2.8 Results using GSTT Data
2.8.1 p-MRSA Data Set
For the analysis of the p-MRSA Data Set, 382 patients were considered whose summary statistics are shown in Tables 2.9 and 2.10.
Results excluding antimicrobial treatment
We fitted the model assuming that there was no information about antimicro-bial treatment. The results using MLE, the summary statistics of the posterior distributions and the posterior correlation between p0and q0are given in Table 2.11. The density plots in Figure 2.5 show the results from MCMC.
no antimicrobial treatment
parameters MLE (st. error) E[ · |S](s.d.) p0 0.8697(0.0147) 0.8537(0.0403) q0 0.1284(0.0158) 0.1455(0.0426) p0, q0posterior correlation −0.9702
Table 2.11:MLEs, summary statistics for parameters p0 and q0 and posterior correlation between p0 and q0 for the p-MRSA Data Set ignoring antimicrobial treatment.
0.75 0.80 0.85 0.90
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Kernel Density Estimate for p0
p0
Density
0.10 0.15 0.20 0.25
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Kernel Density Estimate for q0
q0
Density
Figure 2.5:Kernel density plots for p0 and q0 from the p-MRSA Data Set as-suming no antimicrobial treatment.
We perform the chi-squared goodness-of-fit test using the p-MRSA Data Set using the transitions of one day, two days, three days etc. up to one week day intervals. The results are displayed in Table 2.12. We can see that the model does not fit very well as some of the values of χ22 are much bigger than the critical value χ22 = 13.82 at the 0.001 significance level. The sum of χ22(i), i = 1, ...7, ∑7i=1χ22(i) = 102.6351 also shows that the model does not fit well using the critical value χ214 =36.12 at the 0.001 significance level. Table 2.13 presents the results from the simulations. It can be seen that the results are in agreement with the results from the chi-squared goodness-of-fit tests. A plausible reason for this is that the model is too simplistic, ignoring antimicrobial use.
Goodness of fit Day Intervals
1 2 3 4 5 6 7
χ22 35.6432 6.4387 5.9308 13.677 0.9297 2.5234 37.4817 Table 2.12:Chi-squared statistic for the model using the p-MRSA Data Set
ig-noring antimicrobial treatment. Table 2.13:Model fit for the model of the p-MRSA Data Set without
antimi-crobial treatment. The intervals in red color show that the equal-tailed 95% quantiles include the number of the observed transition counts.
Including antimicrobial treatment
We also obtain estimates from the model including the information about an-timicrobial treatment. The results from the MLEs and the summary statistics of the posterior distributions are given in Table 2.14. The posterior correla-tions between p0, q0, α and β are shown in Figure 2.6. It can be seen that all the parameters are highly correlated. Figure 2.7 shows the posterior density plots of p0+α and q0+β which are the probabilities that a patient remains in a non-colonised state and goes from a colonised state to a non-colonised state re-spectively when they are “on” antimicrobial treatment, along with the density plots of p0and q0which are the same probabilities but when patients are “off”
antimicrobial treatment. In broad terms, it appears that there is some effect on the transition matrix from receiving antimicrobials.
Table 2.15 shows the equal-tailed 95% quantiles from the model fit simulations.
In the same table there are also the observed counts for each day interval and transition. We can see that the model does not fit very well as many of the observed counts are outside the equal-tailed 95% quantiles.
A reason for this is that the model including antimicrobial treatment is probably
still not detailed enough to give a good fit to the data. After the classification of the antimicrobials, it is possible to get better answers since each antimicrobial’s contribution to the model is different.
Antimicrobial treatment
parameters MLE (st. error) E[ · |S](s.d.) p0 0.7142 (0.0743) 0.6893 (0.1373) q0 0.2416 (0.0669) 0.2721 (0.1266) α 0.1825 (0.0759) 0.1591 (0.1104) β −0.1313(0.0682) −0.1109(0.0971)
Table 2.14:MLEs and summary statistics for p0, q0, α and β using the p-MRSA Data Set including antimicrobial treatment.
p0
0.1 0.3 0.5 0.7 −0.4 −0.2 0.0 0.1
0.20.40.60.8
0.10.30.50.7
q0
α
0.00.20.4
0.2 0.4 0.6 0.8
−0.4−0.20.0
0.0 0.1 0.2 0.3 0.4 0.5
β Posterior Correlations
Figure 2.6:Posterior correlations between p0, q0, α and β using the p-MRSA Data Set including antimicrobial treatment.
Day Intervals
1 2 3 4 5 6 7
obs. counts 17 19 19 8 17 31 243
N→N (17, 25) (16, 25) (16, 25) (10, 20) (12, 23) (23, 38) (178, 216)
obs. counts 10 11 15 18 14 26 132
N→C (2, 10) (4, 14) (8, 18) (6, 15) (8, 18) (19, 33) (159, 196)
obs. counts 8 11 8 12 10 26 72
C→N (1, 6) (4, 14) (3, 10) (9, 19) (8, 18) (16, 30) (106, 138)
obs. counts 7 20 9 21 20 24 185
C→C (9, 14) (16, 27) (7, 14) (14, 24) (12, 22) (19, 34) (118, 151) Table 2.15:Model fit for the model using the p-MRSA Data Set including
an-timicrobial treatment. The intervals in red color show that the equal-tailed 95% quantiles include the number of the observed transition counts.
