Interpreting logistic regression results

[Aadil Sham]

Hi all,

I am trying to investigate the effect of breastfeeding on the double burden of malnutrition among mother-child pairs. The breastfeeding variable m4 has 3 categories: never breastfed, ever breastfed but no longer breastfeeding, and still breastfeeding. The outcome variable is binary where 1 = presence of the double burden and 0 = no presence. I ran a multivariate model with various sociodemographic, health and dietary variables as such:

svy: logit DBM i.b4 i.age_child i.sizeatbirth i.diarrhea i.v460 i.v013 i.v106 c.v218 i.short_structure i.v394 c.v453 i.v463a i.m4 i.m3b i.v401 i.v714 i.first_birth i.v467b i.v467d i.v130 i.v190 ib2.v025 c.HHhead_age i.v151 i.improved_water i.improved_sanitation i.s653a i.s653b i.s653c i.s653d i.s653e i.s653f i.s653g i.s653h i.s653i i.s653j i.s653k i.s653l i.s653m i.s653n i.s653o i.s653p i.s653q i.s653r i.s653s i.s653t i.s653u i.s653v, or

The results of the regression are as follows (only top part included to avoid it being too long):

                        
        Linearized
DBM    Odds ratio    std. err.    t    P>t    [95% conf.    interval]
                        
b4    
female    .7977014    .0811424    -2.22    0.026    .6533933    .9738813
    
age_child    
12-    1.443243    .3351756    1.58    0.114    .915109    2.276178
19-    1.623259    .4312487    1.82    0.068    .9639142    2.733616
29-    1.394491    .3956674    1.17    0.241    .7992317    2.433095
39-    1.008225    .2936575    0.03    0.978    .56938    1.785306
49-    1.059838    .3035261    0.20    0.839    .6042769    1.858845
    
sizeatbirth    
2    1.512282    .3164086    1.98    0.048    1.003165    2.279782
3    1.69537    .3276294    2.73    0.006    1.160421    2.476926
4    1.835523    .4701192    2.37    0.018    1.110563    3.033727
5    3.131504    1.149433    3.11    0.002    1.524131    6.434036
    
1.diarrhea    1.027892    .1721993    0.16    0.870    .7399708    1.427842
    
v460    
all children    .8815488    .1543398    -0.72    0.472    .6252876    1.242833
some children    .6968555    .1815756    -1.39    0.166    .417967    1.161832
no net in household    1.015444    .1905204    0.08    0.935    .7027507    1.467272
    
v013    
20-24    2.393979    1.181106    1.77    0.077    .9094378    6.301843
25-29    3.087438    1.450843    2.40    0.017    1.228083    7.761909
30-34    2.945537    1.494631    2.13    0.033    1.08853    7.970553
35-39    4.306002    2.204598    2.85    0.004    1.577121    11.75665
40-44    3.202782    1.834246    2.03    0.042    1.041318    9.850794
45-49    4.583337    3.074994    2.27    0.023    1.229047    17.09209
    
v106    
primary    1.626226    .2969723    2.66    0.008    1.136563    2.326851
secondary    1.191351    .2511549    0.83    0.406    .7878169    1.801584
higher    1.036256    .3389724    0.11    0.913    .5454653    1.968644
    
v218    1.09111    .0470229    2.02    0.043    1.002653    1.187372
1.short_structure    1.84761    .2787333    4.07    0.000    1.374283    2.483959
    
v394    
yes    .774395    .0932031    -2.12    0.034    .611532    .9806316
v453    1.000462    .0005271    0.88    0.381    .9994283    1.001497
    
v463a    
yes    3.031143    1.800266    1.87    0.062    .9453304    9.719169
    
m4    
never breastfed    1.255726    .4795985    0.60    0.551    .5935959    2.656432
still breastfeeding    .7993677    .1818369    -0.98    0.325    .5116077    1.248982

In this result, neither category of breastfeeding is statistically significant. However, if i replace the categorical child age variable with a continuous equivalent b19 (age in months), still breastfeeding becomes statistically significant for reducing the odds of having the double burden:

svy: logit DBM i.b4 c.b19 i.sizeatbirth i.diarrhea i.v460 i.v013 i.v106 c.v218 i.short_structure i.v394 c.v453 i.v463a i.m4 i.early_initiation i.m3b i.v401 i.v714 i.first_birth i.v467b i.v467d i.v130 i.v190 ib2.v025 c.HHhead_age i.v151 i.improved_water i.improved_sanitation i.s653a i.s653b i.s653c i.s653d i.s653e i.s653f i.s653g i.s653h i.s653i i.s653j i.s653k i.s653l i.s653m i.s653n i.s653o i.s653p i.s653q i.s653r i.s653s i.s653t i.s653u i.s653v, or

