Sensitivity analysis

The results of the analysis depend on the model used for analysis and it is important to examine whether changes in the model specifications could potentially change the results. Therefore a sensitivity analysis is carried out in this section. If the results prove to be robust to changes in the model, it is more likely that the results are valid. However, many considerations should go into the evaluation of the validity of the results and these will be discussed in the next chapter.

Model with interactions

The specifications of the adjusted model include all the potential confounders available for this study. However, it does not include any interactions or effect modifiers. Therefore a model has been specified containing interactions between age categories and gender as well as age categories

and cohabitation. As seen in the descriptive analysis there was an indication of non constant incidence rate ratios between men and women over the age categories. A very similar pattern can be seen between age categories and cohabitation, these plots can be found in appendix C.

The results from this model are reported next to the equivalent result of the unadjusted model and the adjusted model in Table 5.4 and Table 5.5 for IHD and AMI respectively. The unadjusted model will yield the same results as in the descriptive analysis and the adjusted model is the same one as used for the results in Figure 5.14.

Incidence rate ratios for IHD death

≤6.65 1.23 (1.20-1.27) 1.12 (1.08-1.15) 1.13 (1.10-1.16) ]6.65,10.3] 1.14 (1.11-1.18) 1.06 (1.03-1.06) 1.07 (1.04-1.08) ]10.3,14.6] 1.11 (1.0.8-1.14) 1.05 (1.02-1.08) 1.05 (1.02-1.08) ]14.6,21.9] 1.08 (1.05-1.12) 1.03 (1.00-1.06) 1.04 (1.01-1.07)

>21.9 1 - 1 - 1

-Table 5.4: -Table showing the incidence rate ratios for IHD between exposure group 5 as reference and all other exposure groups. The IRRs are shown for the unadjusted model, the adjusted model and the model with interactions.

Incidence rate ratios for AMI death

≤6.65 1.38 (1.33-1.44) 1.24 (1.19-1.29) 1.25 (1.19-1.30) ]6.65,10.3] 1.31 (1.26-1.37) 1.19 (1.14-1.24) 1.20 (1.15-1.25) ]10.3,14.6] 1.24 (1.19-1.30) 1.15 (1.10-1.20) 1.16 (1.11-1.21) ]14.6,21.9] 1.20 (1.14-1.25) 1.13 (1.08-1.18) 1.13 (1.08-1.18)

>21.9 1.00 - 1.00 - 1.00

-Table 5.5: -Table showing the incidence rate ratios for AMI between exposure group 5 as reference and all other exposure groups. The IRRs are shown for the unadjusted model, the adjusted model and the model with interactions.

The result from the model with interactions are very similar to the ones from the adjusted model with just slightly larger IRRs. Thus, the results seem robust to the addition of these interaction terms.

Models with effect modification

Another possible misspecification of the original adjusted model is that there might exist some effect modifiers. The effect of magnesium exposure might be affected by some of the confounders and therefore it was examined whether adding this effect to the model would change the results.

The effect modifiers taken into account was both gender and age categories. However, adding the gender and age separately did not prove to have a significant effect, but adding an effect modification as a combination of both of them was significant. All the incidence rates resulting from that are not reported here, but instead an analysis based only on individuals aged 70 or more shows that high levels of magnesium might actually be more important to elderly people than younger.

The analysis based on 70+ year-olds and the original adjusted model gives incidence rate ratios between the highest and lowest exposed group of 1.28 with the confidence interval ranging from 1.22 to 1.35 for AMI. This is should be compared to the 1.24 IRR from the main analysis.

Finally, an attempt in relation to effect modification was made to see if the effect of magnesium might change over time. Using the calender year to modify the effect was significant but when looking at the incidence rate ratios for each year separately, it was evident that no trend was present and that by adding this effect only some random variation was modelled. Since this is not of interest, these specific results are also not reported here.

Analysis including private wells

In the main analysis and all sensitivity analysis so far, the individuals supplied by their own well were not included. However, most of their addresses are located within water supply areas and they could thus be included by assuming their exposure was equal to the exposure of the surrounding area. As mentioned earlier, it is uncertain whether that is a valid assumption or not. In order to examine this a bit further, a sensitivity analysis including these individuals has been carried out. This meant that more than half a million more observations were added to the final data set. The results of this extended analysis were almost identical to the results of the main analysis. When rounded to three significant digits no differences in the IRRs were present. Thus, it can be concluded that assuming the exposure of the private well owners was the same as in the surrounding area did not change the results at all.

Chapter 6

Discussion

In this chapter the study and project in general will be discussed. This includes reflections and recommendations of further work that could be done to affirm the results or potentially reject them. The first part of the discussion will include a summary of results and a discussion on their validity. Then the strengths and limitations of the study and study design will be discussed.

After that there is a discussion on the estimations of magnesium and the matching process of addresses to WSAs. At the end the perspectives of the study will be discussed.

6.1 The results

The results of the present study showed a significant protective effect of magnesium in drinking water on ischemic heart disease and in particular on acute myocardial infarction. The results showed that individuals from the least exposed group have 24% greater risk of dying from AMI than individuals from the most exposed group. In fact, the analysis showed a significantly greater risk for all exposure groups compared to the highest exposure group. A sensitivity analysis also indicated that older individuals might be more affected by the magnesium concentration of their drinking water. They had a 28% increased risk of AMI for the lowest versus highest exposure group.

For both cardiovascular death in general and specifically stroke no significant and meaningful relations between incidence rates and magnesium exposure levels were found.