Utilization of Vector Autoregressive and Linear Transfer Models to Follow Up the Antibiotic Resistance Spiral in Gram-negative Bacteria From Cephalosporin Consumption to Colistin Resistance

Abstract

Background

Increasing antibiotic resistance may reciprocally affect consumption and lead to use of broader-spectrum alternatives; a vicious cycle that may gradually limit therapeutic options. Our aim in this study was to demonstrate this vicious cycle in gram-negative bacteria and show the utility of vector autoregressive (VAR) models for time-series analysis in explanatory and dependent roles simultaneously.

Methods

Monthly drug consumption data in defined daily doses per 100 bed-days and incidence densities of gram-negative bacteria (Escherichia coli, Klebsiella spp., Pseudomonas aeruginosa, and Acinetobacter baumannii) resistant to cephalosporins or to carbapenems were analyzed using VAR models. These were compared to linear transfer models used earlier.

Results

In case of all gram-negative bacteria, cephalosporin consumption led to increasing cephalosporin resistance, which provoked carbapenem use and consequent carbapenem resistance and finally increased colistin consumption, exemplifying the vicious cycle. Different species were involved in different ways. For example, cephalosporin-resistant Klebsiella spp. provoked carbapenem use less than E. coli, and the association between carbapenem resistance of P. aeruginosa and colistin use was weaker than that of A. baumannii. Colistin use led to decreased carbapenem use and decreased carbapenem resistance of P. aeruginosa but not of A. baumannii.

Conclusions

VAR models allow analysis of consumption and resistance series in a bidirectional manner. The reconstructed resistance spiral involved cephalosporin use augmenting cephalosporin resistance primarily in E. coli. This led to increased carbapenem use, provoking spread of carbapenem-resistant A. baumannii and consequent colistin use. Emergence of panresistance is fueled by such antibiotic-resistance spirals.

time-series analysis, antibiotic consumption, carbapenem resistance

Antibiotic consumption is a key selection force for multiresistance [1–9], as documented extensively using linear regression/correlation and time-series analysis [1, 4–6, 8–13]. In theory, when high prevalence of resistance becomes sustained, concern arises among prescribers, leading to preference for broader-spectrum drugs, their overuse, and subsequent emergence of resistance to them. This poses additional concern, leading to usage of even broader-spectrum drugs with consequent resistance and further concern until all therapeutic options are compromised by the developing resistance (Figure 1). This process, termed the “antibiotic spiral” by Carlet et al [3], may become a vicious cycle, threatening selection of panresistant strains [14]. This has been seen with Staphylococcus aureus going from methicillin susceptibility to methicillin resistance and to vancomycin intermediate susceptibility (methicillin-susceptible S. aureus to methicillin-resistant S. aureus [MRSA] and to vancomycin-intermediate S. aureus) [15]. It has also been seen with Klebsiella pneumoniae ST147 going from cephalosporin use to cephalosporin resistance, leading to increased carbapenem use and then to carbapenem resistance, which in turn provoked increasing colistin use [16]. Though the use–resistance relationship is well studied, the vicious cycle as a whole remains a widely accepted, but not proven, theoretical concept that is receiving little research attention.

Figure 1.

Schematic representation of the resistance spiral, prepared based on the idea presented by Carlet et al [3].

This may be due mainly to methodological difficulties. Numerous studies use correlation or linear regression analysis, which is frequently inappropriate as antibiotic use–resistance data violate the important assumption that data points should be independent [8]. Time-series analysis, which is used to model stochastic processes in econometry, was adopted for such analyses [6, 8, 17]. Using linear transfer models (dynamic regression), an assumed cause-and-effect relationship between drug use and resistance was confirmed in various situations [1, 4, 9, 11]. These are stochastic versions of linear regression that use not only explanatory variables as predictors but also their lagged values, circumventing the above-mentioned problem [18]. They require predetermination of variables as explanatory (“cause’”) and dependent (“outcome”). Consequently, though dynamic regression is an excellent tool to model drug use–resistance relationships [1, 4, 9, 11], it is unable to capture interdependencies between the multiple explanatory and outcome variables that are required for follow-up on the above-mentioned spiral. Furthermore, relationships between drug use and resistance may be reciprocal, that is, as resistance to a drug increases, eventually it is replaced in empirical therapy by other drugs perceived to be more effective by prescribers [3]. Thus, growing resistance may not only promote usage of broader-spectrum drugs, but the drug affected will be used less frequently. Modeling of these back-and-forth relationships or multiple interdependencies is not efficient or even possible using dynamic regression, and different methods that do not prejudge the role of the variables involved, for example, vector autoregression (VAR) models, are needed [19, 20]. In VAR models, evolution of each time series is influenced by its own earlier values and by earlier values of all other variables [19]. Thus, all interactions among all variables are modeled at the same time, allowing for detection of various (including reciprocal) interactions between multiple variables simultaneously [19–22].

