Is it wrong to use Chi squared test for paired data?

#1
I'm doing a retrospective analysis of 70 patients with specific blood disease that were evaluated for frequency of renal dysfunction by 5 different ways. Data show that each of 5 approaches yield different frequency of renal disorder among those patients (45%, 37%, 17%, 8% and 6%).
Since McNemar is preferred test for paired categorical data, I used it and got significant difference in comparison of 45% for all proportions but 45% to 37%. I interpret this as "other tests show significantly lower frequency of renal disorder in same people".
However, when I use chi-squared test I do not get any significant difference when mutually comparing proportions - I interpret this as proportions of patients with other types of disorders do not significantly differ between patients with and without gold-standard renal disorder which is not the same thing. Since chi squared and McNemar do not test the same hypothesis, I am in dilemma whether is it absolutely forbidden to use chi sqared test for paired data? I would like to publish my data and I'm not sure is it appropriate to present chi squared comparisons.

In addition, please suggest how to best compare these diagnostic other tests to golden standard (first approach yielding 45% renal dysfunction), ROC curve analysis?
 

Karabiner

TS Contributor
#2
You cannot use the Chi² for independent samples here.
And the non-significant results indicate that you have carried it out incorrectely anyway.

With kind regards

Karabiner
 
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#3
I would like to say that both tests should be used for different information (assess size of proportions measured by different tests - Mc Nemar, assess distribution of proportions in two groups defined by other test - Chi squared). Two different types of contingency tables from same data. Is this flawed? Is there a reason why Chi squired is forbidden to use?

If not considered "tests" these data would be otherwise compared between groups using chi-squared test. They were currently taken to represent renal measurements and are labeled as tests, hence implying paired design. What is puzzling me is that proportions of patients with "renal" impairment are indeed similar between patients patients with and without main dysfunction and it seems that McNemar and Chi-squared test different hypotheses.
 
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Karabiner

TS Contributor
#4
You have dependent data, therefore you cannot use a Chi² test for independent groups.
But maybe I do not understand your design of the research and statistical data analysis.

With kind regards

Karabiner
 
#5
Thank you, I just wanted to hear opinion like yours, but still I don't understand the real reason why both test should not be used as approaches to two different questions. What makes chi-squared illegal?

It is exploratory analysis of retrospective data-set. Main stratification of renal function was by scintigraphy, other variables like creatinine and blood parameters related to renal function, as well es ultrasound were used to define renal dysfunction by other means. Therefore if I was to investigate relationship of gender with any of these variables I would use chi-squared. However, when I investigate relationship with golden standard and define those other variables as tests of same function I suddenly deal with a question of paired analyses. However, does this invalidate the place for chi-squared in such situation as additional analysis? '