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  • #1

    Interpretating interat

    Dear statalist,

    The headline of my question was cut short... Apologies. The question title should read : "Interpretating interaction effects in logistic regression".

    I am investigating the role of comorbidities (measured as ASA-score, categorical 0-4) and age on mortality after surgery. It is well known that both age and comorbidities increase mortality risk. It is less known how the interaction between the two affect the risk. My hypothesis is that a healthy (ASA-score 1 or 2) 70-year old patient have a lower risk of mortality than a sick (ASA-score 3 or 4) 40 year old patient. In other words, I want to examine the interaction effect between age and ASA-score on mortality. I am struggling how to analyze and present this in a scientificially sound way as well as how to perform the actual analyses. My main concerns are the following (if I have understood the concept of interactions of logistic regression correctly):
    1. Interactions (age and ASA in my example) in logistic regression is complicated, and the effect (size and significance) depends on the values of the ASA and Age.
    2. The size interaction effect also depends on the values of the other co-variates. I.e. a male, 50-year old patient with ASA 1 might have a significant interaction effect between age and ASA, but a female 50-year old patient with ASA 1 does not?
    If the above is correctly understood, how do you suggest I should report the interaction effects. It does not make sense to just report a significant / non-significant effect, rather maybe I should discuss a range of values where the effect is significant?

    My idea is the following (please comment if you think there is a better way):
    1. Report that there is an "overall" significant interaction term between age (as continous variable) and ASA-score (categorized 1-4).
    2. Visualize the interactions between all combinations of age (in 5-year categories) and ASA (categorized 1-4) via marginsplot or a contour graph.
    I am unsure how to do this in Stata. Below is my code:

    Code:
    replace Age =95 if Age>95 & Age!=.

logistic Mortality30Days c.Age##i.ASAScore i.Sex i.Income i.Education ib1.TypeOfSurgery_cat i.Hospsize_cat
    Results:
    Code:
         
