A Case Study in MonitoringHospital-Associated Infections

with Count Control ChartsShreyas S. Limaye1,

Christina M. Mastrangelo1,

Danielle M. Zerr2

1Industrial Engineering,

University of Washington,

Seattle, Washington2Children’s Hospital, Seattle,

Washington

ABSTRACT Hospital-associated infections are a major concern in the

medical community due to the potential loss of life and high costs. Monitor-

ing the incidences of infections is an established part of quality maintenance

programs in hospitals. However, traditional methods of analysis are often

inadequate since the incidences of infections are infrequent. In order to

address this issue, techniques such as the cumulative sum (CUSUM) chart

for counted data and the g-type control chart have been suggested. This

article demonstrates how these charts may be applied to infection control

surveillance data from Children’s Hospital and makes recommendations

for a control chart most suitable for monitoring hospital-associated infec-

tions.

KEYWORDS g-type control charts, hospital-associated infections, Poisson

control charts, SPC, statistical process control, surveillance

INTRODUCTION

Hospital-associated (HA) infections are any infections that are acquired or

spread as a direct result of a patient’s hospital stay. The Centers for Disease

Control and Prevention (CDC) estimates that about 2 million people acquire

HA infections each year and that about 90,000 of these patients die as a

result of their infections. Vulnerable populations such as children or ICU

patients are even more susceptible (Health Protection Agency, 2003).

The most common HA infections are central line–associated blood stream

infections (BSI), ventilator-associated pneumonia (VAP), and catheter-

associated urinary tract infections (UTI). Approximately 80,000 BSIs occur

in ICUs each year in the United States, and these infections may prolong a

hospital stay by 7 to 21 days (Champion and Mabee, 2000). Some of the pro-

spective studies indicate up to a 35% increase in mortality due to these

infections. The attributable cost per infection is estimated to be

$34,000–$56,000, and the annual cost of caring for patients with BSIs ranges

from $296 million to $2.3 billion. The incidence of VAP varies greatly,

ranging from 6 to 52% of intubated patients depending on patient risk

factors (AHRQ, 2001). The cumulative incidence is approximately 1–3%

Address correspondence to Shreyas S.Limaye, 5505 15th Ave. NE, Apt. 306,Seattle, WA 98105. E-mail:shreyas@u.washington.edu

Quality Engineering, 20:404–413, 2008Copyright # Taylor & Francis Group, LLCISSN: 0898-2112 print=1532-4222 onlineDOI: 10.1080/08982110802334120

404

per day of intubation. Overall, VAP is associated with

an attributable mortality of up to 30%. The average

cost per episode of VAP is estimated at $3000 to

$6000, and the additional length of stay for patients

who develop VAP is estimated at 13 days (Warren

et al., 2003). Urinary tract infections (UTIs) account

for about 40% of the total number of HA infections

in some reports and affect an estimated 600,000

patients per year (MMWR, 2002). The average cost

of one hospital-associated UTI is estimated to be

between $680 and $1,875 per patient infection, and

additional hospital days per patient due to UTIs

range between 1 to 4 days.

The problem of HA infections is quite significant

in terms of affecting patient lives, adding to the econ-

omic cost of the healthcare, and putting additional

strain on the hospital resources. Effective monitoring

of infection rates can alert clinicians to a change of

infection rates, prompt the quality improvement

teams to identify causes behind the abnormal

increase, and stimulate efforts to look for effective

interventions to reduce them. A control chart is an

effective tool for this.

The control chart is a running record of behavior

over time (Carey, 2002) and usually has one of three

goals: (1) reduce variation, that is, process improve-

ment; (2) signal the need for a process adjustment;

and (3) demonstrate stability. Control charts can

directly address goals 2 and 3. In order to accomplish

goal 1, they can provide useful pointers if used

appropriately. The use of control charts is increas-

ingly being suggested for a variety of applications

in healthcare in an effort to improve the quality of

healthcare delivery. Components of variability exhib-

ited by healthcare data make them attractive candi-

dates to apply control charting techniques (Matthes

et al., 2007). Woodall (2006) gives an excellent sum-

mary of various types of control charts in healthcare

monitoring and in public health surveillance, as well

as discussing the issues related to these charts.

