AMU and AMR correlations- Amphenicol
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 Amphenicol.
Figure 3: Cross correlation of age group 55 and Amphenicol.
Figure 4: Cross correlation of age group 56 and Amphenicol.
Figure 4: Cross correlation of age group 56 and Amphenicol.
Figure 5: Cross correlation of age group 57 and Amphenicol.
Figure 5: Cross correlation of age group 57 and Amphenicol.
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 Amphenicol.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.059
## x2 0.059 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.648
## x2 0.648
Figure 10: Cross correlation of age group 56 and Amphenicol.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.185
## x2 0.185 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.290
## x2 0.290
Figure 11: Cross correlation of age group 57 and Amphenicol.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.270
## x2 -0.270 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.248
## x2 0.248
Figure 12: Cross correlation of age group 55 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.038
## x2 -0.038 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.793
## x2 0.793
Figure 13: Cross correlation of age group 56 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.305
## x2 -0.305 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.055
## x2 0.055
Figure 14: Cross correlation of age group 57 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.170
## x2 0.170 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.260
## x2 0.260
Figure 15: Cross correlation among all age groups (x1 for 55, x2 for 56 and x3 for 57), Amphenicol (x4) and E.coli (x5).
##
## Matrix of Pearson correlations
##
## x1 x2 x3 x4 x5
## x1 1 0.173 -0.056 0.059 -0.169
## x2 0.173 1 -0.142 0.185 -0.297
## x3 -0.056 -0.142 1 -0.270 0.148
## x4 0.059 0.185 -0.270 1 -0.204
## x5 -0.169 -0.297 0.148 -0.204 1
##
## Matrix of p-values
##
## x1 x2 x3 x4 x5
## x1 0.352 0.706 0.648 0.232
## x2 0.352 0.350 0.290 0.085
## x3 0.706 0.350 0.248 0.332
## x4 0.648 0.290 0.248 0.125
## x5 0.232 0.085 0.332 0.125
Figure 15: Cross correlation among all age groups (x1 for 55, x2 for 56 and x3 for 57), Amphenicol (x4) and E.coli (x5).
##
## Matrix of Pearson correlations
##
## x1 x2 x3 x4 x5
## x1 1 0.092 -0.039 0.097 -0.038
## x2 0.092 1 -0.090 0.133 -0.305
## x3 -0.039 -0.090 1 -0.298 0.170
## x4 0.097 0.133 -0.298 1 -0.198
## x5 -0.038 -0.305 0.170 -0.198 1
##
## Matrix of p-values
##
## x1 x2 x3 x4 x5
## x1 0.643 0.801 0.460 0.793
## x2 0.643 0.552 0.399 0.055
## x3 0.801 0.552 0.149 0.260
## x4 0.460 0.399 0.149 0.147
## x5 0.793 0.055 0.260 0.1472 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 all time series, in order to obtain stationarity, was a twice differenced logged value transformation for Ampheniclo cross-correlqation and a one time differencing for E.coli cross-correlations. This double difference may have resulted in over-differencing for Amphebnicl estimates, and negative correlations should be regarded with caution.
There were simultaneous positive and negative associations for age group 55 and Amphenicol, positive at lags -4 and -17 and negative at lags -5, -7 and -18. Positive cross correlations at negative lags suggest higher usage is associated with higher resistance, while negative cross correlations at negative lags suggest higher usage is associated with lower resistance. As such, these are conflicting cross-correlations. However, negative correlations may be disregarded given the double differencing of the time-series values. Both methods were also satisfied for age group 56 and Amphenicol cross-correlation with a negative value at lag 4 suggesting higher resistance leads to lower usage in this age group. This age group was only differenced once, adding to the relevance of the negative results, which may be spurious nevertheless. Positive and negative cross-correlations were present for age group 57 and Amphenicol cross-correlation as well, for lags -14 and -15, respectively. Much like the results for age group 55, these are conflicting results, where higher usage in this age group can lead to both increased and decreased resistance to Amphenicol. Age group 57 and E.coli resistance were significantly and negatively correlated for both approaches at lag -17 suggesting higher usdage in this age group leads to lower resistance in E.coli, Pearson correlations were significant for the negative association between age group 56 and E.coli resistance, for both single and double differenced time-series.
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.