In this study, our goal was to capture cause-and-effect relationships among antibiotic consumption and the provoked resistance in order to expand our understanding of the ongoing antibiotic-resistance spiral. As gram-negative bacteria represent the most immediate problem in critically ill patients in the United States [23], Europe [24], and Hungary [13, 25], the gram-negative resistance spiral was examined. In this study, we compared VARs to dynamic regression used in earlier studies [1, 4, 9, 11] to demonstrate their utility in analyzing drug use–resistance relationships and in capturing the resistance spiral concept in real life.

METHODS

Data

The setting was a tertiary-care center in Hungary with 1667 beds. Monthly consumption (as obtained by wards from the clinical pharmacy) of all cephalosporins/third-generation cephalosporins alone, carbapenems, and colistin, expressed as defined daily doses per 100 occupied bed-days (OBDs) [26], was compared to resistance to cephalosporins, carbapenems, and colistin (incidence density of infections by resistant bacteria per 1000 OBDs) between October 2004 and August 2016. Resistance was monitored among Escherichia coli, Klebsiella spp. (K. pneumoniae and K. oxytoca together), Pseudomonas aeruginosa, and Acinetobacter baumannii isolated from inpatients. These were represented together (referred to as cumulated resistance) by summing resistance data of these species for each drug group. Multiple isolates of the same species isolated from 1 patient in the same month were included only once. There were no changes in infection control practices or antibiotic stewardship activities during the study period.

Hypothesis and Modeling Strategy

We hypothesized that consumption of antibiotics causes an increase in resistance against them, which in turn may result in increased use of a replacement drug, as hypothesized in the antibiotic-resistance spiral theory [3], and that increasing resistance to a certain drug group may result in its decreased use.

First, we built bivariate dynamic regression and VAR models using consumption–resistance or resistance–consumption pairs along the assumed resistance spiral (cephalosporin use–cephalosporin resistance, cephalosporin resistance–carbapenem use, carbapenem use–carbapenem resistance, carbapenem resistance–colistin use, and colistin use–colistin resistance). The effect of other relevant drug groups (aminoglycosides and fluoroquinolones) was also analyzed in dynamic regressions with multiple explanatory variables and in multivariate VAR models. Composite multivariate VAR models were also built with all variables to include the steps along the spiral in the same model.

Dynamic Regression Models

Models were built as described by Pankratz [18] and López-Lozano et al [6] using Eviews 3.1 (Quantitative Micro Software, Irvine, CA). The minimal adequate model was reached by step-by-step backward elimination of nonsignificant lags starting with lags 0–12. The resulting final models were tested for normality (Jarque–Bera test), autocorrelation (Ljung-Box test), and serial correlation (Breusch–Godfrey serial correlation Lagrange multiplier test) of residuals.

Vector Autoregression Models

VAR models were built in R package “vars” [27]. First, presence of unit root and/or trend was tested for each variable using augmented Dickey-Fuller tests (R package “fUnitRoots”). If any variable featured a trend, a trend component was included in the model. As a seasonal component was always detected for at least some variables, this was always included. Optimal lag was determined using the Akaike information criterion [28]. If the lag that was suggested resulted in an invalid model (serial correlation found in residuals), the lowest lag yielding a valid model was used instead. Model diagnosis included examination of residuals for normality, autocorrelation and partial autocorrelation, exclusion of their serial correlation using the multivariate Ljung-Box test, and stability tests using a cumulative sum control chart with ordinary least squares residuals.

VAR models were interpreted using impulse-response functions [19, 29], which explore cause-and-effect relationships within the model in a pairwise manner by applying a shock to a variable (impulse), then monitoring changes in the response variable for a predetermined time horizon (12 months). Confidence intervals were determined by bootstrapping (100 times; as provided in R package “vars”). If the response variable showed significant change within this horizon, it is likely that is was also affected by real-life changes of the impulse variable [29]. Notably, this relationship can be reciprocal; shocks applied to a variable formerly tested as response may generate response in the former impulse variable as well [21, 22]. As it was observed that deviation of the last few data points from the immediate trend of the series may strongly influence the model, modeling was performed in a rolling-window manner to eliminate this effect. All series were truncated by removing 1 through 8 of the most recent datapoints, and models were fitted to all truncated series. Relationships suggested by impulse responses in less than half of all rolling-window models were considered uncertain and were interpreted as lack of a relationship. The ready-to-use R script is provided in the Supplementary Material.

