1 General Purpose
Paired proportions have to be assessed
when e.g. different diagnostic procedures are performed in one
subject. McNemar’s chi-square test is appropriate for analysis. Mc
Nemar’s test can not include predictor variables. The analysis of
paired outcome proportions including predictor variables requires
the module generalized estimating equations. The difference between
the two outcomes and the independent effects of the predictors
variables on the outcomes are simultaneously tested.
2 Schematic Overview of Type of Data File
3 Primary Scientific Questions
Fist, is the numbers of yes-responders
of outcome-1 significantly different from that of outcome-2.
Second, are the predictor variables significant predictors of the
outcomes.
4 Data Example
In a study of 139 general practitioners
the primary scientific question was: is there a significant
difference between the numbers of practitioners who give lifestyle
advise in the periods before and after (postgraduate) education.
The second question was, is age an independent predictor of the
outcomes.
|
Lifestyle advise-1
|
Lifestyle advise-2
|
Age (years)
|
|
,00
|
,00
|
89,00
|
|
,00
|
,00
|
78,00
|
|
,00
|
,00
|
79,00
|
|
,00
|
,00
|
76,00
|
|
,00
|
,00
|
87,00
|
|
,00
|
,00
|
84,00
|
|
,00
|
,00
|
84,00
|
|
,00
|
,00
|
69,00
|
|
,00
|
,00
|
77,00
|
|
,00
|
,00
|
79,00
|
The first ten patients of the data file
is given above. We will use the data of the Chap. 41 once more. The entire data file is
in extras.springer.com, and is entitled “chapter41paired
binary”.
5 2×2 Contingency Table of the Effect of Postgraduate Education
|
Lifestyleadvise after education
|
||||
|
No
|
Yes
|
|||
|
0
|
1
|
|||
|
Lifestyleadvise
|
No
|
0
|
65
|
28
|
|
Before education
|
Yes
|
1
|
12
|
34
|
The above table summarizes the numbers
of practitioners giving lifestyle advise in the periods prior to
and after postgraduate education. Obviously, before education
65 + 28 = 93 did not give lifestyle, while after education this
number fell to 77. It looks as though the education was somewhat
successful. According to the McNemar’s test this effect was
statistically significant (Chap. 41). In this chapter we will assess,
if the effect still exists after adjustment for doctors’
ages.
Start by opening the data file in
SPSS. Prior to a generalized estimation equation analysis which
includes additional predictors to a model with paired binary
outcomes, the data will have to be restructured. For that purpose
the Restructure Data Wizard will be used. The procedure is also
applied in the Chap. 12.
6 Restructure Data Wizard
Command:
-
click Data....click Restructure....mark Restructure selected variables into cases.... click Next....mark One (for example, w1, w2, and w3)....click Next....Name: id (the patient id variable is already provided)....Target Variable: enter “lifestyleadvise 1, lifestyleadvise 2 ”....Fixed Variable(s): enter age....click Next.... How many index variables do you want to create?....mark One....click Next....click Next again....click Next again....click Finish....Sets from the original data will still be in use…click OK.
Return to the main screen and observe
that there are now 278 rows instead of 139 in the data file. The
first 10 rows are given underneath.
|
Id
|
Age
|
Index 1
|
Trans 1
|
|
1
|
89,00
|
1
|
,00
|
|
1
|
89,00
|
2
|
,00
|
|
2
|
78,00
|
1
|
,00
|
|
2
|
78,00
|
2
|
,00
|
|
3
|
79,00
|
1
|
,00
|
|
3
|
79,00
|
2
|
,00
|
|
4
|
76,00
|
1
|
,00
|
|
4
|
76,00
|
2
|
,00
|
|
5
|
87,00
|
1
|
,00
|
|
5
|
87,00
|
2
|
,00
|
The above data file is adequate to
perform a generalized estimation equation analysis. Save the data
file. For convenience of the readers it is given in extras.
springer.com, and is entitled
“chapter42pairedbinaryrestructured”.
7 Generalized Estimation Equation Analysis
For analysis the module Generalized
Linear Models is required. It consists of two submodules:
Generalized Linear Models and Generalized Estimation Models. The
first submodule covers many statistical models like gamma
regression (Chap. 30), Tweedie regression (Chap.
31), Poisson regression (Chaps.
21 and 47), and the analysis of paired
outcomes with predictors (Chap. 3). The second is for analyzing
binary outcomes (current chapter).
Command:
-
Analyze....Generalized Linear Models....Generalized Estimation Equations....click Repeated....transfer id to Subject variables....transfer Index 1 to Within-subject variables....in Structure enter Unstructured....click Type of Model....mark Binary logistic....click Response....in Dependent Variable enter lifestyleadvise....click Reference Category....click Predictors....in Factors enter Index 1....in Covariates enter age....click Model....in Model enter lifestyleadvise and age....click OK.
Tests of model effects
|
Source
|
Type III
|
||
|---|---|---|---|
|
Wald chi-square
|
df
|
Sig.
|
|
|
(Intercept)
|
8,079
|
1
|
,004
|
|
Index1
|
6,585
|
1
|
,010
|
|
age
|
10,743
|
1
|
,001
|
Parameter estimates
|
95% Wald confidence interval
|
Hypothesis test
|
||||||
|---|---|---|---|---|---|---|---|
|
Parameter
|
B
|
Stri. Error
|
Lower
|
Upper
|
Wald chi-square
|
df
|
Sig.
|
|
(Intercept)
|
−2,508
|
,8017
|
−4,079
|
−,936
|
9,783
|
1
|
,002
|
|
[Indexl = 1]
|
,522
|
,2036
|
,123
|
,921
|
6,585
|
1
|
,010
|
|
[Indexl = 2]
|
0a
|
||||||
|
Age
|
,043
|
,0131
|
,017
|
,069
|
10,743
|
1
|
,001
|
|
(Scale)
|
1
|
||||||
In the output sheets the above tables
are observed. They show that both the index 1 (postgraduate
education) and age are significant predictors of lifestyleadvise.
The interpretations of the two significant effects are slightly
different from one another. The effect of postgraduate education is
compared with no postgraduate education at all, while the effect of
age is an independent effect of age on lifestyleadvise, the older
the doctors the better lifestyle advise given irrespective of the
effect of the postgraduate education.
8 Conclusion
Paired proportions have to be assessed
when e.g. different diagnostic procedures are performed in one
subject. McNemar’s chi-square test is appropriate for analysis. Mc
Nemar’s test can not include predictor variables, and is not
feasible for more than two outcomes. For that purpose Cochran’s
tests are required (Chap. 43). The analysis of paired outcome
proportions including predictor variables requires the module
generalized estimating equations as reviewed in the current
chapter.
9 Note
More background, theoretical and
mathematical information of paired binary outcomes are given in
Statistics applied to clinical studies 5th edition, Chap.
3, Springer Heidelberg Germany, 2012,
from the same authors. More information of generalized linear
models for paired outcome data is given in Machine learning in
medicine a complete overview, Chap. 20, Springer Heidelberg Germany,
2015, from the same authors.