                        
        Linearized
DBM    Odds ratio    std. err.    t    P>t    [95% conf.    interval]
                        
b4    
female    .8011144    .0826832    -2.15    0.032    .6542735    .9809114
b19    .9887508    .0044224    -2.53    0.012    .9801128    .9974649
    
sizeatbirth    
2    1.538217    .3256564    2.03    0.042    1.015407    2.330209
3    1.725471    .3389479    2.78    0.006    1.17366    2.536722
4    1.914457    .4995159    2.49    0.013    1.147476    3.194095
5    3.179426    1.18215    3.11    0.002    1.533078    6.593763
    
1.diarrhea    .9882171    .1658365    -0.07    0.944    .7110086    1.373504
    
v460    
all children    .8891045    .1566164    -0.67    0.505    .629321    1.256127
some children    .6958354    .1822213    -1.38    0.166    .4162838    1.163117
no net in household    1.031197    .1930018    0.16    0.870    .7142965    1.488691
    
v013    
20-24    3.433124    2.083032    2.03    0.042    1.0441    11.28852
25-29    4.557931    2.623815    2.64    0.009    1.473349    14.10035
30-34    4.349447    2.679922    2.39    0.017    1.298589    14.56788
35-39    6.43073    3.944805    3.03    0.002    1.930266    21.42414
40-44    4.804882    3.210934    2.35    0.019    1.295151    17.82564
45-49    7.200005    5.517323    2.58    0.010    1.601214    32.37548
    
v106    
primary    1.657486    .303282    2.76    0.006    1.157586    2.373267
secondary    1.173758    .2525981    0.74    0.457    .7695272    1.79033
higher    1.031402    .3411283    0.09    0.926    .5390579    1.973426
    
v218    1.091747    .0470638    2.04    0.042    1.003214    1.188094
1.short_structure    1.82728    .2799426    3.93    0.000    1.352935    2.467932
    
v394    
yes    .7714005    .0965369    -2.07    0.038    .6034708    .9860605
v453    1.000472    .0005165    0.91    0.361    .9994591    1.001486
    
v463a    
yes    2.988678    1.795403    1.82    0.069    .9197134    9.711936
    
m4    
never breastfed    1.149961    .6107756    0.26    0.793    .4056597    3.259898
still breastfeeding    .6109488    .116082    -2.59    0.010    .4208451    .886926

The same occurs if I widen the child age variable into two categories of 5-23 months and 24-59 months. Any narrower categories and breastfeeding becomes insignificant. I am not quite sure how to interpret this. I was thinking that possibly with the narrow age categories, some of the variation caused by breastfeeding is explained by the age categories, with younger age groups more likely to experience the benefits of breastfeeding. With the continuous age variable, age acts as a control which is needed as older children are less likely to still be breastfed. Would this interpretation be valid or am I reaching? I wanted to include age as categorical so I could show which age groups are at greatest risk (and to account for the fact that the effect of age is non-linear). I was then thinking of including this second model as well with age being continuous to show that breastfeeding is a significant factor associated with the double burden. Any comments or advice on how I should handle this would be greatly appreciated.

[Carlo Lazzaro]

Aadi:
you might be interested in reading: https://pubmed.ncbi.nlm.nih.gov/16217841/

[Aadil Sham]

Hi Carlo, thanks a lot for the link, it was very helpful. So from what I understand, dichotomizing the age variables makes the model lose statistical power, especially when used to adjust for the effects of a confounder (breastfeeding). It therefore clearly seems more suitable to keep age as a continuous variable. I plotted the effect of age on the outcome DBM, and there is a positive (but insignificant) linear relationship between the two so I include a single linear age term. However, in the multivariate model the relationship is negative and significant, and still breastfeeding significantly lowers the odds of DBM. When I remove breastfeeding from the model, age becomes insignificant again. I have tested every other variable in the model and only breastfeeding has this effect on age. If I interact the age and breastfeeding terms, I get the following output (b19 is child age and m4 is breastfeeding - base category once breastfed but no longer breastfeeding):