RESULTS

Drug Consumption and Incidence of Resistant Infections

Consumption of third-generation cephalosporins, carbapenems, and colistin as well as resistance to these drug groups in E. coli, Klebsiella spp., P. aeruginosa, and A. baumannii are shown in Figure 2. The series of carbapenem and colistin consumption as well as of carbapenem resistance of gram-negative bacteria and A. baumannii showed an increasing trend (P < .01 in all cases).

Figure 2.

Evolution of consumption of major drug groups (upper panel) in defined daily doses per 100 occupied bed-days (DDDs/100 OBDs) and changes in resistance densities of the major nosocomial gram-negative species (lower panel) in monthly incidence of infections by resistant bacteria per 1000 OBDs between October 2004 and August 2016. Ranges of monthly consumption for aminoglycosides, fluoroquinolones, colistin, cephalosporins, and carbapenems were 0.7–4.0, 3.7–17.9, 0.0–2.2, 4.2–14.5, and 0.4–4.8 DDDs/100 OBDs, respectively. Abbreviations: A. baumannii, Acinetobacter baumannii; E. coli, Escherichia coli; P. aeruginosa, Pseudomonas aeruginosa.

Resistance Spiral in Gram-negative Bacteria

Consumption of third-generation as well as all cephalosporins was associated with increasing cephalosporin resistance in dynamic regression and in bivariate VARs (Table 1, Figure 3). Inclusion of other drugs groups (fluoroquinolones and aminoglycosides) did not alter these results and showed no effect on cephalosporin resistance. Cephalosporin resistance was associated with increasing carbapenem usage without any reciprocal effect in VARs (cephalosporin resistance was not decreased by carbapenem use).

Table 1.

Relationships Found Between Drug Use and Cumulated Drug Resistance of All Gram-negative Bacteria in Bivariate Dynamic Regression and in Vector Autoregressive Models

Regressor/Impulse	Dependent Variable/Response	Dynamic Regression			Vector Autoregressive Models
					Lags and Highest Magnitude of Significant Response (95% CI) in the Response Horizon		Lags and Highest Magnitude of Significant Response of Reciprocal Effecta in the Response Horizon
		Lag	Coefficient (95% CI)	Probability, P	Bivariate Model	Other Drug Groups Includedb	Bivariate Model	Other Drug Groups Includedb
Cephalosporin use	Cephalosporin R	–1	0.035 (.016–.053)	<.001	7–12; 0.362; (.051–.566)	6–12; 0.516; (.117–.769)	NSR; 1.553 (–.317 to 2.985)	5–12; 2.20; (.392–3.731)
		–4	0.033 (.013–.051)	<.001
		Trend	0.004 (.002–.006)	<.001
		AR(1)	0.427 (.269–.585)	<.001
Third-generation cephalosporin use	Cephalosporin R	–4	0.064 (.024–.105)	.002	7–12; 0.373; (.126–.615)	7–12; 0.380; (.089–.602)	NSR; 0.677; (–.197 to 1.206)	NSR; 0.624; (–.312 to 1.163)
		–5	0.067 (.027–.107)	≤.001
		Trend	0.003 (.002–.006)	.001
		AR(1)	0.739 (.475–1.003)	<.001
		MA(1)	–0.43 (–.086 to –.790)	.02
Cephalosporin R	Carbapenem use	–2	0.692 (.265 to –1.090)	<.001	1–12; 0.729; (.304–1.134)	1–12; 0.700; (.253–1.062)	NSR; 0.068 (–.129 to .210)	NSR; 0.070; (–.116 to .219)
		Trend	0.022 (.017–.026)	<.001
		AR(1)	0.923 (.801–1.046)	<.001
		MA(1)	–0.839 (–.657 to –1.022)	<.001
Carbapenem use	Carbapenem R	–4	0.081 (.014–.147)	.019	1–4; 0.325; (.021–.566)	2; 0.297; (.035–.527)	NSR; –0.109; (–.642 to .418)	NSR; –0.109; (–.554 to .384)
		Trend	0.010 (.008–.013)	<.001
		AR(1)	0.842 (.684–1.000)	<.001
		MA(1)	–0.513 (–.261 to –.764)	<.001
Carbapenem R	Colistin use	0	0.307 (.135–.480)	<.001	1–12; 0.450; (.148–.593)	1–12; 0.256; (.058–.424)	3; –0.071; (–.099 to –.012)	1–12; –0.259; (–.464 to –.066)
		Trend	0.005 (.003–.008)	<.001
		MA(5)	0.451 (.288–.614)	<.001
Colistin use	Colistin R	0	0.011 (.002–.021)	.021	NSR; 0.008; (–.013 to .018)	NSR; 0.003; (–.018 to .013)	NSR; 0.115; (–.199 to .027)	NSR; –0.035; (–.166 to .141)
		–1	0.011 (.001–.020)	.028
		AR(1)	0.365 (.186–.545)	<.001