0.2 0.4 0.6 0.8 1.0
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Kernel Density Plot for p0 and p0+ α
Density
density p0+ α density p0
0.2 0.4 0.6 0.8
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Kernel Density Plot for q0 and q0+ β
Density
density q0+ β density q0
Figure 2.7:Kernel density plots for p0and p0+α, q0and q0+β for the p-MRSA Data Set including antimicrobial treatment.
Starting from first positive test
Here we obtain the parameter estimates from the model including antimicrobial treatment starting from the date that a patient was first found colonised. The reason is that in this chapter we only look at the MRSA carriage levels on each patient separately. We do not take into account that there is MRSA transmission between the patients which is unrealistic in some sense. So, starting from a patient’s first positive test is one way to overcome this restriction.
The number of patients with at least one transition was 290. The results from the MLEs and the MCMC are given in Table 2.16. The density plots of p0+α and q0+β along with the density plots of p0and q0are given in Figure 2.8.
The results of the equal-tailed 95% quantiles of the simulations for the model fit are given in Table 2.17 along with the transition counts from the observed data.
We can see that the model does not fit well as some of the observed transitions counts are again outside the equal-tailed 95% intervals.
starting from first positive test Data Set including antimicrobial treatment and starting from pa-tients’ first positive test. Table 2.17:Model fit for the model using the p-MRSA Data Set including
an-timicrobial treatment and starting from patients’ first positive test.
The intervals in red indicate that the observed transition counts are included in the equal-tailed 95% quantiles.
0.6 0.7 0.8 0.9 1.0
01020304050
Kernel Density Plot for p0 and p0+ α
Density
density p0+ α density p0
0.05 0.10 0.15 0.20 0.25
010203040
Kernel Density Plot for q0 and q0+ β
Density
density q0+ β density q0
Figure 2.8:Kernel density plots for p0and p0+α, q0and q0+β for the p-MRSA Data Set including antimicrobial treatment and starting from pa-tients’ first positive test.
Classification of the antimicrobial treatment
So far, we have considered the antimicrobial treatment as a whole. However, only a few antimicrobials were actually MRSA-targeting. These include Chlorhex-idine, which is an antiseptic and was mostly used during the decolonisation pe-riod. Other antimicrobials were Vancomycin and Linezolid which are known to be MRSA targeting (Section 1.2.1). The MLEs and the MCMC results consider-ing Chlorhexidine, Linezolid and Vancomycin as one group, are given in table 2.18. Figure 2.9 shows the posterior density plots of p0+α and q0+β along with the density plots of p0and q0. Comparing this plot with the one in Figure 2.7, we can see that MRSA targeting antimicrobial treatment may have an effect in clearing MRSA carriage.
The results from the equal-tailed 95% quantiles from the simulations for the model fit are shown in Table 2.19. Again, we can see that the model fit is not adequate.
MRSA targeting antimicrobials targeting antimicrobials from p-MRSA Data Set.
Day Intervals Table 2.19:Model Fit for the model using MRSA targeting antimicrobials of the
p-MRSA Data Set. The intervals in red indicate that the observed transition counts are included in the equal-tailed 95% quantiles.
Considering each antimicrobial separately
In this section we are presenting only the MCMC results. The reason is that for some of the antimicrobials we were not able to get estimates via MLE due to the fact that the likelihood is very flat, causing numerical problems for the optimisation methods.
It is known that some of the antimicrobials are more effective than others in treating MRSA. For this reason we fit the model to data which consist of one antimicrobial treatment only . This means that for each group we assume that a patient is “on” a antimicrobial treatment the day they take this particular an-timicrobial, otherwise they are considered “off” antimicrobial treatment mean-ing that they are not receivmean-ing any antimicrobial treatment.
Tables A.1, A.2 and Figures A.1, A.2 show the results from the MCMC for the parameters for each antimicrobial group when all patients’ tests are included.
It can be seen that patients on Oxazolidinone and Penicillin are more likely to be protected against MRSA carriage. Moreover, patients on Oxazolidinone, Ri-famycin and Polymyxin have a higher probability to be cleared while Macrolide
0.5 0.6 0.7 0.8 0.9 1.0
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Kernel Density Plot for p0 and p0+ α
Density
density p0+ α density p0
0.05 0.15 0.25 0.35
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Kernel Density Plot for q0 and q0+ β
Density
density q0+ β density q0
Figure 2.9:Kernel density plots for p0and p0+α, q0and q0+β for the MRSA targeting antimicrobials from p-MRSA Data Set.
has a smaller probability to protect a patient against MRSA. It is also noted that decolonisation treatment using Chlorhexidine (Antiseptic) seems to be effec-tive.
The results of the equal-tailed 95% quantiles from the simulations for the model fit are shown on Table A.3. The equal-tailed 95% quantiles for each antimicro-bial group are compared with the number of observed counts for each day in-terval and each transition . It can be seen that the model does not fit very well as some of the equal-tailed 95% intervals do not include the observed transition counts.
Next, we obtained the parameter estimates for all antimicrobial groups starting from the date that a patient was first found colonised. Tables A.5, A.6 and Fig-ures A.3, A.4 show the results from the MCMC for the parameters p0, q0, α and β for each antimicrobial group. The results show that patients on Aminoglyco-side, Penicillin, Glycopeptide and Nitroimidazole can prevent against coloni-sation. On the other hand, colonised patients on Oxazolidinone are more likely to become non-colonised while Quinolone has the opposite effect.
The equal-tailed 95% quantiles from the simulations for the model fit in Table A.7 show that there has been some improvement but again some of the ob-served transitions counts are outside the equal-tailed 95% intervals.