    [IMG]https://www.statalist.org/forums/core/0.9 StartHTML:0000000105 EndHTML:0000003645 StartFragment:0000000136 EndFragment:0000003612 <HTML><BODY>{C}<!--StartFragment--><TABLE BORDER><tr><td>Logistic regression</td><td>Number of obs</td><td>=</td><td>245,652</td></tr><tr><td>	LR chi2(22)</td><td>=</td><td>2623.22</td></tr><tr><td>	Prob > chi2</td><td>=</td><td>0.0000</td></tr><tr><td>Log likelihood = -6667.8113</td><td>Pseudo R2</td><td>=</td><td>0.1644</td></tr><tr><td> </td><td>	</td><td>	</td></tr><tr><td>Mortality30Days *Odds Ratio</td><td>Std. Err. * * *z</td><td>	P>z * * [95% Conf.</td><td>Interval]</td></tr><tr><td>	</td><td>	</td><td></td></tr><tr><td>Age * *1.108676</td><td>.0313988 * * 3.64</td><td>	0.000 * * 1.048812</td><td>1.171956</td></tr><tr><td> ASAScore </td></tr><tr><td>ASA Score 2 * * 43.88958</td><td>90.83688 * * 1.83</td><td>	0.068 * * .7597249</td><td>2535.517</td></tr><tr><td>ASA Score 3 * * 381.0945</td><td>777.651 * * 2.91</td><td>	0.004 * * 6.983838</td><td>20795.59</td></tr><tr><td>ASA score >3 * * 8844.159</td><td>18450.79 * * 4.36</td><td>	0.000 * * 148.2072</td><td>527768.7</td></tr><tr><td> ASAScore#c.Age </td></tr><tr><td>ASA Score 2 * * .9620611</td><td>.0278646 * *-1.34</td><td>	0.182 * * .9089687</td><td>1.018255</td></tr><tr><td>ASA Score 3 * * .9504435</td><td>.0271475 * *-1.78</td><td>	0.075 * * .8986972</td><td>1.005169</td></tr><tr><td>ASA score >3 * * *.932225</td><td>.0271244 * *-2.41</td><td>	0.016 * * .8805496</td><td>.9869329</td></tr><tr><td> Sex </td></tr><tr><td>Male * * 1.187825</td><td>.0740583 * * 2.76</td><td>	0.006 * * 1.051192</td><td>1.342218</td></tr><tr><td> Income </td></tr><tr><td>Medium Income * * .8368125</td><td>.0625113 * *-2.38</td><td>	0.017 * * .7228396</td><td>.968756</td></tr><tr><td>High Income * * .8475343</td><td>.1446554 * *-0.97</td><td>	0.332 * * *.606563</td><td>1.184237</td></tr><tr><td> Education </td></tr><tr><td>Medium Education * * .8625545</td><td>.0560413 * *-2.28</td><td>	0.023 * * .7594215</td><td>.9796935</td></tr><tr><td>High Education * * .7128518</td><td>.0584647 * *-4.13</td><td>	0.000 * * .6069987</td><td>.8371643</td></tr><tr><td> TypeOfSurgery_cat </td></tr><tr><td>A. Neuro surgery * * 5.078578</td><td>1.211138 * * 6.81</td><td>	0.000 * * 3.182349</td><td>8.10469</td></tr><tr><td>D E. ENT surgery * * 1.942009</td><td>.5918672 * * 2.18</td><td>	0.029 * * 1.068636</td><td>3.529169</td></tr><tr><td>G. Pulmonary & thoracic surgery * * 6.041204</td><td>1.619976 * * 6.71</td><td>	0.000 * * 3.571659</td><td>10.21826</td></tr><tr><td>J. Abdominal surgery * * 6.453883</td><td>1.453572 * * 8.28</td><td>	0.000 * * 4.150589</td><td>10.03535</td></tr><tr><td>K. Urological surgery * * 2.827088</td><td>.6747493 * * 4.35</td><td>	0.000 * * 1.770845</td><td>4.51334</td></tr><tr><td>L. Gynecological surgery * * 1.260899</td><td>.3819491 * * 0.77</td><td>	0.444 * * .6963638</td><td>2.283099</td></tr><tr><td>N. Orthopedic surgery * * 3.088301</td><td>.7067283 * * 4.93</td><td>	0.000 * * 1.972106</td><td>4.836253</td></tr><tr><td>V. Vascular surgery * * 3.638874</td><td>.9102379 * * 5.16</td><td>	0.000 * * 2.228666</td><td>5.941401</td></tr><tr><td> Hospsize_cat </td></tr><tr><td>Central Hospital * * 1.398945</td><td>.11175 * * 4.20</td><td>	0.000 * * 1.196204</td><td>1.636048</td></tr><tr><td>University Hospital * * 1.911023</td><td>.1553724 * * 7.97</td><td>	0.000 * * 1.629523</td><td>2.241153</td></tr><tr><td> _cons * *1.33e-07</td><td>2.71e-07 * *-7.78</td><td>	0.000 * * 2.47e-09</td><td>7.18e-06</td></tr><tr><td>	</td><td>	</td><td></td></tr><tr><td>Note: _cons estimates baseline odds.</td></tr></TABLE>{C}<!--EndFragment--></BODY></HTML>[/IMG]Logistic regression    Number of obs    =    245,652
    LR chi2(22)    =    2623.22
    Prob > chi2    =    0.0000
Log likelihood = -6667.8113    Pseudo R2    =    0.1644

                
Mortality30Days  Odds Ratio    Std. Err.      z        P>z     [95% Conf.    Interval]
                
     
  Age    
   
    1.108676    .0313988     3.64        0.000     1.048812    1.171956
     
  
ASAScore
   
    ASA Score 2     43.88958    90.83688     1.83        0.068     .7597249    2535.517
ASA Score 3     381.0945    777.651     2.91        0.004     6.983838    20795.59
ASA score >3     8844.159    18450.79     4.36        0.000     148.2072    527768.7
     
  
ASAScore#c.Age 
   
    ASA Score 2     .9620611    .0278646    -1.34        0.182     .9089687    1.018255
ASA Score 3     .9504435    .0271475    -1.78        0.075     .8986972    1.005169
ASA score >3      .932225    .0271244    -2.41        0.016     .8805496    .9869329
     
  
Sex
   
    Male     1.187825    .0740583     2.76        0.006     1.051192    1.342218
     
  
Income
   
    Medium Income     .8368125    .0625113    -2.38        0.017     .7228396    .968756
High Income     .8475343    .1446554    -0.97        0.332      .606563    1.184237
     
