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

1 Cross-Correlation

Figure 1: The original data.

Figure 1: The original data.

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

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 Lincosamide.

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

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

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

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

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

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

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

Figure 4: Cross correlation of age group 57 and Lincosamide.

Figure 4: Cross correlation of age group 57 and Lincosamide.

Figure 4: Cross correlation of age group 57 and Lincosamide.

Figure 4: Cross correlation of age group 57 and Lincosamide.

1.2 Robust Pearson correlation results

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

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

## 
## Matrix of Pearson correlations
## 
##         x1     x2
##  x1      1 -0.042
##  x2 -0.042      1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.755
##  x2 0.755
Figure 10: Cross correlation of age group 56 and Lincosamide.

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

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.060
##  x2 0.060     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.679
##  x2 0.679
Figure 10: Cross correlation of age group 56 and Lincosamide.

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

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.160
##  x2 0.160     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.179
##  x2 0.179
Figure 15: Cross correlation among all age groups (x1 for 55, x2 for 56 and x3 for 57), Lincosamide (x4) and E.coli (x5).

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

## 
## Matrix of Pearson correlations
## 
##         x1     x2     x3     x4
##  x1      1  0.600  0.664 -0.039
##  x2  0.600      1  0.723  0.060
##  x3  0.664  0.723      1  0.160
##  x4 -0.039  0.060  0.160      1
## 
## Matrix of p-values
## 
##        x1    x2    x3    x4
##  x1       0.004 0.001 0.781
##  x2 0.004       0.001 0.679
##  x3 0.001 0.001       0.179
##  x4 0.781 0.679 0.179

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. A double difference may have result in over-differencing and negative correlations should be regarded with caution: age group 56 and 57 were differenced twice for stationarity.

No significant cross-correlations were identified between the two methods of choice for age group 55. For age group 56 and Lincosamide resistance, positive cross-correlations were found at lags 10, 11 and -2 and negative associations for lags 11 and 9. These results suggest that higher Lincosamide resistance leads to both higher and lower usage in age group 56, while there is also evidence of higher usage in age group 56 leading to higher resistance. Age group 57 presented positive cross-correlations at lag 10 and had negative associations at lags 11, 9, and -1, suggesting that higher Lincosamide resistance leads to both higher and lower usage in age group 57 and higher resistance can also lead to higher usage. Pearson correlation failed to identify significant associations.

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.