Study of the relationship between bacterial resistance and antimicrobial consumption

5.1. Study of the relationship between bacterial resistance and antimicrobial consumption

We studied the temporal relationship between hospital ceftazidime use and

454 José-María López-Lozano et al. Hospital Vega Baja, a 400-bed general hospital in Southern Spain (López-Lozano

et al., 2000b). During the period July 1991–December 1998, the clinical microbi- ology laboratory isolated 6,244 non-duplicate (López-Lozano et al., 2003) Gram- negative bacilli from hospital inpatients. The average observed monthly percentage of ceftazidime-resistant/intermediate Gram-negative bacilli was 3.3% (extremes: 0–10.9%) (Figure 3).

Based on these monthly data, we built an ARIMA model to predict the per- centage of ceftazidime-resistant/intermediate Gram-negative bacilli. Following Box and Jenkins method, we found that time series had a stationary variance and mean, and therefore did not require stationarization. We identified an ARIMA model with two significant autoregressive terms of order (lag) 3 and

5 (months). The series residuals corresponded to white noise. The Akaike Information Criterion (AIC) was 659 and the determination coefficient (R 2 )

0.38. Between July 1991 and December 1998, the average observed monthly hospital ceftazidime use was 4.4 DDD/1,000 patient-days (extremes: 0–15.0) (Figure 3). On the basis of these monthly data, we built a second ARIMA model to predict ceftazidime use. We identified an ARIMA model with two significant autoregressive terms of order (lag) 1 and 3 (months). We verified that the series residuals corresponded to white noise.

To investigate a possible relationship between the percentage of cef- tazidime-resistant/intermediate gram-negative bacilli and hospital ceftazidime use, we built a transfer function model. The cross-correlation function (CCF) of the series of residuals obtained from the two previous ARIMA models showed only one significant correlation (parameter: 0.399, SE: 0.105) with a lag of 1 month between the hospital ceftazidime use series and the percentage of ceftazidime-resistant/intermediate Gram-negative bacilli series. We intro- duced a 1-month lag in the ceftazidime use series and estimated the parameters of an ARIMA(0, 0, 0) model with the lagged ceftazidime use series as the only dynamic predicting factor. Examination of the CCF of this last model residuals series with the ceftazidime use residuals series showed no other significant lag. Examination of the autocorrelation function (ACF) and the partial auto- correlation function (PACF) of the transfer function to determine the stochas- tic part of the model showed a good adjustment with two autoregressive terms of order 3 and 5. The series residuals corresponded to white noise. The para- meters of the final transfer function model are presented in Table 1. The AIC

was 416 and the R 2 ⫽ 0.44. To predict the percentage of ceftazidime-resistant/intermediate Gram- negative bacilli by using this transfer function model and thus taking into account hospital ceftazidime use, we first needed to predict hospital cef- tazidime use for the first 6 months of 1999. Then we predicted the percentage of ceftazidime-resistant/intermediate Gram-negative bacilli for the first 6 months of 1999 as 8.0, 4.7, 3.9, 4.5, 4.2, 3.4, and 4.2, respectively; which is slightly

Applications of Time-series Analysis 455

Table 1. Transfer function model for percentage ceftazidime-resistant/intermediate Gram- negative bacilli taking into account hospital ceftazidime use, Hospital Vega Baja, Orihuela,

Spain, 1991–8 (R 2 ⫽ 0.44) (López-Lozano et al., 2000b) Independent variable

T-statistic P-value Constant

Lag (months)

Coefficient (SE)

1.78 0.078 Ceftazidime use

different from what was obtained when predicting on the basis of the resistance series alone (data not shown). Finally, to give a graphical representation of the relationship between the series, we plotted both the smoothed resistance and use series using a 5-month moving average transformation (Figure 4). This figure showed an increasing trend in ceftazidime use but no trend for the per- centage of ceftazidime-resistant/intermediate Gram-negative bacilli.

The model allows us to adjust an equation in which the present level of resistance would be a function of: (1) the level of resistance seen 3 months and

5 months before, and (2) ceftazidime use 1 month before in the same hospital. Note that the significant relationship is established with a delay of 1 month; it is not simultaneous. The interpretation of the parameter is: 1 DDD/1,000 patient-days, which is equivalent to 6.5 days of treatment approximately, would imply that resistance would increase 0.42% 1 month later, that is to say, it would change from R ⫽ 5% to R ⫽ 5.42%.