--------------------------------------------------------------------------------------
                     |             Linearized
                 DBM | Odds ratio   std. err.      t    P>|t|     [95% conf. interval]
---------------------+----------------------------------------------------------------
                  b4 |
             female  |   .7898089   .0796394    -2.34   0.019     .6480549    .9625698
                 b19 |   .9850384   .0042554    -3.49   0.001     .9767255    .9934221
                     |
         sizeatbirth |
                  2  |   1.491948   .3045659     1.96   0.050     .9996016    2.226797
                  3  |   1.636046   .3090005     2.61   0.009     1.129479    2.369806
                  4  |   1.749131   .4434057     2.21   0.028     1.063751    2.876104
                  5  |   2.678137   .9364573     2.82   0.005     1.348704     5.31801
                     |
          1.diarrhea |     1.0185   .1666868     0.11   0.911     .7387945    1.404101
                     |
                mother age |
              20-24  |   2.262518   1.059738     1.74   0.082     .9026627    5.670988
              25-29  |   2.931134   1.293977     2.44   0.015     1.232857    6.968813
              30-34  |   3.009925   1.422046     2.33   0.020     1.191315    7.604744
              35-39  |   4.613895   2.260387     3.12   0.002      1.76468    12.06339
              40-44  |   3.582218   1.842382     2.48   0.013     1.306043    9.825315
              45-49  |   4.713869   2.720564     2.69   0.007     1.519339    14.62516
                     |
                mother education |
            primary  |   1.656941   .2638861     3.17   0.002     1.212319     2.26463
          secondary  |   1.307112   .2009673     1.74   0.082     .9667602    1.767286
             higher  |   1.297249   .3525476     0.96   0.338      .761166    2.210891
                     |
                v218 |   1.072881   .0454016     1.66   0.097     .9874095    1.165752
   1.short_structure |   1.800499    .264921     4.00   0.000     1.349062    2.403001
                     |
                v394 |
                yes  |   .7631513   .0874067    -2.36   0.018     .6095761    .9554179
                v453 |   1.000552   .0005059     1.09   0.275     .9995602    1.001545
                     |
               v463a |
                yes  |   3.741827   2.373133     2.08   0.038     1.078278    12.98484
                     |
                  m4 |
    never breastfed  |   .8708385   .8477348    -0.14   0.887     .1289859    5.879398
still breastfeeding  |   .3015025   .0806458    -4.48   0.000     .1784015    .5095461
                     |
            m4#c.b19 |
    never breastfed  |    1.01042   .0248725     0.42   0.674     .9627841    1.060412
still breastfeeding  |   1.047782   .0136611     3.58   0.000     1.021322    1.074928
                     |
               _cons |   .0199635   .0105252    -7.42   0.000     .0070965    .0561604

If I plot the predicted probabilities, I get the following graph:



I think I can make sense of this graph: breastfeeding reduces the probability of DBM until around 30 months, after which it increases the probability compared to those who don't breastfeed (possibly due to breastfeeding not being accompanied by complementary feeding practices after this age). However, I am still unclear why adding breastfeeding to the model makes age significant. The literature suggests that the relationship between age and DBM should be positive, but it is negative in this model. Why would breastfeeding cause child age to be significantly negatively related to DBM, even with the inclusion of the interaction?

[Carlo Lazzaro]

Asadil:
have you already investigated a non-linear relationship between mother's age (plugged in as a continuous variable with both its linear and squared terms)?

[Carlo Lazzaro]

Aadil:
please forget the part about quadratic relationship in my previous reply (whereas the linear term of mother's age as a continuous variabile deserves a shot) and take a look at https://journals.sagepub.com/doi/pdf...867X1001000211

[Aadil Sham]

Hi Carlo, thank you very much for your advice. It seems to me that when looking at interactions the important part is the coefficients for the interactions themselves and the "main" effect of child age is not so important. So would it be fair to say that as breastfeeding is what causes child age to be significant, the interaction between age and breastfeeding is what I should be looking at, and the individual effect for child age can be disregarded?

Regardless, I'm still slightly confused about my results, so I'm trying to re-fit my model. I'm trying to use fractional polynomials to figure out the best way to model child age.

I've used the following command to test this:

fp <b19>, replace : logistic DBM <b19> b4 sizeatbirth diarrhea v013 v106 v218 short_structure v394 v453 v463a m4 birth_assistance v401 v714 first_birth v467b v467d v130 v190 v025 HHhead_age v151 improved_water improved_sanitation

where b19 is the child age variables and the rest are the other independent variables. I get the following output, suggesting that the m2 model is best. I'm a bit unsure about what this output means as the powers are .5 and .5. Surely this doesn't mean including two square root terms, so how would I model child age given these results?

-------------------------------------------------------------------
             | Test              Deviance
         b19 |   df   Deviance       diff.       P   Powers
-------------+-----------------------------------------------------
     omitted |    4   4083.692     14.714    0.005               
      linear |    3   4074.690      5.711    0.127   1           
       m = 1 |    2   4072.647      3.669    0.160   2           
       m = 2 |    0   4068.978      0.000       --   .5 .5       
-------------------------------------------------------------------

[Carlo Lazzaro]

Aadil:
you may find https://www.stata.com/bookstore/flex...nalysis-stata/ useful.

[Aadil Sham]

Hi Carlo. Thanks for your suggestion, unfortunately I do not have access online access to this resource through my university. I did manage to figure it though, so thank you for your help. I am still having trouble modelling my continuous variables though. I have plotted lowess graphs for the variables and outcome DBM to look at the relationship.





