Theorical and methodological background

ViResiST

A new approach for the determination of the lag and size of effect of the relationship between

antimicrobial use and antimicrobial resistance: Time Series Analysis

José-María López-Lozano

Dominique L. Monnet

Hospital Vega BajaHospital Vega Baja Orihuela-Alicante (Spain)

Statens Serum InstitutStatens Serum Institut Copenhagen (Denmark)

ViResiST

Static Model

The effect of each factor on current patients is contemporaneous, and independent of precedent and followings months

Resistance Antimicrobial

use

Hospital hygiene Bacterial flora diversity

Month 1 Month 2 Month 3 Month 4 Month 5 Month 6

ViResiST

If there where no such thing as gravity….

ViResiST

If there where no such thing as

gravity….

Source: “The Seven Year Itch”, Billy Wilder, 1955

this scene would be… impossible

ViResiST

“If there where no such thing as time, everything

would happen all at once ”George Carlin, comedian

Source: Forecasting with Dynamic Regression Models,

Pankratz, A. Wiley & Sons, New York, 1993

ViResiST

Dynamic Model


use


All factor sizes varies while time pass


ViResiST

Dynamic Model


use


Antibiotic effect is delayed and it decay progressively

Month 1 Month 2 Month 3 Month 4 Month 5

ViResiST

Relationship between antibiotic use and resistance is retarded

Dynamic Model


use



ViResiST

Antibiotic use precedes Resistance?

• Evidences: – McGowan: Abrupt changes in antibiotic

resistance– Peña– Corbella

ViResiST

Lagged Reduction of extended-spectrum beta-lactamase-producing Klebsiella pneumoniae (ESBL-KP) incidence after a reduction of antimicrobial use.

Hospital Bellvitge, Barcelona, 1993-95

Source: Pena et al. 1998. Antimicrob Agents Chemother 42:53-8.

ViResiST

Source: Corbella et al.. 2000. J Clin Microbiol 38:4086-95.

Lagged Reduction of Acinetobacter baumannii incidence after a reduction of carbapenems . Hospital

Bellvitge, Barcelona, 1997-98

ViResiST

02468

10

0 500 1000 1500 2000

02468

10

0 500 1000 1500 2000

02468

10

0 500 1000 1500 2000

Gentamicin Use and Percent Gentamicin-Resistant Gram-Negative Bacilli Isolates, Brussels, 1979-1986

R = 0.90p < 0.005%

Gen

tam

icin

-res

ista

ntgr

am-n

egat

ive

baci

lli

Gentamicin usesame year (g/year)

Source: Goossens H, et al. Lancet 1986;2:804.

Gentamicin use previous year (g/year)

ViResiST

0

1

2

3

4

5

6

7

8

9

1991 1992 1993 1994 1995 1996 1997 1998

Ceftazidime-resistantGNB (%)

Ceftazidime use(DDD/1,000 pt-days)

Yearly Percent Ceftazidime-Resistant/Intermediate Gram-Negative Bacilli and Hospital Ceftazidime Use,

Hospital Vega Baja, Spain, 1991-1998

Source: Monnet DL, López-Lozano JM. Clin Microbiol Infect 2001

ViResiST

Source: López-Lozano JM, et al. Int J Antimicrob Agents 2000;14:21-31.

Ho

spit

al c

efta

zid

ime

use

(DD

D/1

,000

pat

ien

t-d

ays)

% C

efta

zidi

me-

resi

stan

t/in

term

edia

tegr

am-n

egat

ive

baci

lli

16 16

14

12

10

8

6

4

2

0

14

12

10

8

6

4

2

Jul. 1

991

0

Nov. 1

991

Mar

. 199

2

Jul. 1

992

Nov. 1

992

Mar

. 199

3

Nov. 1

993

Mar

. 199

4

Jul. 1

993

Jul. 1

994

Mar

. 199

5

Nov. 1

994

Jul. 1

995

Nov. 1

995

Mar

. 199

6

Jul. 1

996

Nov. 1

996

Mar

. 199

7

Jul. 1

997

Nov. 1

997

Jul. 1

998

Mar

. 199

8

Nov. 1

998

Mar

. 199

9

Jul. 1

999

Monthly Percent Ceftazidime-Resistant/Intermediate Gram-Negative Bacilli and Hospital Ceftazidime Use,


ViResiST


0

12

10

8

6

4

2

0

Jul. 1

991

12

10

Nov. 1

991

Mar

. 199

2

8

6

4

2

Jul. 1

992

Mar

. 199

3

Mar

. 199

4

Nov. 1

992

Jul. 1

993

Nov. 1

993

Jul. 1

994

Nov. 1

994

Jul. 1

995

Nov. 1

995

Mar

. 199

5

Jul. 1

996

Mar

. 199

7

Nov. 1

996

Mar

. 199

6

Jul. 1

997

Nov. 1

997

Mar

. 199

8

Nov. 1

998

Mar

. 199

9

Jul. 1

999

Jul. 1

998

Five Period Centered Mpoving Average of the Monthly Percent Ceftazidime-Resistant/Intermediate

Gram-Negative Bacilli and Hospital Ceftazidime Use, Hospital Vega Baja, Spain, 1991-1998

Ho

spit

al c

efta

zid

ime

use

(DD

D/1

,000

pat

ien

t-d

ays)

% C

efta

zidi

me-

resi

stan

t/in

term

edia

tegr

am-n

egat

ive

baci

lli

ViResiST

A Deterministic Process

• Launching a missile: – Very well know physical phenomenon – We can establish a model based on

physical laws– We might calculate the exact trajectory if

we know its direction and its velocity

ViResiST

Weather Forecast

• Very complex phenomenon dependent of many complex and unstable circumstances

• Impossible to establish a mathematical model to predict its future behaviour because we don’t know all its causal factors