The use of control charts is also widely used for

monitoring infections in an effort to improve patient

safety. Benneyan (1998) reasons that the use of SPC

in other fields that is, understanding current process

performance, achieving a consistent level of process

quality, monitoring for process deterioration and

reducing process variation, is very much applicable

to the case of monitoring infections as well. In order

to address some of the concerns of traditional control

charts in this setting, alternate charts have been

suggested. Gustafson (2000) suggests the use of

risk-adjusted control charts based on a standardized

infection ratio calculated by dividing the observed

number of infections by the expected number of

infections during a particular period. Benneyan

(2001a) develops the g-type and h-type control

charts based on inverse sampling from geometric

and negative binomial distributions for evaluating

number of cases or number of days between

HA infections as they can exhibit greater detection

power over conventional binomial-based approa-

ches. Morton et al. (2001) demonstrate use of

counted-data EWMA and CUSUM charts for effective

monitoring of hospital-associated infections.

This article compares different control charting

techniques for monitoring hospital-associated infec-

tions. It demonstrates a u-chart, a CUSUM chart for

low count data, and g-type control chart. The next

section describes the data, the application of control

charts to the data, and the merits of these charts. The

following section concludes by providing recom-

mendations regarding use of a suitable control chart-

ing technique for monitoring hospital-associated

infections based on this case study.

DATA DESCRIPTION

Five years of infection surveillance data (from

2002 to 2006) from the pediatric ICU of the Children’s

Hospital, Seattle, is used. The data represents the

total number of HA infections as well as ‘‘patient

days,’’ which is the total number of days patients

spent in the ICU that quarter. Quarterly data on three

of the main infection types, that is, catheter-related

blood stream infections (BSI), urinary tract infections

(UTI) and ventilator-associated pneumonia (VAP), of

infections is also available. In addition, the data

contain each infection incidence. The data are shown

in the Appendix.

The current practice is to use a control chart for

individuals on a quarterly basis to monitor the rate

of infections per unit, where the unit is 1000:1000

patient days, 1000 central line days, 1000 ventilator

days, or 1000 catheter days. In the infectious disease

field, it is common practice to collect data in this

manner and is how it is reported to the CDC. As

such, this data is readily available, and the methods

described here may easily be used in other infection

405 Monitoring Hospital-Associated Infections

monitoring applications (as shown by Benneyan,

1998, 2006; Smyth and Emmerson, 2000).

Figure 1 plots the total number of infections from

2002 to 2006. The data show an increase in the num-

ber of infections after 2002, followed by an upward

trend in 2004–2005 and a decreasing trend in 2005–

2006. In 2002, Children’s performed about 50 cardiac

surgeries; in the following years, between 200 and

250 cardiac surgeries were performed. In 2006, an

intensive hospital-wide initiative to reduce blood-

stream infections began. The yearly variation in the

data is not unsurprising since hospitals continuously

strive to improve the quality of their services with

new interventions and procedures to reduce the

possibility of infection transmission. Given this con-

dition of 24 subgroups and non-constant infection

rates, determining an appropriate control chart is a

challenge and is the goal of this article. Since it is

clear from Figure 1 that there is a difference in infec-

tion rates between 2002 and the subsequent years,

the control charts in this article will exclude 2002.

MONITORING INFECTION RATES

There are two distinct phases of control chart

practice (Alt, 2006; Woodall, 2000): Phase I uses

the charts for retrospectively testing whether or not

the process has been in statistical control, and phase

II uses the control charts to detect any departure of

the process from the standard values. Rather than

determining the control limits for one type of control

chart based on stable retrospective data, this case

study explores the type of control chart that is most

suitable for infection control data, which is typically

collected in terms of number of infections and

number of patient days or line days over a certain

period of time (quarter or month). In order to

achieve this, a u-chart, a CUSUM chart for low count

data, and g-type control chart are applied to the

infections data and their applications are discussed.