From what I can interpret from these, child age does not have a linear relationship - it looks a bit like a log or a cubic function. The other three seem to be fairly linear. However, for age of household head and hemoglobin level these have strong variation at the start, and then are linear after this. In this case, how would I model these variables?

If I do a multivariate fractional polynomial model with only the continuous variables, I get the following results suggesting all variables should be modelled as linear, except for child age which should be modelled as square root of age and ln(square root of age).

mfp : logistic DBM b19 v212 v218 v453 HHhead_age

Final multivariable fractional polynomial model for DBM
--------------------------------------------------------------------
    Variable |    -----Initial-----          -----Final-----
             |   df     Select   Alpha    Status    df    Powers
-------------+------------------------------------------------------
         b19 |    4     1.0000   0.0500     in      4     .5 .5
        v212 |    4     1.0000   0.0500     in      1     1
        v218 |    4     1.0000   0.0500     in      1     1
        v453 |    4     1.0000   0.0500     in      1     1
  HHhead_age |    4     1.0000   0.0500     in      1     1
--------------------------------------------------------------------

This is different for my second outcome TBM, which suggests age should be modelled as linear as well.

Final multivariable fractional polynomial model for TBM
--------------------------------------------------------------------
    Variable |    -----Initial-----          -----Final-----
             |   df     Select   Alpha    Status    df    Powers
-------------+------------------------------------------------------
         b19 |    4     1.0000   0.0500     in      1     1
        v212 |    4     1.0000   0.0500     in      1     1
        v218 |    4     1.0000   0.0500     in      1     1
        v453 |    4     1.0000   0.0500     in      1     1
  HHhead_age |    4     1.0000   0.0500     in      1     1
--------------------------------------------------------------------

If I do a multivariate polynomial model with all my independent variables, it shows that a linear model is best for all the continuous variables, which is the same for DBM and TBM (v130 and v190 are categorical so I have ignored these powers):

mfp : logistic DBM b19 b4 sizeatbirth diarrhea v013 v106 v218 short_structure v394 v453 v463a m4 birth_assistance v401 v714 v212 v467b v467d v130 v190 v025 HHhead_age v151 improved_water improved_sanitation

Final multivariable fractional polynomial model for DBM
--------------------------------------------------------------------
    Variable |    -----Initial-----          -----Final-----
             |   df     Select   Alpha    Status    df    Powers
-------------+------------------------------------------------------
         b19 |    4     1.0000   0.0500     in      1     1
          b4 |    1     1.0000   0.0500     in      1     1
 sizeatbirth |    2     1.0000   0.0500     in      1     1
    diarrhea |    1     1.0000   0.0500     in      1     1
        v013 |    4     1.0000   0.0500     in      1     1
        v106 |    2     1.0000   0.0500     in      1     1
        v218 |    4     1.0000   0.0500     in      1     1
short_str... |    1     1.0000   0.0500     in      1     1
        v394 |    1     1.0000   0.0500     in      1     1
        v453 |    4     1.0000   0.0500     in      1     1
       v463a |    1     1.0000   0.0500     in      1     1
          m4 |    1     1.0000   0.0500     in      1     1
birth_ass... |    1     1.0000   0.0500     in      1     1
        v401 |    1     1.0000   0.0500     in      1     1
        v714 |    1     1.0000   0.0500     in      1     1
        v212 |    4     1.0000   0.0500     in      1     1
       v467b |    1     1.0000   0.0500     in      1     1
       v467d |    1     1.0000   0.0500     in      1     1
        v130 |    2     1.0000   0.0500     in      2     -2
        v190 |    2     1.0000   0.0500     in      2     -1
        v025 |    1     1.0000   0.0500     in      1     1
  HHhead_age |    4     1.0000   0.0500     in      1     1
        v151 |    1     1.0000   0.0500     in      1     1
improved_... |    1     1.0000   0.0500     in      1     1
improved_... |    1     1.0000   0.0500     in      1     1
--------------------------------------------------------------------

I feel like I am making this more complicated than it needs to be. It seems for most of these variables keeping them linear would suffice. Although child age does not seem linear, modelling it at square root of age and ln(square root of age) seems like it would add non-needed complexity to the model, especially as I am more interested in child age being a control for confounders such as breastfeeding rather than investigating the actual impact of age. Would you have any advice on how to tackle this? Apologies for all the questions, but this dissertation is causing lots of trouble and unfortunately I do not have a supervisor to help me!

[Carlo Lazzaro]

Aadil:
keep it linear, child_age included.

[Aadil Sham]

Thank you so much for your help Carlo, I really appreciate it!