• However, it is possible to construct a model in order to calculate the probability of a future value lying between two specified limits, basing our estimation in past values and in some known influencing factors (atmospheric pressure, seasonal moment, etc.. )

• Such a model is called a probability model or a stochastic stochastic modelmodel

ViResiST

Stochastic processes and stochastic models

• When there is many phenomenon interacting simultaneously and producing a variable outcome we

denominate it as a stochastic processstochastic process. In order to improve our knowledge of such phenomenon

we construct a so called stochastic modelstochastic model

ViResiST

Our Proposal: Resistance is a Stochastic Process

• Antimicrobial resistance measured ecologically and across time depends of:– The impact of antimicrobial use (variable)– Transmission of resistant strains from one patient

to another (conditioned by hospital hygiene situation also variable)

– The probability of spontaneous bacterial mutations unpredictable, variable

– The number of identified strains that is conditioned also by the number of medical analytical solicitations variable, also.

ViResiST

What is a Time Series?a group of observations taken sequentially in time

0

20

40

60

80

100

120

abr-95

jul-9

5

oct-9

5

ene-96

abr-96

jul-9

6

oct-9

6

ene-97

abr-97

jul-9

7

oct-9

7

ene-98

abr-98

jul-9

8

oct-9

8

ene-99

abr-99

jul-9

9

oct-9

9

ene-00

abr-00

jul-0

0

oct-0

0

Observed Series

ViResiST

Our time series is only one between many other possible realizations of the underlying stochastic process

0

20

40

60

80

100

120

Apr-95

Jul-95

Oct

-95

Jan-96

Apr-96

Jul-96

Oct

-96

Jan-97

Apr-97

Jul-97

Oct

-97

Jan-98

Apr-98

Jul-98

Oct

-98

Jan-99

Apr-99

Jul-99

Oct

-99

Jan-00

Apr-00

Jul-00

Oct

-00

Observed Series Serie2 Serie3 Serie4

ViResiST

Modelling Stochastic Processes

• Time series representing stochastic processes can’t be analysed using classical regression techniques, i.e. time regression, because it is necessary that consecutive observations be independent: – It is necessary that there is not autocorrelation

• Autocorrelation is, precisely, a very interesting circumstance on the Time Series Analysis domain

ViResiST

Is there autocorrelation on monthly time series of resistance?

Antwerp University Hospital. 1997-2001

0

5

10

15

20

25

30

Jan-9

7

Apr-97

Jul-9

7

Oct-9

7

Jan-9

8

Apr-98

Jul-9

8

Oct-9

8

Jan-9

9

Apr-99

Jul-9

9

Oct-9

9

Jan-0

0

Apr-00

Jul-0

0

Oct-0

0

Jan-0

1

Apr-01

Jul-0

1

Oct-0

1

%

Monthly %IMIPENEM Resistant Pseudomonas aeruginosa

ViResiST

Dynamic Regression Concept

ViResiST

Dynamic Regression

0

10

20

30

40

50

60

70

DD

D/1

000

pat-d

ay

0

10

20

30

40

50

60

%ci

prof

loxa

cin

resi

stan

t-int

erm

edia

te (P

A)

Monthly Use of ciprofloxacin and Monthly % of ciprofloxacin Resistant-intermediate P. aeruginosa

Hospital Vega Baja. 1991-2001

ViResiST

Dynamic Regression

0

10

20

30

40

50

60

70

DD

D/1

000

pat-d

ay

0

10

20

30

40

50

60

%ci

prof

loxa

cin

resi

stan

t-int

erm

edia

te (P

A)

Monthly Use of ciprofloxacin and Monthly % of ciprofloxacin Resistant-intermediate P. aeruginosa

Hospital Vega Baja. 1991-2001

ViResiST

Date %Res UseCIP01/06/91 0,0 53,801/07/91 20,0 33,301/08/91 0,0 40,001/09/91 0,0 25,501/10/91 25,0 47,901/11/91 0,0 58,101/12/91 0,0 44,001/01/92 25,0 27,801/02/92 25,0 11,401/03/92 0,0 16,501/04/92 0,0 22,001/05/92 25,0 25,301/06/92 16,7 28,101/07/92 40,0 29,101/08/92 0,0 27,001/09/92 20,0 22,001/10/92 0,0 21,701/11/92 20,0 37,0

Contemporaneous Correlation Coefficient = - 0.04 (NS)

0

10

20

30

40

50

60

UseSmooth %ResSmooth

ViResiST

Date %Res UseCIP UseCip(t-1) UseCip(t-2) UseCip(t-3)UseCip(t-4)UseCip(t-5)UseCip(t-6)UseCip(t-7)01/06/91 0,0 53,801/07/91 20,0 33,3 53,801/08/91 0,0 40,0 33,3 53,801/09/91 0,0 25,5 40,0 33,3 53,801/10/91 25,0 47,9 25,5 40,0 33,3 53,801/11/91 0,0 58,1 47,9 25,5 40,0 33,3 53,801/12/91 0,0 44,0 58,1 47,9 25,5 40,0 33,3 53,801/01/92 25,0 27,8 44,0 58,1 47,9 25,5 40,0 33,3 53,801/02/92 25,0 11,4 27,8 44,0 58,1 47,9 25,5 40,0 33,301/03/92 0,0 16,5 11,4 27,8 44,0 58,1 47,9 25,5 40,001/04/92 0,0 22,0 16,5 11,4 27,8 44,0 58,1 47,9 25,501/05/92 25,0 25,3 22,0 16,5 11,4 27,8 44,0 58,1 47,901/06/92 16,7 28,1 25,3 22,0 16,5 11,4 27,8 44,0 58,101/07/92 40,0 29,1 28,1 25,3 22,0 16,5 11,4 27,8 44,001/08/92 0,0 27,0 29,1 28,1 25,3 22,0 16,5 11,4 27,801/09/92 20,0 22,0 27,0 29,1 28,1 25,3 22,0 16,5 11,401/10/92 0,0 21,7 22,0 27,0 29,1 28,1 25,3 22,0 16,501/11/92 20,0 37,0 21,7 22,0 27,0 29,1 28,1 25,3 22,001/12/92 0,0 22,3 37,0 21,7 22,0 27,0 29,1 28,1 25,301/01/93 0,0 17,8 22,3 37,0 21,7 22,0 27,0 29,1 28,101/02/93 0,0 21,5 17,8 22,3 37,0 21,7 22,0 27,0 29,1