Figure 2 shows the method currently used for

monitoring infection rates. A control chart for indivi-

duals is used, and the control limits are recalculated

at the end of the year using the preceding two years

of data. The challenge with the current method is

that the process is actually producing attributes data

that follows a Poisson distribution.

The U Chart

Figure 3 illustrates a u-chart for the quarterly num-

ber of infections per 1000 days patient days in the

ICU. This presentation is consistent with the National

Nosocomial Infections Surveillance system (NNIS

Report, 2004). The u-chart is used here because each

patient day is an ‘‘area of opportunity’’ in which one

or more infections could occur. If the data had been

FIGURE 1 Plot of total infections per quarter. FIGURE 2 Current method: control chart for individuals moni-

toring total quarterly infections per 1000 patients.

FIGURE 3 U-chart for number of infections per quarter per 1000

patient days.

S. S. Limaye et al. 406

recorded as the number of patient days with one or

more infections, a p-chart would be more appropriate.

P-charts also work best if the rate of non-conforming

is greater than 0.05% (Montgomery, 2005). The HA

infection rates are typically smaller than that (.009

per day). In addition, even if the data were collected

in that manner, it follows that other charts that

handle low-count attribute data would be more

appropriate.

In this application, the number of infections per

quarter represents the number of nonconformities

and the number of patient days in the ICU per quar-

ter represents the sample size. To account for the dif-

ference in opportunity for initiation of infections, the

ratio of number of infections to total number of line

days per quarter is calculated (Carey, 2002). The cen-

ter line remains constant, whereas the control limits

shift for every observation to account for the differ-

ence in the number of ICU days.

It should be noted that more than 20 subgroups

are generally recommended for starting a control

chart. A monthly based control chart may be more

appropriate in that a sufficient number of samples

would be available as well as increased opportunities

to detect significant increases (or decreases) in infec-

tion rates. While the data contains the date of each

infection, the number of patient days per month is

not available. Figure 4 shows the u-chart for the

monthly number of infections per 1000 patient days

assuming that the patient days are equal in each

month of the quarter. The monthly based u-chart

may be more effective in pointing out some of the

sharp increases in the infection rate when compared

to the quarterly one.

Counted Data CUSUM Chart

The cumulative sum chart may also used to moni-

tor adverse events in health care (Morton et al., 2001;

Woodall, 2006). The CUSUM chart plots the cumulat-

ive sum deviations from the mean and places empha-

sis on keeping the process on aim rather than

allowing it to drift between the upper and lower con-

trol limits (Lucas, 1985). As a result, an out-of-control

signal indicates that action should be taken to pre-

vent the adverse events from exceeding the target.

The CUSUM charts in health care are typically one

sided, with the part corresponding to a decrease in

the number of hospital-acquired infections not

included. However, we use a two-sided CUSUM.

The upper CUSUM is designed to detect worsening

performance, and the lower CUSUM is designed to

detect improvement in performance (Woodall,

2006). By including both an upper and lower

CUSUM one will not only be able to determine what

is causing an increase in infection rates but also be

able to determine factors that will decrease the infec-

tion rate.

Figure 5 shows a CUSUM chart for count data that

follows the Poisson distribution for the number of

monthly hospital associated infections in the pedi-

atric ICU. While creating a CUSUM chart, one needs

to choose the reference value (k) and the decision

interval value (h). The parameter k is chosen to be

between the acceptable process mean (la) and the

mean that the CUSUM aims to detect quickly (ld).

Lucas (1985) recommends the approach given in

Table 1.

The average number of infections per month is

5.2, a target of 5 (la) infections per month is reason-

able, and the CUSUM aims to detect the shift to 7 (ld)

FIGURE 4 U-chart for the number of infections per month per

1000 patient days. FIGURE 5 CUSUM control charts for monthly infections.

407 Monitoring Hospital-Associated Infections

infections per month. For this shift, using the above

formula, k� 6. Once k is chosen, the value of h is

chosen. It should give an appropriately large ARL

when the counts are at the acceptable level and an

appropriately small ARL value when the process is

running at the count level that should be detected

quickly. For a k value of 6, an h value of 5 is chosen

(see Lucas, 1985). For detecting an increase in the

infection rate, a positive head start of 4 is used

whereas a head-start is not used for detecting

decrease in the infection rate. The corresponding

ARL1s for the counted data CUSUM are 9.5 and

1.32, respectively.