Abbreviations: AR, autoregressive component; CI, confidence interval; MA, moving average component; NSR, no significant response over the response horizon; R, resistance.

^aThe reciprocal effect means that the impulse is the former response and the response is the former impulse, for example, the reciprocal effect of cephalosporin use on cephalosporin resistance means the effect of cephalosporin resistance on cephalosporin use.

^bOther drug groups were aminoglycosides, fluoroquinolones, and, when applicable, cephalosporins.

Figure 3.

The resistance spiral in bivariate vector autoregressive models. Impulse response functions with drug consumption (defined as daily doses per 100 occupied bed-days [OBDs]) as impulses (left panel) and reciprocally with resistance densities of gram-negative bacteria (incidence densities of infections by resistant bacteria per 1000 OBDs) as impulses (right panel). The x-axis shows the response horizon, and the y-axis is the magnitude of effect of the impulse. Solid lines are estimates, and dashed lines are the 95% confidence intervals determined by bootstrapping of 100 repetitions. Note that the scales are different.

Carbapenem consumption significantly provoked carbapenem resistance in dynamic regression and bivariate VAR (Table 1, Figure 3). In dynamic regression, but not in VARs, consumption of cephalosporins 3 months earlier (coefficient 0.07) and of fluoroquinolones 4 months earlier (coefficient 0.02) also contributed to increases in carbapenem resistance, while aminoglycosides used in the same month and 3 months earlier were protective (cumulated coefficients –0.19; data not shown).

Both methods revealed the immediate effect of carbapenem resistance on colistin consumption. In VAR, colistin usage was also associated with a slight but significant decrease in carbapenem resistance (Table 1, Figure 3). In multivariate VARs, the association between carbapenem resistance and colistin usage was similar, while the association of carbapenem usage and carbapenem resistance was shown less markedly (only significant at lag 2 of the response horizon; Table 1). Carbapenem use was also associated with increasing colistin consumption, which decreased carbapenem use (significant through the whole response horizon in both cases). Colistin consumption similarly decreased use of other drug groups, markedly for fluoroquinolones and aminoglycosides and less strongly for cephalosporins. Aminoglycoside usage was also associated with decreasing colistin use (data not shown).

The link between colistin consumption and resistance was found to be weak in dynamic regression and remained insignificant in VARs (Table 1).

When the complete spiral from cephalosporin consumption to colistin resistance together was modeled, the relationships between resistance and consumption of the replacement drug were the most marked. Thus, the effect of cephalosporin resistance on carbapenem usage and the effect of carbapenem resistance on colistin usage was exhibited throughout the response horizon in both cases. In contrast, neither consumption of third-generation nor of all cephalosporins showed an effect on cephalosporin resistance, while the effect of carbapenem consumption on carbapenem resistance, though shown, was less marked than in pairwise models.

Resistance Spiral in Different Species

In the case of E. coli, both dynamic regression and VARs indicated an association between cephalosporin consumption and cephalosporin resistance as well as between cephalosporin resistance and carbapenem consumption (Table 2). Further associations were not tested as carbapenem resistance in E. coli was consistently low throughout the study period.

Table 2.

