SPSS for Starters and 2nd Levelers Ton J Cleophas And Aeilko H Zwinderman

1 General Purpose

Clinical studies often have categories as outcome, like various levels of health or disease. Multinomial regression is suitable for analysis (see Chap. 44). However, if one or two outcome categories in a study are severely underpresented, multinomial regression is flawed, and ordinal regression including specific link functions may provide a better fit for the data. Strictly, ordinal data are, like nominal data, discrete data, however, with a stepping pattern, like severity scores, intelligence levels, physical strength scores. They are usually assessed with frequency tables and bar charts. Unlike scale data, that also have a stepping pattern, they do not necessarily have to have steps with equal intervals. This causes some categories to be underpresented compared to others.

2 Schematic Overview of the Type of Data File

3 Primary Scientific Question

This chapter is to assess how ordinal regression performs in studies where clinical scores have inconsistent frequencies.

4 Data Example

This chapter assesses the effect of the levels of satisfaction with the doctor on the levels of quality of life (qol). In 450 patients with coronary artery disease the satisfaction level of patients with their doctor was assumed to be an important predictor of patient qol (quality of life).

Qol (outcome)	Treatment	Counseling	Sat doctor
4	3	1	4
2	4	0	1
5	2	1	4
4	3	0	4
2	2	1	1
1	2	0	4
4	4	0	1
4	3	0	1
4	4	1	4
3	2	1	4

qol = quality of life score (1 = very low, 5 = vey high)

treatment = treatment modality (1 = cardiac fitness, 2 = physiotherapy, 3 = wellness, 4 = hydrotherapy, 5 = nothing)

counseling = counseling given (0 = no, 1 = yes)

sat doctor = satisfaction with doctor (1 = very low, 5 = very high)

The above table gives the first 10 patients of a 450 patients study of the effects of doctors’ satisfaction level and qol. The entire data file is in extras.springer.com and is entitled “chapter48ordinalregression”. Start by opening the data file in SPSS.

5 Table Qol Score Frequencies

Command:

Analyze….Descriptive Statistics....Frequencies....Variable(s): enter “qol score”....click OK.

Qol score

		Frequency	Percent	Valid percent	Cumulative percent
Valid	Very low	86	19,1	19,1	19,1
	Low	73	16,2	16,2	35,3
	Medium	71	15,8	15,8	51,1
	High	109	24,2	24,2	75,3
	Very high	111	24,7	24,7	100,0
	Total	450	100,0	100,0

The above table shows that the frequencies of the qol scores are pretty heterogeneous with 111 patients very high scores and only 71 patients medium scores. This could mean that multinomial regression is somewhat flawed and that ordinal regression including specific link functions may provide a better fit for the data.

6 Multinomial Regression

For analysis the statistical model Multinomial Logistic Regression in the module Regression is required.

Command:

Analyze....Regression....Multinomial Regression....Dependent: enter qol.... Factor(s): enter treatment, counseling, sat (satisfaction) with doctor....click OK.

The next page table is in the output sheets. It shows that the effects of several factors on different qol scores are very significant, like the effect of counseling on very low qol, and the effects of satisfaction with doctor levels 1 and 2 on very low qol. However, other effects were insignificant, like the effects of treatments on very low qol, and the effects of satisfaction with doctor levels 3 and 4 on very low qol. In order to obtain a more general overview of what is going-on an ordinal regression will be performed.

7 Ordinal Regression

For analysis the statistical model Ordinal Regression in the module Regression is required.

Command:

Analyze....Regression....Ordinal Regression....Dependent: enter qol....Factor(s): enter “treatment”, “counseling”, “sat with doctor”....click Options....Link: click Complementary Log-log....click Continue....click OK.

