AMU and AMR correlations- Tetracyclines
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: Plots of the original data.
Figure 2: Logged dataplots. ALR values are already in log scale, so the logged transformation was performed for the age group variables.
1.1 Robust and Standard Cross-Correlation results
Figure 3: Cross correlation of age group 55 and Tetracycline.
Figure 3: Cross correlation of age group 55 and Tetracycline.
Figure 4: Cross correlation of age group 56 and Tetracycline.
Figure 4: Cross correlation of age group 56 and Tetracycline.
Figure 5: Cross correlation of age group 57 and Tetracycline.
Figure 5: Cross correlation of age group 57 and Tetracycline.
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 Tetracycline.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 0.053
## x2 0.053 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.756
## x2 0.756
Figure 10: Cross correlation of age group 56 and Tetracycline.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.140
## x2 -0.140 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.409
## x2 0.409
Figure 11: Cross correlation of age group 57 and Tetracycline.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.076
## x2 -0.076 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.634
## x2 0.634
Figure 12: Cross correlation of age group 55 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.347
## x2 -0.347 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.056
## x2 0.056
Figure 13: Cross correlation of age group 56 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.316
## x2 -0.316 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.066
## x2 0.066
Figure 14: Cross correlation of age group 57 and E. coli.
##
## Matrix of Pearson correlations
##
## x1 x2
## x1 1 -0.153
## x2 -0.153 1
##
## Matrix of p-values
##
## x1 x2
## x1 0.189
## x2 0.189
Figure 15: Cross correlation among all age groups(x1 for 55, x2 for 56 and x3 for 57), Tetracycline (x4) and E.coli (x5).
##
## Matrix of Pearson correlations
##
## x1 x2 x3 x4
## x1 1 0.637 0.600 -0.347
## x2 0.637 1 0.820 -0.316
## x3 0.600 0.820 1 -0.153
## x4 -0.347 -0.316 -0.153 1
##
## Matrix of p-values
##
## x1 x2 x3 x4
## x1 0.011 0.008 0.056
## x2 0.011 0.001 0.066
## x3 0.008 0.001 0.189
## x4 0.056 0.066 0.1892 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. This double difference may have produced over-differencing in time-series data and as a result negative correlations should be regarded with caution.
There was no significant association between age group 55 and Tetracycline antimicrobial resistance under both cross-correlations methods. However, for the robust method alone, a significant and negative cross-correlation was present for age group 55 and Tetracycline ALR at lag 3. This suggests that higher than average Tetracycline resistance is associated to lower usage among these age groups 3 months later. Under both methods, positive cross-correlation was identified for age group 56 and Tetracycline ALR at lags -10 and 10, being stronger for the -10, and significant but negative cross-correlation was identified at lags -9 and -18, being stronger for the -9. The positive cross-correlation at -10 suggests higher usage in this age group leads to higher resistance 10 months later, while the also strong but negative cross correlation at lag -9 suggests higher usage leads to lower resistance. The information is conflicting and results are therefore inconclusive for age group 56. For age group 57 and Tetratcycline resistance, significant negative cross-correlation was identified at -18 lag, suggesting higher usage leads to lower resistance. For age group 57 and E.coli, significant and negative cross correlation was found at lag -9, suggesting higher usage in this group leads to lower resistance. Pearson cross-correlation methods failed to identify moments of positive correlation. For this approach, over-differencing for stationarity may have resulted in the negative correlations for age groups 55 and 56 and E.coli resistance.
Once differenced variables ACF plots (not shown) produced negative and bellow -0.5 autocorrelation at lag-1 for age groups 56 and 57, indicating further differencing was not needed. However, and to achieve stationarity by the ADF and KPSS tests, a second difference was determined and these twice differenced age groups, metagenome and phenotype variables may have been over-differenced.The cross-correlations found in this analysis should therefore be interpreted conservatively.
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.