Relationships Found Between Drug Use and Drug Resistance of Different Gram-negative Bacteria in Dynamic Regression and in Vector Autoregressive Models

Species	Regressor/Impulse → Dependent Variable/Response	Dynamic Regression			Vector Autoregressive Model
		Lag	Coefficient (95% CI)	Probability, P	Lags and Highest Magnitude of Significant Response in the Response Horizon		Lags and Highest Magnitude of Significant Response of Reciprocal Effecta in the Response Horizon
					Bivariate Model	Other Drug Groups Includedb	Bivariate Model	Other Drug Groups Includedb
Escherichia coli	Cephalosporin use →cephalosporin R	−1	0.017 (.010–.024)	<.001	3–12; 0.170; (.065–.231)	2–12; 0.146; (.040–.232)	NSR; 1.753; (–.463 to 2.916)	NSR; 1.167; (–.227 to 2.402)
		–4	0.010 (.003–.017)	.007
		AR(1)	0.330 (.163–.495)	<.001
	Cephalosporin R →carbapenem use	–1	3.13 (2.130–4.131)	<.001	1–12; 0.322; (.052–.738)	1–12; 0.352; (.113–.614)	NSR; 0.019; (–.023 to .063)	NSR; 0.032; (–.013 to .082)
		–2	1.84 (.861–2.824)	<.001
		–3	1.12 (.135–2.102)	.027
		–4	1.73 (.763–2.705)	<.001
		–5	1.07 (.109–2.028)	.031
		–6	1.41 (.415–2.398)	<.001
		AR(1)	0.35 (.164–.484)	<.001
		AR(3)	0.32 (.194–.514)	<.001
	Carbapenem use →carbapenem R	NT			NT	NT	NT	NT
	Carbapenem R →colistin use	NT			NT	NT	NT	NT
Klebsiella spp.	Cephalosporin use →cephalosporin R	–4	0.025 (.015–.035)	<.001	NSR; 0.190; (–.093 to .368)	1–6; 0.196; (.027–.319)	NSR; 0.713; (–1.594 to 2.548)	NSR; 0.740; (–1.308 to 2.485)
		–5	0.019 (.009–.029)	<.001
		AR(1)	0.810 (.650–.971)	<.001
		MA(1)	–0.370 (–.622 to –.118)	.005
	Cephalosporin R →carbapenem use	–2	0.920 (.423–1.417)	<.001	NSR; 0.312; (–.344 to .749)	NSR; 0.318; (–.186 to .688)	NSR; 0.096; (–.166 to .265)	NSR; 0.014; (–.157 to .172)
		Trend	0.024 (.022–.027)	<.001
		AR(3)	0.312 (.150–.475)	<.001
	Carbapenem use →carbapenem R	–6	0.005 (.003 to –.006)	<.001	NSR; 0.004; (–.011 to .015)	NSR; 0.001; (–.010 to .008)	NSR; 0.004; (–.521 to .368)	NSR; 0.190; (–.093 to .368)
		AR(1)	–0.582 (–.990 to –.174)	.006
		MA(1)	0.782 (.476–1.089)	<.001
	Carbapenem R →colistin use	C	–0.400 (–.541 to –.260)	<.001	NSR; 0.225; (–.080 to .407)	NSR; 0.234; (–.092 to .517)	NSR; 0.011; (–.004 to .020)	NSR; 0.005; (–.010 to .010)
		Trend	0.013 (.012–.015)	<.001
		AR(3)	0.381 (.224–.539)	<.001
Pseudomonas aeruginosa	Cephalosporin use →cephalosporin R	Trend	0.003 (.002–.004)	<.001	NSR; 0.115; (–.281 to .242)	NSR; 0.140; (–.172 to .316)	NSR; 1.422; (–.504 to 2.785)	NSR; 1.662; (–.707 to 2.997)
		AR(1)	0.902 (.801–1.003)	<.001
		MA(1)	–0.516 (–.715 to –.316)	<.001
	Cephalosporin R →carbapenem use	–2	1.074 (.378–1.771)	.003	3–12; 0.701; (.172–1.155)	5–12; 0.547; (.132–.887)	NSR; –0.089; (–.278 to .089)	NSR; 0.067; (–.106 to .167)
		Trend	0.025 (.021–.028)	<.001
		AR(1)	0.946 (.876–1.016)	<.001
		MA(1)	–0.835 (–.972 to –.697)	<.001
	Carbapenem use →carbapenem R	0	0.087 (.060–.114)	<.001	2; 0.127; (.012–.234)	1–2; 0.072; (.012–.176)	NSR; 0.284; (–.300 to .708)	NSR; 0.189; (–.200 to .404)
		–1	0.109 (.082–.136)	<.001
		AR(1)	0.452 (.302–.603)	<.001
	Carbapenem R →colistin use	Trend	0.009 (.008–.011)	<.001	NSR; 0.288; (–.021 to .491)	NSR; 0.259; (–.024 to .548)	1–12; –0.136; (–.240 to –.045)c	2–12; –0.177; (–.252 to –.055)c
		AR(3)	0.509 (.356–.663)	<.001
		MA(5)	0.256 (.085–.426)	.0038
Acinetobacter baumannii	Cephalosporin use →cephalosporin R	NT			NT	NT	NT	NT
	Cephalosporin R →carbapenem use	NT			NT	NT	NT	NT
	Carbapenem use →carbapenem R	–4	0.052 (.006–.098)	.030	1; 0.177; (.005–.344)	1–4; 0.138; (.027–.275)	NSR; –0.304; (–.772 to .317)c	NSR; –0.216; (–.649 to –.221)c
		Trend	0.005 (.004–.007)	<.001
		AR(1)	0.802 (.630–.973)	<.001
		MA(1)	–0.396 (–.660 to –.132)	.004
	Carbapenem R →colistin use	0	0.745 (.572–.917)	<.001	0–12; 0.392; (.142–.550)	1–6; 0.248; (.036–.375)	NSR 0.045; (.180–.166)	NSR; –0.015; (–.165 to .132)
		–6	0.604 (.423–.786)	<.001
		AR(3)	0.387 (.218–.555)	<.001
		MA(1)	0.225 (.056–.394)	.001

