How to interpret a mediation analysis results?

Question

I am new to mediation analysis and would like to know how to interpret the results of a mediation analysis obtained using R.

The independent variable is gender (1 Men /2 Women, categories).

The dependent variable is COPD (0 No COPD / 1 COPD, categories).

The mediator is tobacco habit (0 no tobacco habit / 1 yes tobacco habit, categories).

   ## Test for Total Effect

   fit.totaleffect=lm(EPOC~SEX,Episcan_total_e1)
   summary(fit.totaleffect)

   Call:
   lm(formula = EPOC ~ SEX, data = Episcan_total_e1)

   Residuals:
        Min       1Q   Median       3Q      Max 
   -0.03086 -0.03086  0.00000  0.00000  0.96914 

   Coefficients:
         Estimate Std. Error t value Pr(>|t|)    
   (Intercept)  0.030864   0.006477   4.765 2.29e-06 ***
   SEX2        -0.030864   0.008759  -3.524 0.000452 ***
   ---
   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

   Residual standard error: 0.1166 on 713 degrees of freedom
   Multiple R-squared:  0.01712,    Adjusted R-squared:  0.01574 
   F-statistic: 12.42 on 1 and 713 DF,  p-value: 0.0004525

   # sig
   ## Test for IV on Mediator - Needs to be sig. for mediation to occur

   fit.mediator=lm(tabaco_mediation~SEX,Episcan_total_e1)
   summary(fit.mediator)


   Call:
   lm(formula = tabaco_mediation ~ SEX, data = Episcan_total_e1)

   Residuals:
       Min      1Q  Median      3Q     Max 
   -0.7346 -0.4808  0.2654  0.5192  0.5192 

   Coefficients:
        Estimate Std. Error t value Pr(>|t|)    
   (Intercept)  0.73457    0.02638  27.844  < 2e-16 ***
   SEX2        -0.25375    0.03567  -7.113 2.77e-12 ***
   ---
   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

   Residual standard error: 0.4749 on 713 degrees of freedom
   Multiple R-squared:  0.06626,    Adjusted R-squared:  0.06495 
   F-statistic: 50.59 on 1 and 713 DF,  p-value: 2.771e-12

   ## Test for IV and Mediator's effect on DV simultaneously

   fit.dv=lm(EPOC~SEX+tabaco_mediation,Episcan_total_e1)
   summary(fit.dv)

   Call:
   lm(formula = EPOC ~ SEX + tabaco_mediation, data = Episcan_total_e1)

   Residuals:
        Min       1Q   Median       3Q      Max 
   -0.03360 -0.03360 -0.00534  0.00495  0.97669 

   Coefficients:
                      Estimate Std. Error t value Pr(>|t|)   
   (Intercept)        0.023306   0.009356   2.491   0.0130 * 
   SEX2              -0.028253   0.009063  -3.118   0.0019 **
   tabaco_mediation1  0.010289   0.009193   1.119   0.2634   
   ---
   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

   Residual standard error: 0.1166 on 712 degrees of freedom
   Multiple R-squared:  0.01884,    Adjusted R-squared:  0.01609 
   F-statistic: 6.837 on 2 and 712 DF,  p-value: 0.001145

In overrall I summarised all values in this graph:

I would like to know how to interpret that there is a negative association and that the effect between the mediator and dependent variable is not significant.

Thank you in advance.

Answer 1

It seems to me that gender is directly related to both smoking and COPD, and mediation is not happening. I.e. men are more likely to be smokers, and more likely to have COPD, but smoking does not mediate men's higher likelihood of having COPD.

Answer 2

On the face of it,

• the direct effect of sex to COPD is only slightly lower than the total effect, and
• there is no significant link between tobacco use and COPD in this data (and so no evidence of mediation).

But we know that smoking directly causes most COPD cases so I would wonder whether the dataset or study design is correct to be able to answer the question you are interested in. Can you add some detail about the study design, cross-tabulations of your variables etc?

Answer 3

Linked to the previous answers, I confirm that mediation does not occur. However, since the variables are dichotomous, I suggest using a generalised linear model glm with family=binomial(logit) option for a better model fitting. Lastly, be coherent between description and variable name for better understanding.