Parameter Estimates

Qol score^a		B	Std. error	Wald	df	Sig.	Exp(B)	95 % confidence interval for Exp (B)
Qol score^a		B	Std. error	Wald	df	Sig.	Exp(B)	Lower bound	Upper bound
Very low	Intercept	−1,795	,488	13,528	1	,000
	[treatments]	−,337	,420	,644	1	,422	,714	,314	1,626
	[treatment = 2]	,573	,442	1,678	1	,195	1,773	,745	4,216
	[treatment = 3]	,265	,428	,385	1	,535	1,304	,564	3,015
	[treatment = 4]	0^b	.	.	0	.	.	.	.
	[counseling = 0]	1,457	,328	19,682	1	,000	4,292	2,255	8,170
	[counseling = 1]	0^b	.	.	0	.	.	.	.
	[satdoctor = 1]	2,035	,695	8,579	1	,003	7,653	1,961	29,871
	[satdoctor = 2]	1,344	,494	7/413	1	,006	3,834	1/457	10,089
	[satdoctor = 3]	,440	,468	,887	1	,346	1,553	,621	3,885
	[satdoctor = 4]	,078	,465	,028	1	,867	1,081	,435	2,687
	[satdoctor = 5]	0^b	.	.	0	.	.	.	.
Low	Intercept	−2,067	,555	13,879	1	,000
	[treatment = 1]	−,123	,423	,084	1	,771	,884	,386	2,025
	[treatment = 2]	,583	,449	1,684	1	,194	1,791	,743	4,320
	[treatment = 3]	−,037	,462	,006	1	,936	,964	,389	2,385
	[treatment = 4]	0^b	.	.	0	.	.	.	.
	[counseling = 0]	,846	,323	6,858	1	,009	2,331	1,237	4,392
	[counseling = 1]	0^b	.	.	0	.	.	.	.
	[satdoctor = 1]	2,735	,738	13,738	1	,000	15,405	3,628	65,418
	[satdoctor = 2]	1,614	,581	7,709	1	,005	5,023	1,607	15,698
	[satdoctor = 3]	1,285	,538	5,704	1	,017	3,614	1,259	10,375
	[satdoctor = 4]	,711	,546	1,697	1	,193	2,036	,699	5,933
	[satdoctor = 5]	0^b	.	.	0	.	.	.	.
Medium	Intercept	−1,724	,595	8,392	1	,004
	[treatment = 1]	−,714	,423	2,858	1	,091	,490	,214	1,121
	[treatment = 2]	,094	,438	,046	1	,830	1,099	,465	2,594
	[treatment = 3]	−,420	,459	,838	1	,360	,657	,267	1,615
	[treatment = 4]	0^b	.	.	0	.	.	.	.
	[counseling = 0]	,029	,323	,008	1	,929	1,029	,546	1,940
	[counseling = 1]	0^b	.	.	0	.	.	.	.
	[satdoctor = 1]	3,102	,790	15/425	1	,000	22,244	4,730	104,594
	[satdoctor = 2]	2,423	,632	14,714	1	,000	11,275	3,270	38,875
	[satdoctor = 3]	1/461	,621	5,534	1	,019	4,309	1,276	14,549
	[satdoctor = 4]	1,098	,619	3,149	1	,076	2,997	,892	10,073
	[satdoctor = 5]	0^b	.	.	0	.	.	.	.
High	Intercept	−,333	,391	,724	1	,395
	[treatment = 1]	−,593	,371	2,562	1	,109	,552	,267	1,142
	[treatment = 2]	−,150	,408	,135	1	,713	,860	,386	1,916
	[treatment = 3]	,126	,376	,113	1	,737	1,135	,543	2,371
	[treatment = 4]	0^b	.	.	0	.	.	.	.
	[counseling = 0]	−,279	,284	,965	1	,326	,756	,433	1,320
	[counseling = 1]	0^b	.	.	0	.	.	.	.
	[satdoctor = 1]	1,650	,666	6,146	1	,013	5,208	1,413	19,196
	[satdoctor = 2]	1,263	,451	7,840	1	,005	3,534	1,460	8,554
	[satdoctor = 3]	,393	,429	,842	1	,359	1,482	,640	3/432
	[satdoctor = 4]	,461	,399	1,337	1	,248	1,586	,726	3,466
	[satdoctor = 5]	0^b	.	.	0	.	.	.	.

^aThe reference category is: very high

^bThis parameter is set to zero because it is redundant

Model fitting information

Model	−2 Log likelihood	Chi-square	df	Sig.
Intercept only	578,352
Final	537,075	41,277	8	,000

Link function: Complementary Log-log

Parameter estimates

		Estimate	Std. error	Wald	df	Sig.	95 % confidence interval
		Estimate	Std. error	Wald	df	Sig.	Lower bound	Upper bound
Threshold	[qol = 1]	−2,207	,216	103,925	1	,000	−2,631	−1,783
	[qol = 2]	−1,473	,203	52,727	1	,000	−1,871	−1,075
	[qol = 3]	−,959	,197	23,724	1	,000	−1,345	−,573
	[qol = 4]	−,249	,191	1,712	1	,191	−,623	,124
Location	[treatments]	,130	,151	,740	1	,390	−,167	,427
	[treatment = 2]	−,173	,153	1,274	1	,259	−.473	,127
	[treatment = 3]	−,026	,155	,029	1	,864	−,330	,277
	[treatment = 4]	0^a	.	.	0	.	.	.
	[counseling = 0]	−.289	,112	6,707	1	,010	−,508	−,070
	[counseling = 1]	0^a	.	.	0	.	.	.
	[satdoctor = 1]	−,947	,222	18,214	1	,000	−1,382	−,512
	[satdoctor = 2]	−,702	,193	13,174	1	,000	−1,081	−,323
	[satdoctor = 3]	−,474	,195	5,935	1	,015	−,855	−,093
	[satdoctor = 4]	−,264	,195	1,831	1	,176	−,646	,118
	[satdoctor = 5]	0^a	.	.	0	.	.	.

Link function: Complementary Log-log

^aThis parameter is set to zero because it is redundant

The above tables are in the output sheets of the ordinal regression. The model fitting information table tells that the ordinal model provides an excellent overall fit for the data. The parameter estimates table gives an overall function of all predictors on the outcome categories. Treatment is not a significant factor, but counseling, and the satisfaction with doctor levels 1–3 are very significant predictors of the quality of life of these 450 patients. The negative values of the estimates can be interpreted as follows: the less counseling, the less effect on quality of life, and the less satisfaction with doctor, the less quality of life.

8 Conclusion

Clinical studies often have categories as outcome, like various levels of health or disease. Multinomial regression is suitable for analysis, but, if one or two outcome categories in a study are severely underpresented, ordinal regression including specific link functions may better fit the data. The current chapter also shows that, unlike multinomial regression, ordinal regression tests the outcome categories as an overall function.

9 Note

More background, theoretical and mathematical information of ordinal regression and ordinal data is given in Machine learning in medicine a complete overview, Chaps. 11 and 37, Springer Heidelberg Germany, 2015, from the same authors.

48. Ordinal Regression for Data with Underpresented Outcome Categories (450 Patients)

1 General Purpose

2 Schematic Overview of the Type of Data File

3 Primary Scientific Question

4 Data Example

5 Table Qol Score Frequencies

6 Multinomial Regression

7 Ordinal Regression

8 Conclusion

9 Note

SPSS for Starters and 2nd Levelers