Each bar in Figure 5 represents the cumulative

sum deviation from the target mean. In addition,

the individual observations for each period on the

CUSUM status chart are also plotted as the solid dots.

The primary advantages of the CUSUM chart are

its ability to detect small shifts in the process and

its ability to provide early warning. In addition, the

CUSUM is particularly helpful in determining when

the assignable cause has occurred by just counting

backward from the out-of-control signal to the time

period when the CUSUM lifted above zero. The

CUSUM chart does provide an early warning regard-

ing increasing infection rates in January 2003 when

the CUSUM crosses center line after being below it

during 2002 and again in early 2005 after higher

infection rates are observed.

G-Type Control Chart

The g-type control chart provides an alternate way

to look at infection data. The g-type (geometric) con-

trol charts track the number of cases or amount of

time between events. These charts are particularly

useful when the data are low-count (Benneyan,

2001a).

Benneyan (2001a) observes that events between

infections do not follow the typical Poisson,

binomial, or normal distributions. Instead, these data

follow that of a geometric random variable. Figure 6

shows the actual days between infections and the

theoretical geometric distribution for p¼ .2 and

how the data closely follow the geometric distri-

bution. However, in this application, p is unknown,

so �xx will be used and the control parameters esti-

mated using the equations in Table 2. Note that

n¼ 1 and when the lower limit is negative, it is

rounded up to zero.

Figure 7 shows a g-type chart for the days

between infections. It is important to note that the

g-chart operates differently from a typical control

chart. It does not follow the standard intuition, which

is if a point is above the upper control limit an

assignable cause is present. In this case, a point

above the upper control limit signals an above aver-

age number of days between infections, which is a

desired goal (Benneyan, 2001b). While the lower

control limit is typically zero, it may be beneficial

to set the lower control limit slightly above zero so

in the rare case of an infection ‘‘outbreak’’ it would

be more readily detected.

The g-chart indicates an increase in the frequency

of infections. The annotations in Figure 7 point to

the two quarters (4th quarter of 2003 and 2nd quarter

of 2005) that had the highest infections rates (see

Figure 1). In addition, one can also note that even

though the number of infections in 2003–2004 and

TABLE 1 Calculation of k

Formula la ld k

k ¼ ðld�laÞðlnðldÞ�lnðlaÞÞ

5 7 ð7�5Þðlnð7Þ�lnð5ÞÞ � 6

FIGURE 6 The actual number of days between infections and

the values of the geometric distribution.

TABLE 2 Control Limits for the G-type Control Chart

Chart type UCL CL LCL

G-type chart (infection

rate known)

1�pp þ k

ffiffiffiffiffiffiffi1�pp2

q1�p

p1�p

p � kffiffiffiffiffiffiffi1�pp2

q

G-type chart (infection

rate estimated)

�xx ¼ kffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�xxð�xx þ 1Þ

p�xx �xx � k

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�xxð�xx þ 1Þ

p

where �xx¼ the average number of days between infections, p¼ therate of infection (if known), and k¼ the number of standard deviationsused in the control limits.

S. S. Limaye et al. 408

2005–2006 are approximately the same, infections

occur at more regular time intervals after December

2004 (as evidenced by the lower number of spikes).

A g-type control chart has an advantage in that

each data point can be plotted immediately, and the

overall effects can be seen quickly as well. Figure 8

shows g-type charts for BSI, UTI, VAP, and total

infections from 2003 to 2006. The plots indicate a

slight decrease in the number of BSIs in 2006 and

an increase in the days between infections. For

2006, UTIs and VAPs show a decrease in frequency

and increased days between occurrences.

CONCLUSIONS

This case study illustrates how control charting is

used currently in the pediatric ICU at the Children’s

Hospital and then demonstrates the use of different

techniques for the infection surveillance data. The

u-chart monitors the number of infections per 1000

FIGURE 7 G-type control chart for number of days between HA-infection incidences.