Correlation coefficient = 0.10 (NS)

0

10

20

30

40

50

60


ViResiST

Date %Res UseCIP UseCip(t-1) UseCip(t-2) UseCip(t-3) UseCip(t-4) UseCip(t-5) UseCip(t-6) UseCip(t-7)01/06/91 0,0 53,801/07/91 20,0 33,3 53,801/08/91 0,0 40,0 33,3 53,801/09/91 0,0 25,5 40,0 33,3 53,801/10/91 25,0 47,9 25,5 40,0 33,3 53,801/11/91 0,0 58,1 47,9 25,5 40,0 33,3 53,801/12/91 0,0 44,0 58,1 47,9 25,5 40,0 33,3 53,801/01/92 25,0 27,8 44,0 58,1 47,9 25,5 40,0 33,3 53,801/02/92 25,0 11,4 27,8 44,0 58,1 47,9 25,5 40,0 33,301/03/92 0,0 16,5 11,4 27,8 44,0 58,1 47,9 25,5 40,001/04/92 0,0 22,0 16,5 11,4 27,8 44,0 58,1 47,9 25,501/05/92 25,0 25,3 22,0 16,5 11,4 27,8 44,0 58,1 47,901/06/92 16,7 28,1 25,3 22,0 16,5 11,4 27,8 44,0 58,101/07/92 40,0 29,1 28,1 25,3 22,0 16,5 11,4 27,8 44,001/08/92 0,0 27,0 29,1 28,1 25,3 22,0 16,5 11,4 27,801/09/92 20,0 22,0 27,0 29,1 28,1 25,3 22,0 16,5 11,401/10/92 0,0 21,7 22,0 27,0 29,1 28,1 25,3 22,0 16,501/11/92 20,0 37,0 21,7 22,0 27,0 29,1 28,1 25,3 22,001/12/92 0,0 22,3 37,0 21,7 22,0 27,0 29,1 28,1 25,301/01/93 0,0 17,8 22,3 37,0 21,7 22,0 27,0 29,1 28,1

Correlation coefficient = 0.28 (p<0.05)

0

10

20

30

40

50

60


ViResiST

Significant relationship between the use of ciprofloxacin and resistance:

- 7 month later

- exponential decay

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12 14 16 18 20 22 24

CORR. COEF

95%LCL

95%UCL

Max. relation

Cross-correlation Function Concept

ViResiST

0

10

20

30

40

50

60

%ResSmooth USE (t=0) USE (t-1) USE (t-2) USE (t-3)

USE (t-4) USE (t-5) USE (t-6) USE (t-7)

ViResiST

0

10

20

30

40

50

60

70

UseCIP SmoothedUse

Autocorrelation Concept for Univariate Series

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9

Corr Coef UCL LCL

Ciprofloxacin use

is related to

its previous values

1 and 3 month before

ViResiST

What Is Time Series Analysis?

• Origin in econometric sciences • The analysis of time series, i.e. series of data collected series of data collected

over time at regular and short intervals, as compared to over time at regular and short intervals, as compared to the study periodthe study period

• Ability to take into account the possible dependence of consecutive measurements (autocorrelation)

• In 1976, Box &Jenkins provided a practical method to build time series models

• Increasing access to personal computers and specific software applications enable routine use of this method

• To modelize and analyze Stochastic Process

ViResiST

Statistical Methodology• For univariate series: ARIMA models

– to predict expected resistance from past local resistance data

– to predict expected antimicrobial use from past local use data

• For multivariate series: Transfert Function models (similar to ARIMA models but adding other independents variables)– to study the relationship between antimicrobial use and

resistance – to better predict expected resistance taking into account

antimicrobial use

ViResiST

Box-Jenkins (ARIMA) Models

• AR (Autoregressive): previous values• I (Integrated): trends• MA (Moving Average): abrupt changes in

the near past• e.g., for ceftazidime-resistant gram-negative

bacilli:

%R(t) = 3.314 + 0.346 AR3 + 0.266 AR5

Sources : Helfenstein U. Int J Epidemiol 1991;20:808-815. López-Lozano JM, et al. Int J Antimicrob Agents 2000;14:21-31.