  
Education
   
    Medium Education     .8625545    .0560413    -2.28        0.023     .7594215    .9796935
High Education     .7128518    .0584647    -4.13        0.000     .6069987    .8371643
 
     
  TypeOfSurgery_cat
   
    A. Neuro surgery     5.078578    1.211138     6.81        0.000     3.182349    8.10469
D+E. ENT surgery     1.942009    .5918672     2.18        0.029     1.068636    3.529169
G. Pulmonary & thoracic surgery     6.041204    1.619976     6.71        0.000     3.571659    10.21826
J. Abdominal surgery     6.453883    1.453572     8.28        0.000     4.150589    10.03535
K. Urological surgery     2.827088    .6747493     4.35        0.000     1.770845    4.51334
L. Gynecological surgery     1.260899    .3819491     0.77        0.444     .6963638    2.283099
N. Orthopedic surgery     3.088301    .7067283     4.93        0.000     1.972106    4.836253
V. Vascular surgery     3.638874    .9102379     5.16        0.000     2.228666    5.941401
 
     
  Hospsize_cat
   
    Central Hospital     1.398945    .11175     4.20        0.000     1.196204    1.636048
University Hospital     1.911023    .1553724     7.97        0.000     1.629523    2.241153

_cons    1.33e-07    2.71e-07    -7.78        0.000     2.47e-09    7.18e-06
                
Note: _cons estimates baseline odds.


    Code:
    margins, at(Age =(20(5)95) ASAScore =(1(1)4))

                      
        Delta-method
    Margin    Std. Err.    z    P>z    [95% Conf.    Interval]
                        