FIGURE 8 G-type control charts for overall infections, BSI, UTI, and VAP infections.

409 Monitoring Hospital-Associated Infections

patient days. The counted data CUSUM chart does

not use denominators and monitors the number of

infections per month directly. The g-type control

chart monitors the number of days between interven-

tions. Each chart has a set of advantages and

disadvantages.

The u-chart is simple to construct, capable of hand-

ling low-count data, and easy to interpret. It also takes

into account the change in the sample size which in

case is the varying number of patient days, line days

or ventilator days. In Figure 9, the quarterly based

u-chart did not detect a change in infection rates as

would be expected since the control chart was

developed from the data being monitored. A u-chart

for monthly data may provide more information.

However as Figure 10 shows, such a chart for rare

infections like UTI or VAP would not be very useful

since many months would have infection rates of 0.

The counted data CUSUM chart does provide an

early warning and can track small changes effec-

tively. However, it is slightly more complicated to

build, understand, and explain. Moreover, it is very

sensitive to the selection of k and h parameter values,

which affects the usability of this chart. Also, as one

can see in Figure 5, the CUSUM chart shows out-of-

control signals only in February and April 2006 while

actually the months preceding February 2006 have

higher infection rates. This is counterintuitive to the

user and not the preferred option.

The g-type control chart is simple to construct; it

can quickly point out the years in which the number

of infections is low; and it can quickly indicate long

periods having no infection occurrences. However,

the g-charts are not very helpful in detecting

increased rates of infection.

Children’s Hospital can certainly improve their

infection monitoring practices. The simplest and

effective way to achieve that would be the use of

u-chart as it would take into account the changing

number of patient, line, and ventilator days. For

FIGURE 9 U-type control charts for quarterly rates of BSI, UTI, and VAP infections.

S. S. Limaye et al. 410

monitoring overall infection rates and BSI, a u-chart

based on monthly infection rates would be more

effective, whereas for UTI and VAP, a u-chart based

on quarterly infection rates would be more suitable.

One of the disadvantages for the control charts

discussed is that they do not account for the differ-

ences between patients. Patients differ on their sever-

ity of illness, so it is expected that this variability

affects a patient’s likelihood of contracting a hospi-

tal-acquired infection. Risk-adjusted control charts

aim to address this issue by accounting for the vul-

nerability of a patient to infections (Alemi and Oliver,

2001). The vulnerability is established by key clinical

findings, diagnosis codes, or by consensus among

clinicians. The expected rate of infection is calcu-

lated using logistic regression to determine the

expected probability of an infection for each individ-

ual patient and then averaging these to calculate the

expected rate of infection for the period. The control

chart monitors the observed rate of infections versus

their expected rate.

In practice, an index to account for patient con-

dition is difficult to determine because the existing

methods are subjective. Unless a credible system to

compute the vulnerability of a patient for the specific

infection is developed, it may not be practical to use

risk-adjusted control charts. The data used in this

article do not provide information regarding the

vulnerability of each patient for different type of

infection so it is not possible to include this chart

in this case study or use it in most healthcare applica-

tions either.

ABOUT THE AUTHORS

Shreyas S. Limaye is a doctoral candidate at the

University of Washington, Seattle, and Advanced

Process Control Engineer at the Hitachi Global

Storage Technology, San Jose, CA. His professional

and research interests include applications of com-

plex system modeling, statistical analysis and process

control in healthcare, semiconductor manufacturing

FIGURE 10 U-type control charts for monthly rates of BSI, UTI, and VAP infections.

411 Monitoring Hospital-Associated Infections

and transportation logistics. He is a member of

INFORMS and IIE.

Dr. Christina M. Mastrangelo is an Associate

Professor of industrial engineering at the University

of Washington. She holds a BS, MS and PhD

degrees in Industrial Engineering from Arizona State

University. Prior to joining UW in 2002, she was an

Associate Professor of systems and information

engineering at the University of Virginia.

Dr. Danielle M. Zerr is an Associate Professor of

pediatric infectious diseases at the University of

Washington and the Medical Director of infection

control at Seattle Children’s Hospital.