ViResiST

Transfer Function (TF) Models

• For multivariate series: (similar to ARIMA models but adding other independents variables)

• To assess relationships between a target (output) series and one or several explanatory (input) series, i,e.:– to study the relationship between antimicrobial use and resistance – to better predict expected resistance taking into account

antimicrobial use• Usual in econometrics• Previous applications in medicine, e.g.:

– individual: exercise and blood glucose – population: climatic variables and mortality, influenza and mortality

ViResiST

Modelling Transfer Functions

•Methods:–Box-Jenkins

–Haugh

–Pankratz

ViResiST

Box-Jenkins Method

1. To estimate an ARIMA for explaining series, save residuals (Re)2. To filter dependent series using explaining series model, save

residuals (Rd)3. Cross-correlation function between both residuals series (Re & Rd)4. To estimate Transfer Function retarding Input series according to

detected significant lags in steep 35. To modelize residual series (Rtf) (univariant ARIMA)6. To add ARIMA residual series components to Transfer Function7. To reestimate TF8. To examine residual series9. Cross-correlation function between Rtf and Re in order to detect other

possible significant lags

Explaining series: antimicrobial use series

Dependent series: resistance series

ViResiST

Haugh Method

• Similar to Box-Jenkins approach but identifying and estimating a model for Dependent series in steep 2

1. To estimate an ARIMA for explaining series, save residuals (Re)

2.2. To estimate an ARIMA for dependent series, To estimate an ARIMA for dependent series, save residuals (Rd)save residuals (Rd)

3. Cross-correlation function between both residuals series (Re & Rd)

4. To estimate Transfer Function retarding Input series according to detected significant lags in steep 3

5. To modelize residual series (Rtf) (univariant ARIMA)6. To add ARIMA residual series components to Transfer Function7. To reestimate TF8. To examine residual series9. Cross-correlation function between Rtf and Re in order to detect

other possible significant lags

Explaining series: antimicrobial use series

Dependent series: resistance series

ViResiST

Dynamic Regression Method (Pankratz)

1. To estimate directly a Transfer Function with several lags for explaining series and a AR(1) term for disturbance

2. To eliminate not significant lags3. To identify a disturbance model4. To add disturbance terms to TF5. To estimate TF6. To eliminate not significant lags7. To examine residuals8. To reformulate TF if necessary

Allows for simultaneous exploration of several explaining series

ViResiST

TSA Available SoftwareTransfer Function methods Other more sophisticated

techniques

Box-Jenkins

Haugh Pankratz PDL, VARMA, ECM, Cointegration

SPSS Trends

* *** * -

SCA (1) ***** ***** ********** **

Eviews (2) ** ***** ***** ***********

Others: SAS(3), Minitab, etc..

***** * * *

(1) Expensive, allows automatic exploration and modelisation of multi-series databases (Used on ViResiST Project)

(2) Cheap, very easily to use

(3) Very Expensive

ViResiST

Example

• Using Haugh method• In this example we use Ceftazidime

resistant-intermediate Gram negative - Bacilli identified in our Hospital (400 beds) from 1991 to 1998

• Both series are expressed as:– Dependent: Monthly percentage of resistant

strains to the antibiotic– Explaining: Ceftazidime use: Monthly sum of

DDD per 1000 beddays used in our Hospital

ViResiST


Ho

spit

al c

efta

zid

ime

use

(DD

D/1

,000

pat

ien

t-d

ays)

% C

efta

zidi

me-

resi

stan

t/in

term

edia

tegr

am-n

egat

ive

baci

lli

16 16

14

12

10

8

6

4

2

0

14

12

10

8

6

4

2

Jul. 1

991

0

Nov. 1

991

Mar

. 199

2

Jul. 1

992

Nov. 1

992

Mar

. 199

3

Nov. 1

993

Mar

. 199

4

Jul. 1

993

Jul. 1

994

Mar

. 199

5

Nov. 1

994

Jul. 1

995

Nov. 1

995

Mar

. 199

6

Jul. 1

996

Nov. 1

996

Mar

. 199

7

Jul. 1

997

Nov. 1

997

Jul. 1

998

Mar

. 199

8

Nov. 1

998

Mar

. 199

9

Jul. 1

999

Monthly Percent Ceftazidime-Resistant/Intermediate Gram-Negative Bacilli and Hospital Ceftazidime Use,


Study of resistance series 1. Graphical Examination

ViResiST

Study of resistance series 2. Series Correlograms

Ceftazidima(% resistencias)

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F

1.0

.5

0.0

-.5

-1.0

Límites confidencial

es

Coeficiente

Ceftazidima(% resistencias)

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F p

arc

ial

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

ViResiST

Study of resistance series 3. Identifiying the Model

• There is no need for differentiation or logarithmic transformation

• Two possibilities: AR(1,2,3), AR(1,3)– Significant spike in the 3 first lags in PACF– Coefficients decay in a slower and more

progressive fashion in ACF (so it’s not an MA)

• This is necessary to fit both models and to compare

ViResiST

Study of resistance series 4 AR(1,2,3) model parameter estimation

FINAL PARAMETERS:

Number of residuals 90Standard error 2.6464511Log likelihood -213.55027AIC 435.10054SBC 445.09978

Analysis of Variance:

DF Adj. Sum of Squares Residual Variance

Residuals 86 605.90503 7.0037034

Variables in the Model:

B SEB T-RATIO APPROX. PROB.

AR1 .1639045 .10105938 1.6218634 .10849329AR2 .1541121 .10165424 1.5160423 .13317584AR3 .3204726 .10274661 3.1190579 .00246879CONSTANT 3.2509346 .73974641 4.3946609 .00003153

ViResiST

Study of resistance series 4. AR(1,3) model parameter estimation

FINAL PARAMETERS: Number of residuals 90 Standard error 2.6666731 Log likelihood -214.71092 AIC 435.42184 SBC 442.92127 Analysis of Variance: DF Adj. Sum of Squares Residual Variance Residuals 87 621.96364 7.1111452 Variables in the Model: B SEB T-RATIO APPROX. PROB. AR1 .2011368 .09869501 2.0379636 .04459089 AR3 .3533373 .10091469 3.5013467 .00073282 CONSTANT 3.2619116 .61196775 5.3302018 .00000076

ViResiST

Study of resistance series 5. Model diagnostics

• Parameter significance:– AR(1,2,3) model: 1 and 2 lag parameters are not significant – AR(1,3) model, all lag parameters are significant

• Stationarity Control:– AR(1,2,3) model:

• AR1: (1- 0’1639045) / 0’10105938 > 1’96 • AR2: (1-0’1541121) / 0’10165424 > 1’96

• AR3: (1- 0’3204726) / 0’10274661 > 1’96 – AR(1,3) model:

• AR1: (1-0’011368) / 0’09869501 > 1’96

• AR3:(1-0’3533373)/0’10091469 > 1’96 • Invertibility Control:

– There are not moving average terms

ViResiST

Study of resistance series 5. Model diagnostics:

• Residuals correlogram: white noise in AR(1,2,3) and significant lag 5 in AR(1,3)

Error for SACEFT_1 from ARIMA, MOD AR(1,2,3)

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

Error for SACEFT_1 from ARIMA, MOD AR(1,2,3)

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F p

arc

ial

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

Error for SACEFT_1 from ARIMA, MOD AR(1,3)

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F

1.0

.5

0.0

-.5

-1.0


es

Coeficiente


Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F p

arc

ial

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

ViResiST

Study of resistance series 6. Reformulating the model

• We must to re-estimate the AR(1,3) model adding the term AR5:

FINAL PARAMETERS:


Analysis of Variance: DF Adj. Sum of Squares Residual VarianceResiduals 86 584.61547 6.7394458

Variables in the Model: B SEB T-RATIO APPROX. PROB.AR1 .1596705 .09744083 1.6386406 .10494173AR3 .3054853 .09972109 3.0633971 .00292184AR5 .2375548 .10189580 2.3313502 .02207383CONSTANT 3.3092262 .85126011 3.8874442 .00019880

ViResiST

Study of resistance series 6a. Reformulating the model

• We eliminate the AR1 term

FINAL PARAMETERS:



Variables in the Model: B SEB T-RATIO APPROX. PROB.AR3 .3456772 .09724915 3.5545522 .00061478AR5 .2662334 .10096849 2.6367967 .00991133CONSTANT 3.3138856 .66776498 4.9626526 .00000342

ViResiST

Study of resistance series 6b. New model diagnostics

• All parameters are significant• All autoregresive parameters are different to the unit

(stationarity)• Residual correlograms: white noise


Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F

1.0

.5

0.0

-.5

-1.0


es

Coeficiente


Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F p

arc

ial

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

ViResiST

Study of resistance series 7. Comparing models:

• AR(3,5) is better than AR(1,2,3):– < AIC and Residual Var.

• AR(3,5) is better than AR(1,3,5):– All parameters are significant ( AR(1) term not significant in AR(1,3,5) model)– More parsimonious: (simpler, less parameters)

Model AIC *Residual Variance

AR(3,5) 432 6’86

AR(1,3,5) 431 6’73

AR(1,2,3) 435 7’11

* AIC: Akaike Information Criterion

ViResiST

Study of resistance serie 8. Predictions using the model

Date Observed resistance

Forecasts using AR(3,5) model

95% Confidence Interval lower limit

95% Confidence Interval upper limit

SEP 1998 7.4 2.8 -2.4 -2.4 OCT 1998 7.1 5.3 .1 10.6 NOV 1998 6.0 5.2 .0 10.4 DEC 1998 4.5 6.4 1.1 11.6 JAN 1999 6.0 .8 11.2 FEB 1999 5.3 .1 10.6 MAR 1999 4.7 -.5 10.0 APR 1999 5.0 -.6 10.5 MAY 1999 4.3 -1.2 9.9 JUN 1999 4.5 -1.2 10.3

ViResiST

Study of resistance series 8. Adjusted Model and Forecasts Plot

-6

-4

-2

0

2

4

6

8

10

12

14

Jan-9

1

Jul-9

1

Jan-9

2

Jul-9

2

Jan-9

3

Jul-9

3

Jan-9

4

Jul-9

4

Jan-9

5

Jul-9

5

Jan-9

6

Jul-9

6

Jan-9

7

Jul-9

7

Jan-9

8

Jul-9

8

Jan-9

9

% C

eft

azi

dim

e-r

es

ista

nt/

inte

rme

dia

te g

ram

-n

eg

ati

ve

ba

cill

i

Monthly %CR_GNB FIT for CR_GNB from AR(3,5)Model

95% LCL for CR_GNB_FIT from AR(3,5) model 95% UCL for CR_GNB_FIT from AR(3,5) model

Prediction period

ViResiST

Study of Ceftazidime use series1. Fitting an ARIMA model

FINAL PARAMETERS:



Variables in the Model: B SEB T-RATIO APPROX. PROB.AR1 .2089066 .10287861 2.0306127 .04534779AR3 .2998711 .10471464 2.8636976 .00524672CONSTANT 4.4038403 .53592437 8.2172794 .00000000

We identified a possible AR(1,3) model (identification process not shown)

ViResiST

Transfer Function1. Searching the lag

• Cross-correlation between residuals of ARIMA AR(3,5) resistance series model and residuals of ARIMA AR(1,3) cefta use series model

A lag 1 significant correlation is observed

ErrUDA with ErrRes

Nº de retardos

76543210-1-2-3-4-5-6-7

CC

F

1.0

.5

0.0

-.5

-1.0

Límites confianza

Coeficiente

ViResiST

Reading SPSS CCF graphics

A lag 1 significant correlation is observed, but correlation values decreases slowly: exponentially?

