# Measuring the Effect of Mental Health on Type 2 Diabetes
## 5 Results
### Four Steps of Causal Inference
\begin{tabular}{l l} \hline \hline
**Propensity_score_stratification** & **Causal Estimate *** \\ \(\#\) Identified estimand & \\ Estimand type: nonparametric-ate & \\ \(\#\)Estimand: 1 & \\ Estimand name: backdoor & \\ Estimand expression: & \\ d & \\ \hline \hline \end{tabular}   
(Expectation (Diabetes | Physical activity, Fruits, BMI, Blood pressure, Vegetable))  
d[Mental health]  
Estimand assumption 1, Unconfoundedness: If U\(\rightarrow\)[Mental health] and U\(\rightarrow\)Diabetes  
then P(Diabetes| Mental health, Physical activity, Fruits, BMI, Blood pressure, Vegetable,U) = P(Diabetes| Mental health, Physical activity, Fruits, BMI, Blood pressure, Vegetable)  
\(\#\) Realized estimand  
b: Diabetes \(\sim\) Mental health + Physical activity + Fruits + BMI + Blood pressure + Vegetables  
Target units: ate  
\(\#\) Estimate  
Mean value: 0.1455803874296158 \begin{table} \end{table} 
Table 4: Propensity score method. The results show that stress increases the incidence of diabetes by about 15% (mean value: 0.146). It is unclear whether the causal relationship established here is a genuine causal relationship. Mechanisms other than stress may also play a role in the development of diabetes. DoWhy performs the analysis based on the assumptions we made during the first step; hence, the results need to be tested by three methodologies to verify the reliability of the causal relationship. **Step 4: Refute results. ** The results of causal inference are not derived from data, but from assumptions that lead to identification. The data are simply used for statistical estimation. Therefore, checking whether our assumptions in the first step were correct is essential. Thus, refutation tests are performed using the random common cause, placebo treatment refuter, and data subset refuter. First, the assumptions are tested according to the random common cause method. This method adds a randomly drawn covariate to the data and reruns the analysis to see if the causal estimate changes. If our assumptions were initially correct, the causal estimate should not change significantly. According to the random common cause method results, there is little difference between the estimated effect and the new effect. However, initial assumptions are verified because the \(p\)-value of more than 0.05 means the difference between the two effects is insignificant. Refute: Add a random common cause  
Estimated effect: 0.1434609341207403  
New effect: 0.14346045351871675  
\(p\)-value: 0.5  
The second refutation method is the placebo treatment refuter, which will randomly assign any covariate to the treatment and rerun the analysis. If our assumptions are correct, this newly discovered estimate should be close to 0. The \(p\)-value tests whether the new effect is statistically significantly different from 0; if the \(p\)-value is less than 0.05, the causal estimate is problematic because the new effect is different from 0. However, the result of this example has a \(p\)-value of 0.45, so the causal estimate does not seem to be a problem. Refute: Use a Placeb Treatment  
Estimated effect: 0.1434609341207403  
New effect: 0.00026096492182590356  
\(p\)-value: 0.45  
Third, we test our assumption using a data subset refuter. This method creates a subset of the data (similar to cross-validation) and checks whether the causal relationship estimate differs across subsets. If our assumptions are correct, the variance is not large. The \(p\)-value tests whether the new effect is statistically significantly different from the estimated effect. A \(p\)-value lower than 0.05 means that the causal estimate is problematic, as the two effects differ. However, looking at the results of this example, the \(p\)-value is 0.48, so there seems to be no problem with the causal estimate. Refute: Use a Subset of Data  
Estimated effect: 0.1434609341207403  
New effect: 0.14336716568282687  
\(p\)-value: 0.48  
In short, it can be seen that the assumptions in the above model pass the three refutation tests.