Abbreviations: AR, autoregressive component; C, constant; CI, confidence interval; MA, moving average component; NSR, no significant response over the response horizon; NT, not tested; R, resistance.

^aThe reciprocal effect means that the impulse is the former response and the response is the former impulse, for example, the reciprocal effect of cephalosporin use on cephalosporin resistance means the effect of cephalosporin resistance on cephalosporin use.

^bOther drug groups were aminoglycosides, fluoroquinolones, and, when applicable, cephalosporins.

^cCarbapenem resistance was inversely associated with colistin use; increasing colistin use was associated with decreasing carbapenem resistance.

In the case of Klebsiella spp., in contrast, associations between cephalosporin consumption and resistance, between cephalosporin resistance and carbapenem consumption, and between carbapenem consumption and resistance were found in dynamic regression. In multivariate VARs, only cephalosporin consumption and resistance was associated; in bivariate VARs, there was no association (Table 2). Carbapenem resistance was not associated with colistin consumption.

In the case of P. aeruginosa, cephalosporin consumption did not affect cephalosporin resistance, but cephalosporin resistance was associated with carbapenem use. This was, in turn, associated with increasing carbapenem resistance, but carbapenem resistance was not associated with colistin consumption. However, a reciprocal association was found in VARs, that is, colistin consumption was associated with decreased incidence of carbapenem-resistant P. aeruginosa (Table 2).

In the case of A. baumannii, the putative spiral was followed starting with carbapenem consumption (as cephalosporin susceptibility is not routinely tested according to recommendations of the European Committee on Antimicrobial Susceptibility Testing). Carbapenem consumption was associated with increased incidence of carbapenem-resistant A. baumannii in both model systems. Furthermore, this was associated with increased colistin consumption. A reciprocal association between colistin consumption and carbapenem resistance was not found with A. baumannii (Table 2).

An association between colistin use and colistin resistance was never detected. Inclusion of other drug groups in the VARs did not alter the results.

Hypothetical Resistance Spiral in the University

Based on the above data, key drug resistances to the putative resistance spiral were identified in different species, and a hypothesis on the probable structure of the spiral was formed and tested, that is, cephalosporin usage provoked spread of cephalosporin resistance in Klebsiella spp. and later in E. coli, leading to increased carbapenem use. This, in turn, provoked emergence of carbapenem-resistant P. aeruginosa and A. baumannii, which finally led to increased colistin usage. Colistin resistance was not included in the model of the spiral as the relationship was scarcely identified in less-comprehensive models.

Among the hypothetical spiral of relationships (Figure 4, Table 3), the most marked ones were always resistance provoking increased use of replacement drugs. Cephalosporin resistance of E. coli, but notably not of Klebsiella spp., was strongly associated with carbapenem consumption. Carbapenem resistance in A. baumannii, but not in P. aeruginosa, provoked colistin use. In the model of the complete spiral, the association between resistance and usage of replacement drugs was always more pronounced than relationships between consumption and resistance marked in models concerned with all gram-negative pathogens.

