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 Neomycin.

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

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

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

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

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

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

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

1.2 Robust Pearson correlation results

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

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

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.178
##  x2 0.178     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.188
##  x2 0.188
Figure 10: Cross correlation of age group 56 and Neomycin.

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

## 
## Matrix of Pearson correlations
## 
##        x1    x2
##  x1     1 0.310
##  x2 0.310     1
## 
## Matrix of p-values
## 
##        x1    x2
##  x1       0.074
##  x2 0.074
Figure 15: Cross correlation among all age groups (x1 for 55, x2 for 56 and x3 for 57), Neomycin (x4) and E.coli (x5).

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

## 
## Matrix of Pearson correlations
## 
##        x1    x2    x3
##  x1     1 0.670 0.178
##  x2 0.670     1 0.310
##  x3 0.178 0.310     1
## 
## Matrix of p-values
## 
##        x1    x2    x3
##  x1       0.139 0.188
##  x2 0.139       0.074
##  x3 0.188 0.074

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 transformation for stationarity was applied to the time series values for age group 56. Age group 57 was excluded from analysis due to many zero entries.

Negative cross-correlation between age group 55 and Neomycin usage was verified at lag 7 suggesting higher resistance leads to lower usage 7 months later for this age group. There were no cross-correlations meeting the required threshold values of significance for robust or standard methods for age group 56. Pearson correlation identified a significant and positive correlation between age group 56 usage and Neomycin resistance.

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.