1	.021	.496
	IVHX3	-.796	.268	8.839	1	.003	.451
	RACE	.545	.273	3.990	1	.046	1.725
	TREAT	.525	.208	6.352	1	.012	1.691
	SITE	.504	.258	3.807	1	.051	1.656
	NAGE	-.020	.007	9.100	1	.003	.980
	RACESITE	-1.251	.539	5.393	1	.020	.286
	Constant	-7.800	1.300	36.024	1	.000	.000
a Variable(s) entered on step 1: AGE, NDRGFP1, NDRGFP2, IVHX2, IVHX3, RACE, TREAT, SITE, NAGE, RACESITE.

page 190 Table 5.11 Estimated odds ratios and 95% confidence intervals for treatment and history of IV drug use in the UIS (N = 575).

NOTE: The code above also gives the values for this table.

page 192 Table 5.12 Estimated odds ratios and 95% confidence intervals for race within site in the UIS (n = 575).

NOTE: We were unable to reproduce these values using SPSS.

page 194 Figure 5.9 Estimated odds ratio and 95% confidence limits for a five-year increase in age based on the model in Table 5.10.

NOTE: We were unable to reproduce this graph.

page 197 Figure 5.10 Estimated odds ratios and 95% confidence limits for an increase of one drug treatment from the plotted value of NDRGTX for a subject of age (a) 20, (b) 25, (c) 30 and (d) 35.

NOTE: We were unable to reproduce this graph.

page 199 Figure 5.11 Estimated odds ratios and 95% confidence limits . comparing zero, two, three up to 10 previous drug treatments to one previous treatment for a subject of age (a) 20, (b) 25, (c) 30 and (d) 35.

NOTE: We were unable to reproduce this graph.