ErrUDA with ErrRes

Nº de retardos

76543210-1-2-3-4-5-6-7

CC

F

1.0

.5

0.0

-.5

-1.0

Límites confianza

Coeficiente

Lag 0: Contemporaneous relationship

Negative lags: Resistance(t-n) precedes Use(t)

Positive lags: Use (t-n) precedes Resistance (t)

ViResiST

Transfer Function 2. Lagging ceftazidime use series

• Using the LAG SPSS function we create a new variable: DDDLAG1 corresponding to the original ceftazidime use series lagged by 1 month

ViResiST

Transfer Function 3. Estimating parameters

• Results:FINAL PARAMETERS:



Variables in the Model: B SEB T-RATIO APPROX. PROB.AR3 .3522779 .09562566 3.6839264 .00040065AR5 .2650410 .09755863 2.7167353 .00796999DDDLAG1 .4196736 .09561494 4.3892053 .00003218CONSTANT 1.3536466 .76000187 1.7811095 .07842531

ViResiST

Transfer Function 4. Model Diagnostics

• Parameters Significance:– All three are significant

• Residuals series is white noise

Error for SACEFT_1 from ARIMA, MOD AR(3,5) DDDLAG1

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F

1.0

.5

0.0

-.5

-1.0


es

Coeficiente

Error for SACEFT_1 from ARIMA, MOD AR(3,5) DDDLAG1

Nº de retardos

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

AC

F p

arc

ial

1.0

.5

0.0

-.5

-1.0

Límites confianza

Coeficiente

• Stationarity Control:– AR3: (1 - 0’3522779)/0’09562566 >

1’96 – AR5: (1 - 0’2650410) / 0’09755863 >

1’96

ViResiST

Transfer Function 5. Goodness of fit

• Comparing with the univariant model:

Model AIC * R2 ** ResidualVariance

AR(3,5) 432 0.38 6.86

AR(3,5) ULAG1 416 0.44 5.67

* AIC: Akaike Information Criterion** R2: determination coefficient

ViResiST

Transfer Function 6. Predictions using the model

-10

-5

0

5

10

15

ene-91

jul-9

1

ene-92

jul-9

2

ene-93

jul-9

3

ene-94

jul-9

4

ene-95

jul-9

5

ene-96

jul-9

6

ene-97

jul-9

7

ene-98

jul-9

8

ene-99

% C

eft

azi

dim

e-r

es

ista

nt/

inte

rme

dia

te g

ram

-n

eg

ati

ve

ba

cill

i

Monthly %CR_GNB FIT for CR_GNB from TFModel

95% LCL for CR_GNB_FIT from TF model 95% UCL for CR_GNB_FIT from TF model

Prediction period

Comparing predictions from both modelsTransfer Function

6. Predictions using the model

-2

0

2

4

6

8

10

12

14

% C

efta

zid

ime

-re

sis

ta

nt/in

te

rm

ed

iate

gra

m-

ne

ga

tiv

e b

ac

illi

Monthlu %CR_BGN FIT for CR_GNB from TFModel 95% LCL for CR_GNB_FIT from TF model 95% UCL for CR_GNB_FIT from TF model

Univariate AR(3,5) MODEL8. Adjusted Model and Forecasts Plot

-2

0

2

4

6

8

10

12

14

% C

efta

zid

ime

-re

sis

ta

nt/in

te

rm

ed

iate

gra

m-

ne

ga

tiv

e b

ac

illi

Monthlu %CR_BGN FIT for CR_GNB from AR(3,5)Model

95% LCL for CR_GNB_FIT from AR(3,5) model 95% UCL for CR_GNB_FIT from AR(3,5) model

ViResiST

Transfer Function7. Interpretation of the model

• Dynamic Relationship:– The relationship occurs 1 month after the increase

in AU (p < 0’05)

• Magnitude of the effect: the estimated effect is the parameter of the lagged cefta use series: 0.42 (p<0.0001)

• For every 1 DDD/1000 beddays change in Ceftazidime use, a similar (positive or negative) change of 0.42% in the % of resistance, will be expected 1 month later

ViResiST

Interpretation

• As DDD is a rate per 1000 pat/days, in our case, with an average of near 6000 beddays per month, this use is equivalent to 6 absolute DDD per month.

• Each new treatment (aprox: 6 DDD) in our hospital will ADD 0.42% OVER THE PRECEDENT RESISTANCE LEVEL, one month later. That is to say, if the precedent resistance level is, for example, 10%, then next month it will be: 10+0.42% = 10.42%

• This is the risk of ceftazidime use on our hospital resistance level per each treated patient

• Quantifying risk allows us to compare several antibiotic among them: wich antibiotic must I use in my hospital?: that one with lowest risk to generate resistance

ViResiST

And later….?

• Our period study was from 1991 to 1998

• But what happened afterwards?

ViResiST

Monthly Percent Ceftazidime-Resistant/Intermediate Gram-Negative Bacilli and Hospital Ceftazidime Use, Hospital

Vega Baja, Spain, July 1991-April 2002

0

2

4

6

8

10

12

14

16

18

20

Jan-9

1

Jul-9

1

Jan-9

2

Jul-9

2

Jan-9

3

Jul-9

3

Jan-9

4

Jul-9

4

Jan-9

5

Jul-9

5

Jan-9

6

Jul-9

6

Jan-9

7

Jul-9

7

Jan-9

8

Jul-9

8

Jan-9

9

Jul-9

9

Jan-0

0

Jul-0

0

Jan-0

1

Jul-0

1

Jan-0

2

Ho

spit

al c

efta

zid

ime

use

(D

DD

/1,0

00 p

atie

nt-

day

s)

0

2

4

6

8

10

12

14

16

% C

efta

zid

ime-

resi

stan

t/in

term

edia

te g

ram

-n

egat

ive

bac

illi

And later….?

Five Period Centered Moving Average of the Monthly Percent Ceftazidime-Resistant/Intermediate Gram-

Negative Bacilli and Hospital Ceftazidime Use, Hospital Vega Baja, Spain, July 1991-April 2002

0

2

4

6

8

10

12

% C

eft

azid

ime

-

res

ista

nt/

inte

rme

dia

te g

ram

-

ne

ga

tiv

e b

ac

illi

0

2

4

6

8

10

12

14

16

Ho

sp

ita

l c

eft

azid

ime

us

e

(DD

D/1

,00

0 p

ati

en

t-d

ays

)

And later….?

