AMU and AMR correlations- Erythromycin

arpm@dtu.dk

There are two sections to this report: robust cross-correlation and Pearson cross-correlation.

1 Cross-Correlation

Figure 1: The original data.

Figure 2: Logged data. Performed for the age group variables.

1.1 Robust and Standard Cross-Correlation results

Figure 3: Cross correlation of age group 55 and Erythromycin.

Figure 3: Cross correlation of age group 55 and Erythromycin.

Figure 4: Cross correlation of age group 56 and Erythromycin.

Figure 4: Cross correlation of age group 56 and Erythromycin.

Figure 5: Cross correlation of age group 57 and Erythromycin.

Figure 5: Cross correlation of age group 57 and Erythromycin.

1.2 Robust Pearson correlation results

Figure 9: Cross correlation of age group 55 and Erythromycin.

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.152
##  x2 0.152     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.286
##  x2 0.286

Figure 10: Cross correlation of age group 56 and Erythromycin.

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.241
##  x2 0.241     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.172
##  x2 0.172

Figure 11: Cross correlation of age group 57 and Erythromycin.

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.307
##  x2 0.307     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.042
##  x2 0.042

Figure 15: Cross correlation among all age groups (x1 for 55, x2 for 56 and x3 for 57), Erythromycin (x4) and E.coli (x5).

## 
## Matrix of Pearson correlations
## 
##        x1    x2    x3    x4
##  x1     1 0.780 0.799 0.152
##  x2 0.780     1 0.796 0.241
##  x3 0.799 0.796     1 0.307
##  x4 0.152 0.241 0.307     1
## 
## Matrix of p-values
## 
##        x1    x2    x3    x4
##  x1       0.000 0.000 0.286
##  x2 0.000       0.000 0.172
##  x3 0.000 0.000       0.055
##  x4 0.286 0.172 0.055

2 Results

This analysis considered the necessary case-by-case transformation of time-series data and the analysis of two correlation approaches (cross-correlation and Pearson bivariate/multivariate correlation), with robust and standard approaches, simulteaneously. The needed transformation applied to age 55 and 56 time series, in order to obtain stationarity, was a twice differenced logged value transformation. This double difference may have resulted in over-differencing and negative correlations should be regarded with caution. Age group 57 was differenced once for stationarity.

Cross correlation for age group 55 and Erythromycin ALR were positive for two lags (10 and -2) and negative for lag 11. For this age group, the two strongest cross-correlations were conflicting in their interpretation of the relationship between usage and resistance: positive cross-correlation at lag 10 suggests higher resistance leads to higher usage while the negative cross-correlation at lag 11 suggests higher resistance leads to lower usage in age group 55. The positive cross-correlation at lag -2 suggests higher usage leads to higher Erythromycin resistance. Age group 56 also showed varying cross-correlations, with positive value for lag -2 and 10 and negative at lag -1. The strongest cross-correlation at lag -2 suggests higher usage leads to higher Erythromycin resistance. Conflicting though less expressive cross-correlation was found at lag -1, suggests higher usage leads to lower Erythromycin resistance 1 month later. The positive cross-correlation at lag 10 suggests higher Erythromycin resistance leads to higher usage 10 months later.Age group 57 had positive cross-correlation with E.coli resistance for lag -5, which suggests higher usage leads to higher Erythromycin resistance 5 months later.

Pearson robust method identified positive correlation between age group 57 and erythromycin resistance for first order differencing, reinforced by the again verified positive correlation for a second order differencing in the full matrix of Pearson correlations. This mathces the finding in the cross-correlation analysis by robust and standard methods.

3 References

Dalla V, Giraitis L, Phillips PCB (2019). “Robust Tests for White Noise and Cross-Correlation.” Cowles Foundation, Discussion Paper No. 2194, URL https://cowles.yale.edu/sites/ default/files/files/pub/d21/d2194.pdf.