Table 3.

Relationships Found Between Drug Use and Drug Resistance in the Vector Autoregressive Model Representing the Complete Resistance Spiral

Regressor/Impulse	Dependent Variable/ Response	Vector Autoregressive Model
		Lags and Highest Magnitude of Significant Response (95% CI) in the Response Horizon	Lags and Highest Magnitude of Significant Response of Reciprocal Effecta in the Response Horizon
Cephalosporin use	Cephalosporin R in Klebsiella spp.	NSR;	NSR;
		0.106;	0.305;
		(–.110 to .275)	(–.505 to .954)
Cephalosporin use	Cephalosporin R in Escherichia coli	NSR;	NSR;
		0.010;	0.196;
		(–.052 to.058)	(–.600 to .699)
Cephalosporin R in Klebsiella spp.	Carbapenem use	NSR;	NSR;
		0.154;	0.038;
		(–.473 to .554)	(–.154 to .160)
Cephalosporin R in E. coli	Carbapenem use	1–7;	NSR;
		0.404;	0.043;
		(.097–.903)	(–.026 to .080)
Carbapenem use	Carbapenem R in Pseudomonas aeruginosa	NSR;	NSR;
		0.086;	0.035;
		(–.102 to .237)	(–.479 to .383)
Carbapenem use	Carbapenem R in Acinetobacter baumannii	NSR;	3–5;
		0.103;	–0.190;
		(.068–.434)	(–.436 to –.038)b
Carbapenem R in P. aeruginosa	Colistin use	NSR;	1–12;
		0.275;	–0.129;
		(–.095 to .411)	(–.185 to –.020)c
Carbapenem R in A. baumannii	Colistin use	1–12;	NSR;
		0.275;	–0.026;
		(.065–.411)	(–.184 to .098)

Abbreviations: A. baumannii, Acinetobacter baumannii; CI, confidence interval; E. coli, Escherichia coli; NSR, no significant response over the response horizon; P. aeruginosa, Pseudomonas aeruginosa; R, resistance.

^aThe reciprocal effect means that the impulse is the former response and the response is the former impulse, for example, the reciprocal effect of cephalosporin use on cephalosporin resistance means the effect of cephalosporin resistance on cephalosporin use.

^bCarbapenem use was inversely associated with carbapenem resistance; increasing carbapenem resistance was associated with decreasing carbapenem use.

^cCarbapenem resistance was inversely associated with colistin use; increasing colistin use was associated with decreasing carbapenem resistance.

Figure 4.

The resistance spiral in the same vector autoregressive model. Impulse response functions for cephalosporin consumption affecting cephalosporin resistance in Klebsiella spp. and E. coli are not shown. Consumption is defined in daily doses per 100 OBDs), and resistance is shown as resistance densities of gram-negative bacteria (incidence densities of infections by resistant bacteria per 1000 OBDs). The x-axis shows the response horizon, and the y-axis is the magnitude of effect of the impulse. Solid lines are estimates, and dashed lines are the 95% confidence intervals determined by bootstrapping of 100 repetitions. Note that the scales are different. Abbreviations: A. baumannii, Acinetobacter baumannii; E. coli, Escherichia coli; P. aeruginosa, Pseudomonas aeruginosa.

DISCUSSION

Evolution of the resistance spiral was largely as expected. However, in contrast to resistance spirals recognized in a single species (eg, see Zowawi et al [16]), in our setting the spiral involved multiple species in a complex interplay of drug use patterns and different nosocomial species exhibiting drug resistance, drawing attention to the importance of interactions between different species [7], or even strains [5], in hospital ecology. Resistance to a key drug group was mostly due to 1 or 2 species, and resistance to the replacement drug appeared first and became a problem in another species. The link between cephalosporin use and resistance was detected in Klebsiella spp. and E. coli. Cephalosporin resistance of E. coli but not of Klebsiella spp. was strongly associated with increasing carbapenem use and may be consequent to emergence of E. coli as a major cause for broad-spectrum cephalosporin resistance [30]. As carbapenems are the drugs of choice against these [30], their increasing prevalence provoked a massive increase in carbapenem consumption [31, 32], reflecting fear of cephalosporin resistance in clinicians and the resulting preference for carbapenems in empirical therapy [33, 34]. The influence of cephalosporin resistance in P. aeruginosa, which has been documented extensively [12], was also important; however, it appeared mostly together with carbapenem resistance.

