AMU and AMR correlations- Sulphonamides
Ana Rita Marques
17/10/2020
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 Sulphonamide.
Figure 3: Cross correlation of age group 55 and Sulphonamide.
Figure 4: Cross correlation of age group 56 and Sulphonamide.
Figure 4: Cross correlation of age group 56 and Sulphonamide.
Figure 5: Cross correlation of age group 57 and Sulphonamide.
Figure 5: Cross correlation of age group 57 and Sulphonamide.
Figure 6: Cross correlation of age group 55 and E. coli.
Figure 6: Cross correlation of age group 55 and E. coli.
Figure 7: Cross correlation of age group 56 and E. coli.
Figure 7: Cross correlation of age group 56 and E. coli.
Figure 8: Cross correlation of age group 57 and E. coli.
Figure 8: Cross correlation of age group 57 and E. coli.
1.2 Robust Pearson correlation results
Figure 9: Cross correlation of age group 55 and Sulphonamide.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.395
## x2 0.395 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.030
## x2 0.030
Figure 10: Cross correlation of age group 56 and Sulphonamide.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.325
## x2 0.325 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.039
## x2 0.039
Figure 11: Cross correlation of age group 57 and Sulphonamide.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.032
## x2 0.032 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.844
## x2 0.844
Figure 12: Cross correlation of age group 55 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.132
## x2 -0.132 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.269
## x2 0.269
Figure 13: Cross correlation of age group 56 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.283
## x2 -0.283 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.050
## x2 0.050
Figure 14: Cross correlation of age group 57 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.044
## x2 0.044 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.734
## x2 0.734
Figure 15: Cross correlation among all age groups(x1 for 55, x2 for 56 and x3 for 57), Sulphonamide (x4) and E.coli (x5).
##
## Matrix of Pearson correlations
##
## x1 x2 x3 x4 x5
## x1 1 0.669 -0.201 0.387 -0.125
## x2 0.669 1 -0.065 0.325 -0.283
## x3 -0.201 -0.065 1 0.068 0.063
## x4 0.387 0.325 0.068 1 -0.026
## x5 -0.125 -0.283 0.063 -0.026 1
##
## Matrix of p-values
##
## x1 x2 x3 x4 x5
## x1 0.001 0.346 0.011 0.345
## x2 0.001 0.652 0.039 0.050
## x3 0.346 0.652 0.680 0.693
## x4 0.011 0.039 0.680 0.852
## x5 0.345 0.050 0.693 0.8522 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 double-differenced transformation was applied to age group 56 and 57 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.
Positive cross-correlations were present for age group 55 and Sulphonamide ALR at lag 0, and then negative for lag 13. The strong cross-correlation at 0 shows that the usage in this age group and resistance to Sulphonamides are strongly contemporaneously correlated. This strong positive correlation can indicate that both series respond similarly and simultaneously to some other exogenous factors. The negative cross-correlation at lag 13 suggests that high resistance can lead to high usage in this age group as well and 13 days later. Positive cross-correlation was identified only for age group 56 cross-correlation with Sulphonamide ALR at 0 lag for the robust method alone, suggesting that in this age group usage and resistance to Sulphonamides are also strongly contemporaneously correlated. Negative cross-correlation was identified for age group 55 and E.coli resistance at -9, suggesting high usage leads to low resistance. For age group 56 there was positive cross-correlation at lags -1, suggesting high usage leads to high resistance one month later, while positive correlation at lag 4 suggests high resistance to Sulphonamides leads to high usage in this age group.
Pearson cross-correlation methods identified moments of positive correlation for age groups 55 and 56 and Sulphonamides, and negative cross-correlation for age group 56 and E.coli when using double-differenced series, the later possibly due to over-differencing.
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.