_at    
1    4.32e-06    6.32e-06    0.68    0.494    -8.06e-06    .0000167
2    .0000875    .0000293    2.99    0.003    .0000301    .0001448
3    .0005952    .00013    4.58    0.000    .0003405    .00085
4    .0092659    .0035629    2.60    0.009    .0022827    .016249
5    7.24e-06    9.58e-06    0.76    0.450    -.0000115    .000026
6    .0001207    .0000367    3.29    0.001    .0000487    .0001928
7    .0007731    .0001541    5.02    0.000    .000471    .0010752
8    .0109019    .0038274    2.85    0.004    .0034004    .0184035
9    .0000121    .0000144    0.84    0.400    -.0000161    .0000403
10    .0001667    .0000457    3.65    0.000    .0000771    .0002562
11    .0010041    .0001811    5.54    0.000    .000649    .0013591
12    .0128217    .0040745    3.15    0.002    .0048358    .0208076
13    .0000203    .0000213    0.95    0.341    -.0000215    .0000621
14    .0002301    .0000562    4.10    0.000    .00012    .0003402
15    .0013038    .0002107    6.19    0.000    .000891    .0017167
16    .0150723    .0042912    3.51    0.000    .0066617    .0234829
17    .000034    .0000311    1.09    0.275    -.000027    .0000951
18    .0003176    .0000681    4.66    0.000    .0001841    .0004511
19    .0016929    .0002418    7.00    0.000    .001219    .0021669
20    .0177082    .0044614    3.97    0.000    .0089641    .0264523
21    .000057    .0000446    1.28    0.202    -.0000305    .0001444
22    .0004384    .0000812    5.40    0.000    .0002793    .0005974
23    .0021978    .0002732    8.05    0.000    .0016624    .0027332
24    .0207915    .0045658    4.55    0.000    .0118427    .0297404
25    .0000954    .0000625    1.53    0.127    -.0000271    .0002179
26    .000605    .0000946    6.39    0.000    .0004195    .0007905
27    .0028526    .0003025    9.43    0.000    .0022598    .0034454
28    .0243934    .0045835    5.32    0.000    .0154099    .033377
29    .0001598    .0000852    1.87    0.061    -7.28e-06    .0003269
30    .0008349    .0001075    7.77    0.000    .0006243    .0010456
31    .0037014    .0003266    11.33    0.000    .0030613    .0043416
32    .0285943    .004494    6.36    0.000    .0197862    .0374025
33    .0002676    .0001136    2.36    0.018    .000045    .0004902
34    .0011521    .0001185    9.73    0.000    .0009199    .0013843
35    .0048012    .0003421    14.04    0.000    .0041307    .0054717
36    .0334847    .0042852    7.81    0.000    .0250859    .0418835
37    .0004482    .0001524    2.94    0.003    .0001495    .0007468
38    .0015895    .000128    12.42    0.000    .0013386    .0018404
39    .0062248    .0003473    17.92    0.000    .0055442    .0069055
40    .0391657    .0039732    9.86    0.000    .0313783    .0469531
41    .0007504    .0002267    3.31    0.001    .0003061    .0011946
42    .0021925    .0001438    15.25    0.000    .0019106    .0024743
43    .0080658    .0003508    23.00    0.000    .0073784    .0087533
44    .0457488    .0036538    12.52    0.000    .0385875    .0529102
45    .001256    .0004106    3.06    0.002    .0004513    .0020607
46    .0030231    .0001916    15.78    0.000    .0026477    .0033986
47    .0104433    .0003913    26.69    0.000    .0096764    .0112102
48    .0533561    .0035997    14.82    0.000    .0463009    .0604112
49    .0021013    .0008462    2.48    0.013    .0004428    .0037598
50    .0041667    .0003121    13.35    0.000    .003555    .0047784
51    .0135083    .0005466    24.71    0.000    .012437    .0145796
52    .0621185    .0042562    14.59    0.000    .0537765    .0704605
53    .0035127    .0017793    1.97    0.048    .0000254    .007
54    .0057393    .0005464    10.50    0.000    .0046684    .0068103
55    .0174508    .0008848    19.72    0.000    .0157166    .019185
56    .0721752    .0058908    12.25    0.000    .0606295    .083721
57    .0058644    .0036564    1.60    0.109    -.001302    .0130307
58    .0078989    .0009455    8.35    0.000    .0060457    .0097522
59    .0225077    .0014535    15.48    0.000    .0196588    .0253565
60    .0836701    .0084797    9.87    0.000    .0670502    .10029
61    .0097688    .0072834    1.34    0.180    -.0045065    .0240441
62    .0108588    .0015861    6.85    0.000    .0077501    .0139675
63    .0289705    .0023154    12.51    0.000    .0244325    .0335086
64    .0967488    .0119699    8.08    0.000    .0732884    .1202093
    Code:
    marginsplot, ytitle("Predicted probability of 30-day mortality") xtitle("Age") title("Predicted probability of 30-day mortality") subtitle("By age and ASA score")
    Ok, I am terribly sorry for the long post. But I need to show the results.


    Is the following a correct interpretation of the findings:
    1. There is a significant interaction effect between age and ASA-score, but only between age and the highest ASA-score (ASA score >3, p = 0.016).
    2. Looking at "margins results", there is a significant (none-zero) interaction effect between almost all combinations of age (categories of 5 years) and ASA-score. Those combinations that are none-significant ( _at: 1, 5, 9, 13, 17, 21, 25, 29, 57, 61) are younger patients with ASA-score ==1. The two last combinations (57 and 61) are really old patients with low ASA-score (very few fit these criterias).

    How can point 1. and 2. above exist together? Is the results from the logistic regression an overall interaction effect? I.e. that there is a none-significant overall interaction effect when taking into acount the young patients with low ASA-score, who have a non-significant interaction effect. The lack of significance "overall" in lower categories of ASA-score in the logistic regression is explained by the young patients with low ASA-score?

    Can someone help me interpret the results or possibly give suggestions how to perform a better interaction analysis?

    All the best, and thank you for this forum.

    /Jesper
    Last edited by Jesper Eriksson; 11 Mar 2024, 02:59.
    Tags: None
  • #2
    I post the graphs for analysis without (1st picture) and with an interaction term (second picture). You can see that with the interaction term between age and ASA-score that the line for the patients with most comorbidities (ASA-score ≥3) flattens out.

    Graph without interaction term:

    Click image for larger version Name: no_interaction.png Views: 1 Size: 140.6 KB ID: 1746184


    Graph with interaction term:

    Click image for larger version Name: interaction.png Views: 1 Size: 137.5 KB ID: 1746185

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