Carbapenem resistance was remarkably more important in nonfermenting gram-negative bacteria than in enterobacteria and accounted for the bulk of carbapenem resistance. This is in contrast to many European reports [30] but in line with the Hungarian epidemiological situation (Á. Tóth, personal discussion). Colistin use was provoked by carbapenem-resistant A. baumannii, emerging in 2009–2010 as the main pathogen responsible for carbapenem resistance [13].

Though colistin is mostly used to target carbapenem-resistant bacteria, in our setting it emerged as the current routine empirical treatment in some intensive care units, frequently replacing meropenem (G. Kardos, unpublished observations). This explains the strong reciprocal relationship between consumption of carbapenems and colistin, that is, the reason why colistin use is associated with decreasing use of carbapenems and other drug groups. Colistin partly supplanted other drugs, becoming the preferred drug in empirical therapy of severe infections. Previous colistin use is a significant risk factor for infections by bacteria with acquired colistin resistance [35, 36]. However, this link was barely detectable in our study, probably due to the appearance of colistin resistance late in the study. The resistance spiral was thus characterized by alternating emergence and recession of different species with clinically worrisome resistance.

Results obtained with the 2 model types corresponded well, mutually supporting each other, though VAR models were generally stricter and indicated fewer relationships. VARs offered the possibility of testing variable combinations that dynamic regression models did not allow, that is, testing interdependencies between drug consumption and resistance instead of prejudging the role of variables and including multiple variables that were dependent in dynamic regression in the same model [37]. Ultimately, dynamic regression allows testing of only a single stage of the resistance spiral, while VARs can be used to analyze all stages simultaneously. Nevertheless, VARs has some limitations: testing all variables at the same time lag, thus failing to take into account differences in latencies of the different effects; requiring longer series to build valid models compared to dynamic regression; and the impulse responses being sensitive to the order of variables in the model and to the similarity of the last few values of the series to the general characteristics of the series, though the latter can be circumvented by the rolling-window method used in this work. Moreover, dynamic regression models are easier to interpret, and quantitative interpretation is more straightforward (coefficients can be translated directly to effect size). Utility of dynamic regression models is extensively proven [1, 4–7, 9], but this work is, to our knowledge, the first to report use of VARs for such a purpose.

Differences in provoking the effects of different drugs, even within the same family [9], may drive or improve countermeasures. For example, as aminoglycosides were frequently inversely associated with resistance to beta-lactams, exploitation of their synergistic effect should be encouraged. The impact of such differences on strain dynamics was shown for MRSA and E. coli [1, 5, 9]. These methods may point out the drugs that should be restricted in order to eliminate the driving force for an outbreak or as a stewardship activity [11].

Cephalosporin resistance promoted carbapenem use and carbapenem resistance was linked to increasing colistin use, which was in turn associated with decreasing use of other drugs. Thus, colistin seemed to replace other drugs. These results indicate that Carlet et al correctly expressed concern regarding resistance among prescribers as the major driver for prescribing broader-spectrum antibiotics [3]. This suggests that this concern is the reason for changes in prescribing habits [38, 39] and is of major importance. The threatening panresistance underlines the importance of analyzing the relationship between drug use and resistance, as better understanding of its dynamics will be crucial to extending the lifespan of currently available drugs [40], a goal that is necessary to avoid the postantibiotic era.

Supplementary Data

Supplementary materials are available at Clinical Infectious Diseases online. Consisting of data provided by the authors to benefit the reader, the posted materials are not copyedited and are the sole responsibility of the authors, so questions or comments should be addressed to the corresponding author.

Notes

Acknowledgments. The valuable technical advice of José-María López-Lozano with time-series analysis and of Márton Kormanik with vector autoregressive models is gratefully acknowledged, as well as inspiring discussions in the THRESHOLDS study group.

Financial support. This work was supported by the ÚNKP-17-2 New National Excellence Program of the Ministry of Human Capacities to H. T. and by Bolyai Research Scholarships of the Hungarian Academy of Sciences to K. S. Z (Grant No: BO/00568/15) and G. K (Grant No: BO/01030/15).

Potential conflicts of interest. B. B. reports conference travel grant EFOP-3.6.3-VEKOP-16-2017-00009. L. M. reports conference travel support from Merck Sharp and Dohme, Pfizer, and Astellas and nonfinancial support from Cidara Therapeutics outside the submitted work. All remaining authors: No reported conflicts. All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed.