Super simple case: how to do hierarchical chi square test?

Chi square test study X and Y The difference of ,X and Y Are category data . At present, another disturbing factor layering item needs to be further considered . Like smoking or not （X) And whether you are ill (Y) The relationship between , Taking gender into account （ That is, confounding factors , Hierarchical item Factor）. This is called hierarchical chi square , Layered chi square is also known as Cochran-Mantel-Haenszel test （CMH test ）, Layered chi square can be a good solution ‘ Simpson paradox ’ problem .SPSSAU Support 2*2*K Structural data （ namely X and Y Are all 2 classification ,K layer ）.

One 、 Theoretical explanation

Hierarchical chi square is based on Chi square test , Further consider the interference of layered terms （ Confounding factors ）, It is usually necessary to analyze confounding factors （ Hierarchical item ） There is a certain degree of foreknowledge （ Or references ）, Then the hierarchical chi square test .

• For layered chi square , It involves the following theoretical knowledge , The following table ：

Usually , First of all to see ‘ Odds ratio homogeneity test ’, If it shows significance （p  Less than 0.05）, It indicates that there are confounding factors , That is, you need to consider hierarchical items , That is to view the data results under different layers . On the contrary, if it fails ‘ Odds ratio homogeneity test ’, That is to say, there are no confounding factors and there is no need to consider the stratification item , Just report the overall results （ Including chi square test , as well as OR value ）. Cochran–Mantel–Haenszel Conditional independence was used to study confounding factors （ Hierarchical item ） after ,X And Y Whether there are still differences between , Relatively small .

Two 、 Layered chi square case

1、 background

There is a current study on the impact of smoking on the risk of colds , share 1046 Research subjects , And record whether you have a cold , Smoking or not , And gender information .

2、 Data description

Raw data （ Analog data ） as follows ：

The raw data is in a weighted format .

• Whether to smoke , Numbers 1 Express ‘ smoking ’, Numbers 2 Express ‘ No smoking ’;
• Do you have a cold , Numbers 1 Express ‘ Catch a cold ’, Numbers 2 Express ‘ No colds ’.
• When stratified by gender , Numbers 1 Express ‘ male ’, Numbers 2 Express ‘ Woman ’, Numbers 3 Express ‘ A secret ’.
• Weighted terms weight Indicates the number of combinations of categories of each research object , such as 465 Express , The number of men who smoke and have a cold .
• Tips ：
  • For layered chi square ,SPSSAU Support 2*2*k structure , namely X and Y Are all 2 Categories , Whether to smoke and whether to catch a cold ,k Indicates the number of categories of hierarchical items ,（ The cases are divided into ‘ male ’,‘ Woman ’ and ‘ A secret ’, Then for 3 layer ）.

3、 Operation steps
This case uses the weighted data format , The operations for placing analysis items are as follows ：

Use path ：SPSSAU→ experiment / Medical research → Layered chi square

4、SPSSAU Output results

SPSSAU Co output 5 Class table , Here's how ：

form	explain
Cochran-Mantel-Haenszel test Basic explanation	Basic summary of analysis items .
Hierarchical chi square test summary table	√ When showing layers and non layers ,X And Y Chi square test of ;√ Use fisher Chi square test , And show OR Values and 95% Section .
Mantel-Haenszel Common Ratio OR Value estimate	Exhibition Mantel-Haenszel Common Ratio OR value , as well as OR The logarithm of the value , And show 95% Section .
Odds ratio homogeneity test (Breslow-Day-Tarone)	Exhibition Breslow-Day Odds ratio homogeneity test .
Cochran–Mantel–Haenszel Conditional independence test	Exhibition chran–Mantel–Haenszel Conditional independence test .

① Hierarchical chi square test summary table

The table above shows each layer （ And no layering ） In this case , Data of each cross category item , And output OR Values and fisher Chi square value , For example, when there is no layering , That is, when gender is not considered at all ,‘ Smoking or not ’ And ‘ Do you have a cold ’ There is a significant difference between （χ2=15.136, p =0.000<0.01）,OR The value is 2.077, That means smoking is a risk factor on the whole , And the risk of smoking is not smoking 2.077 times . But when considering hierarchically , Significant only in men （χ2=5.514, p =0.024<0.05）, However, there is no significant difference between women and secret groups ( p > 0.05）. That is to say, the existence of confounding factors may need to be considered （ That is, hierarchical items exist ）, Next, the corresponding layered items will be inspected and explained .

②Mantel-Haenszel Common Ratio OR Value estimate

• Tips ：
• here 95% The calculation of the confidence interval is based on the assumption that OR value =1 Calculate .

The table above shows Mantel-Haenszel Common Ratio OR value ,OR The value is 1.772, That means smoking is a risk factor on the whole , And the risk of smoking is not smoking 1.772 times (95% CI: 1.1760 ~ 2.6701).

③ Odds ratio homogeneity test results

The table above shows the odds ratio homogeneity test , By default Breslow-Day Method , The table above shows that the odds ratio homogeneity test was not passed （χ2=1.089, p=0. 5801>0.1）, This means that the layers are homogeneous , There is no confounding , That is, there are no confounding factors （ Gender ）, That is, it is not necessary to report the corresponding values of each layer separately （ such as OR value ）, The overall report is sufficient , The overall... Can be reported here Mantel-Haenszel Common Ratio OR Value is 1.772.

SPSSAU Automatic output of intelligent analysis results ：

④Cochran–Mantel–Haenszel Conditional independence test

The above table shows the conditional independence results ,Mantel-Haenszel Common The law rejects the original assumption （χ2=7.0547, p=0. 0079<0.01）, That is to say, controlling confounding interference factors （ Gender ） after , There is still a significant difference between smoking and cold , and OR The value is 1.772, Smoking is a risk factor , And the risk of smoking is not smoking 1.772 times .

5、 Analysis of key points

① Layered chi square ,SPSSAU Support weighted and unweighted formats , A weighted format is usually used , Drop down selection during analysis ‘ Weighted terms ’ that will do .

② Whether there are confounding factors in the study of odds ratio homogeneity test （ That is, whether the existence of hierarchical items is meaningful ）.

③ Mantel-Haenszel Common Ratio OR value , As a whole when chi square test is performed separately OR The values are not consistent ,Mantel-Haenszel Common Ratio OR The value can be understood as a correction OR value , But they have the same meaning .