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APPENDIX

TABLE A1 Total Number of Infections and ICU Patient Days

Quarter

# of

Infections

Patient

days

Infections per 1000

patient days Quarter

# of

Infections

Patient

days

Infections per 1000

patient days

Q1 2002 8 1451 5.51 Q3 2004 17 1526 11.14

Q2 2002 4 1207 3.31 Q4 2004 18 1543 11.67

Q3 2002 10 1372 7.29 Q1 2005 20 1629 12.28

Q4 2002 6 1413 4.25 Q2 2005 24 1453 16.52

Q1 2003 21 1481 14.18 Q3 2005 20 1552 12.89

Q2 2003 12 1256 9.55 Q4 2005 20 1519 13.17

Q3 2003 17 1275 13.33 Q1 2006 19 1934 9.82

Q4 2003 22 1348 16.32 Q2 2006 18 1950 9.23

Q1 2004 13 1432 9.08 Q3 2006 16 2066 7.74

Q2 2004 16 1596 10.03 Q4 2006 15 1857 8.08

S. S. Limaye et al. 412

TABLE A3 Total Number of UTI and ICU Foley Catheter Days

Quarter # of UTI

Foley

catheter days

UTI per 1000

Foley catheter days Quarter # of UTI

Foley

catheter days

UTI per 1000

Foley catheter days

Q1 2002 1 778 1.28 Q3 2004 1 718 1.39

Q2 2002 1 471 2.12 Q4 2004 3 848 3.53

Q3 2002 3 625 4.80 Q1 2005 2 921 2.17

Q4 2002 1 657 1.52 Q2 2005 4 844 4.73

Q1 2003 5 801 6.24 Q3 2005 6 873 6.87

Q2 2003 2 659 3.03 Q4 2005 4 768 5.20

Q3 2003 2 689 2.90 Q1 2006 1 752 1.32

Q4 2003 5 757 6.60 Q2 2006 3 624 4.80

Q1 2004 2 599 3.33 Q3 2006 1 808 1.23

Q2 2004 2 708 2.82 Q4 2006 0 512 0

TABLE A4 Total Number of VAP and ICU Ventilator Days

Quarter # of VAP

Ventilator

days

VAP per 1000

ventilator days Quarter # of VAP

Ventilator

days

VAP per 1000

ventilator days

Q1 2002 0 586 0 Q3 2004 2 713 2.80

Q2 2002 0 405 0 Q4 2004 1 766 1.30

Q3 2002 1 692 1.44 Q1 2005 0 1023 0

Q4 2002 0 594 0 Q2 2005 0 807 0

Q1 2003 1 840 1.19 Q3 2005 0 913 0

Q2 2003 0 480 0 Q4 2005 0 739 0

Q3 2003 1 602 1.66 Q1 2006 1 749 1.33

Q4 2003 2 703 2.84 Q2 2006 0 987 0

Q1 2004 1 571 1.75 Q3 2006 1 973 1.02

Q2 2004 3 724 4.14 Q4 2006 2 722 2.77

TABLE A2 Total Number of BSI and ICU Central Line Days

Quarter # of BSI

Central

line days

BSI per 1000

central line days Quarter # of BSI

Central

line days BSI per 1000 central line days

Q1 2002 4 821 4.87 Q3 2004 3 875 3.43

Q2 2002 3 510 5.88 Q4 2004 10 1160 8.62

Q3 2002 3 775 3.87 Q1 2005 9 1250 7.20

Q4 2002 2 801 2.50 Q2 2005 8 1121 7.14

Q1 2003 3 950 3.16 Q3 2005 7 1388 5.04

Q2 2003 5 768 6.51 Q4 2005 9 1054 8.54

Q3 2003 6 835 7.19 Q1 2006 10 1147 8.72

Q4 2003 6 897 6.69 Q2 2006 6 1055 5.69

Q1 2004 7 855 8.19 Q3 2006 8 1104 7.25

Q2 2004 4 892 4.48 Q4 2006 5 882 5.67

413 Monitoring Hospital-Associated Infections