ViResiST

Tranfer Function model for Monthly Percent Ceftazidime-Resistant/Intermediate Gram-Negative Bacilli and Hospital

Ceftazidime Use, Hospital Vega Baja, Spain, July 1991-April 2002

FINAL PARAMETERS: Number of residuals 131 Standard error 3.6040386 Log likelihood -352.39089 AIC 710.78177 SBC 719.40737 Analysis of Variance: DF Adj. Sum of Squares Residual Variance Residuals 128 1664.1818 12.989094 Variables in the Model: B SEB T-RATIO APPROX. PROB. AR3 .2014225 .08685400 2.3190930 .02197448 DDDLAG1 .3623209 .08095011 4.4758541 .00001663 CONSTANT 3.0570468 .65710783 4.6522757 .00000807

ViResiST

Discussion• This methodology suggests the possibility of quantifying the effect of

antimicrobial use on resistance, and also the time interval necessary for this, adjusting by other factors: – related to the past values of resistance seriesrelated to the past values of resistance series( maybe they represent adjustments

at the ecosystem, i.e.: the ecologic competition between different strains): • AR terms (autoregressive): they comprehend the influence of resistance past values

(X periods before) on the current levels. • MA terms (moving average): they comprehend the influence of previous random

variations (X periods before) on the current levels

– Due to third factorsDue to third factors i.e. % of R2 not explained by the model: – Use of other antibiotics: of the same or other families– Other possible factors:

• Compliance degree to hospital hygiene protocols• Use of antimicrobials in animal food• etc...

ViResiST

0

1

2

3

4

5

6

DD

D/1

00 p

at-d

ays

0

5

10

15

20

25

30

%C

R-P

A

Monthly Carbapenems use Monthly %IMIPENEM Resistant Pseudomonas aeruginosa

Imipenem Meropenem

Evolution of the Monthly % of Carbapenem Resistant Pseudomonas aeruginosa (%CR-PA) and Monthly Consumption of Carbapenems (imipenem until Dec-97 and

meropenem from Jan-97 to Dec-01). Antwerp University Hospital

ViResiST

0

1

2

3

4

5

6

DD

D/1

00 p

at-d

ays

0

5

10

15

20

25

30

%C

R-P

A

Monthly Carbapenems use Smoothed Monthly Carbapenems use

Monthly %CARBAPENEM Resistant PA Smoothed Monthly %CARBAPENEM Resistant PA

Imipenem Meropenem



ViResiST

Time Series Analysis model interpretation

• %CR-PA = 5*Imp(-2) + 1.4*Mer(0) + 1.98*Mer(-2) + 0.27*%CR-PA(-1) – 0.34*%CR-PA(-4)

• The observed Monthly percentage of carbapenem resistant Pseudomonas aeruginosa (%CR-PA) is a function of:

– Imipenem used two months before– Meropenem used contemporaneously and two months before– Inertia of resistance of previous month and 4 months before___________________________________________________________– Imipenem impact on resistance is 5 (*)– Meropenem impact on resistance is = 1.4 + 1.98 = 3.38 (**)– Meropenem impact on resistance is 67% of imipenem impact

– (*) per each DDD/100 pat-day of imipenem used, two months later, resistance will increase 5%

– (**) per each DDD/100 pat-day of meropenem used, two months later, resistance will increase 3.38%



ViResiST

% I

mip

enem

-res

ista

nt/in

term

edia

teP

seud

omon

as a

erug

inos

a

Ho

spit

al i

mip

enem

use

(DD

D/1

,000

pat

ien

t-d

ays)

Mar

. 199

4

Nov. 1

994

Mar

. 199

5

Jul. 1

995

Nov. 1

995

Mar

. 199

6

Jul. 1

996

Nov. 1

996

Mar

. 199

7

Jul. 1

997

Nov. 1

997

Mar

. 199

8

Jul. 1

998

Fuente: López-Lozano JM, et al. Int J Antimicrob Agents 2000;14:21-30.

35

30

25

20

15

10

5

0

45

40

35

30

25

20

15

10

5

0

Jul. 1

991

Jul. 1

992

Nov. 1

991

Mar

. 199

3

Nov. 1

993

Jul. 1

993

Nov. 1

992

Mar

. 199

2

Jul. 1

994

Jul. 1

999

Nov. 1

998

Mar

. 199

9

Lag effect = 1 month1 DDD/1,000 pat-days +0.40% R

5-Month Moving Average Percent Imipenem-Resistant/Intermediate P. aeruginosa and Hospital Imipenem Use, Hospital Vega Baja, Spain,

1991-1998

ViResiST

Source: Lepper et al. Antimicrob Agents Chemother, 2002; 46:2920-25.

Evolution of the monthly % of Imipenem-Resistant/Intermediate P. aeruginosa and Hospital Imipenem Use, Ulm University Hospital,

Germany, 1997-1999

ViResiST

Cross-correlation function of the monthly % of Imipenem-Resistant/Intermediate P. aeruginosa and Hospital Imipenem Use,

Ulm University Hospital, Germany, 1997-1999

Source: Lepper et al. Antimicrob Agents Chemother, 2002; 46:2920-25.

* Significant lag

ViResiST

Monthly evolution of %MRSAAberdeen Royal Infirmary and Woodend Hospital. 1996-2002

0

10

20

30

40

50

60

70

Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02

Aberdeen Royal Infirmary

Woodend

ViResiST

Evolution of the monthly %MRSA and monthly use of macrolides(MAC), third-generation cephalosporins(3GC) and fluoroquinolones(FQU), Aberdeen Royal Infirmary,

January 1996 - December 2000

020406080

100120140160180200

Jan-96 Jan-97 Jan-98 Jan-99 Jan-00

An

tim

icro

bia

l co

ns

um

pti

on

(D

DD

/1,0

00

pa

tie

nt-

da

ys)

0

5

10

15

20

25

30

35

40

45

MR

SA

(%

)

Third-generation cephalosporins Macrolides Fluoroquinolones %MRSA

%MRSA(t)= %MRSA(t-1) + MAC(t-1 to -3) +

3GC(t-4 to -7) + FQU(t-4 to -5)

ViResiST

Evolution of the monthly %MRSA and monthly sum of lagged antimicrobial use: macrolides (lags of 1 to 3 months), third-generation cephalosporins (lags of 4 to 7 months) and fluoroquinolones (lags of 4 and 5 months), Aberdeen Royal Infirmary,

January 1996 - December 2000

500

600

700

800

900


DD

D/1

000

bed

day

s

0

5

10

15

20

25

30

35

40

45

Mo

nth

ly %

MR

SA

Sum of lagged antimicrobial consumption %MRSA

ViResiST

Monthly %MRSA at Aberdeen Royal Infirmary and in the surrounding Grampian Region, January 1996-February 2002

0

10

20

30

40

50

ene-96 ene-97 ene-98 ene-99 ene-00 ene-01 ene-02

0

5

10

15

20

Monthly %MRSA in hospital

Monthly % MRSA in communityExplaining

variableLag(months)

Estimated coefficient

T Statistic (Prob.)

MRSACOMMMRSACOMM 3 0.27 2.07(p = 0.042)

MRSACOMM*DMRSACOMM*D0000

3 -0.32 -1.89(p = 0’063)

D00D00 - 4.66 4.76(p < 0.0001)

MRSAARIMRSAARI 1 0.10 5.12(p < 0.0001)

CC - 0.47 1.99 (p = 0.051)

R2R2 - 90.8% -

ViResiST

The Aberdeen MRSA Outbreak

0

10

20

30

40

50

60

70

Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02

Aberdeen Royal Infirmary

Woodend

500

600

700

800

900


DD

D/1

000

bed

day

s

0

5

10

15

20

25

30

35

40

45

Mo

nth

ly %

MR

SA

Sum of lagged antimicrobial consumption %MRSA

0

10

20

30

40

50

ene-96 ene-97 ene-98 ene-99 ene-00 ene-01 ene-02

0

5

10

15

20

1: Woodend outbreak

2: Woodend transmit MRSA to ARI

3: ARI antimicrobial use select resistance

4: ARI transmit resistance to Woodend

5: ARI transmit resistance to Community

ViResiST

Project ViResiST

José-María López-Lozano

Dominique L. Monnet

Hospital Vega BajaHospital Vega Baja Orihuela-Alicante (Spain)

Statens Serum InstitutStatens Serum Institut Copenhagen (Denmark)

ViResiST

What is ViResiST?the Spanish acronym for:

• Vigilancia de la • Resistencia • por medio del

Análisis de Series Temporales

• Surveillance of• Resistance• by means of • Time Series

Analysis

ViResiST

Participating Hospitals

Hospital Vega Baja. Spain 400

Hospital Clínico. Valencia. Spain 574

Hospital General de Castellón. Spain 635

Hospital Dr. Peset. Valencia. Spain 538

Hospital G. Universitario. Elche. Spain 433

Academic Hospital Rótterdam. Holland 1200

Royal Infirmary Aberdeen. Scotland 1200

Hospital Ramón y Cajal. Madrid. Spain 1000

Centre Hospitalier Universitaire. Besançon. France

1300

No. beds

ViResiST

EXPORT

RESULTS

TIME SERIES ANALISYS

MACRO

ANTIBIOTIC PROFILE SERIES

ISOLATE SERIES

RESISTANCE SERIES

ANTIBIOTIC USE SERIES

Automatic process Semi-automatic process

ViResiST

Expected % of imipenem-resistant

P.aeruginosa for current month

Expected resistance percentage for each microorganism-antibiotic combination

ViResiST

Expected microorganism in concrete specimen at a concrete service

ViResiST

SpecimenMicroorg. AntibioticSetting

Save graphics

Saving results(Excel format)

Evolution of monthly percentage

of resistance

Number of resistant

isolates

Total number of

isolates

ViResiST

Monthly no. DDD per

1,000 patient-days

Evolution of the hospital antimicrobial use

ViResiST

Monthly no.DDD/1,000 inhab.-days

Antibiotic use in the community

ViResiST

Resistance series comparison among several hospitals or community centers

ViResiST

Comparing antimicrobial use among different hospitals

ViResiST

Combined evolution of antimicrobialuse in several primary health care regions

ViResiST

Monthly hospital erythromycin use

Monthly hospital clarithromycin use

Monthly % erythromycin-resistant coag.-negative staph.

Comparing resistance and antibiotic use series

ViResiST

Investigators• Main researcher

José María López Lozano

• Amparo Burgos San José

• Pilar Campillos Alonso

• Nieves Gonzalo Giménez

• Dominique L. Monnet

• Alberto Yagüe Muñoz

• Alberto Cabrera

• Arielle Beyaert

• Epidemiologist. HVB

• Farmacist. HVB

• Farmacist. HVB

• Microbiologist. HVB

• Microbiologist. SSI

• Microbiologist. HVB

• Epidemiologist. HVB

• Professor of Econometrics. UM

HVB: Hospital Vega Baja, Orihuela, Alicante, España

SSI: Statens Serum Institut. Copenhague, Dinamarca

UM: University of Murcia

Documents

Theorical and methodological background