Local Hospital Perspective on a Nationwide Outbreak of Pseudomonas aeruginosa Infection in Norway
Objective. To implement a system for monitoring of rare events based on statistical process control charts.
Design. Statistical process control plotting by g chart of clinical microbiology laboratory data.
Setting. Primary and secondary care Norwegian hospital with a 9-bed intensive care unit.
Results. During the winter of 2001–2002 in Norway, there was a national monoclonal nosocomial outbreak of Pseudomonas aeruginosa infection mainly affecting patients in intensive care units. In the present work, we demonstrate how the use of SPC at one of the affected hospitals would have detected this outbreak several weeks before the alert from the Norwegian National Public Health Institute (NIPH). By plotting the monthly incidence rate of P. aeruginosa infection (with a c chart), we found that the hospital would have been alerted in February; by plotting the number of days between events (with a g chart), we found that the hospital would have detected a process already out of control in early January 2002. Not until 9 weeks later (ie, mid-March) did the NIPH declare the P. aeruginosa outbreak to be national, and a commercially produced mouth swab contaminated during the manufacturing process was found to be the source.
Conclusion. The plotting of rare events, such as an outbreak of nosocomial infection, with a g chart may be used for early detection of a process out of control.
Received December 29, 2007; accepted April 11, 2008; electronically published June 19, 2008.
All types of industries have for a long time monitored their production processes by continuously measuring some quality criterion, like thickness of paper or the proportion of defective items in a sample. This approach has increasingly been adopted by hospitals. Having decided on reasonable indicators, one can monitor a process and measure quality improvement by the use of simple, but statistically rigorous, charts. An effective method of monitoring a process by use of these control charts is called statistical process control (SPC).1,2
In a control chart, the observed values of an indicator are plotted consecutively, usually against time. Such charts give a quick overview of the performance of a process, in terms of both the general level of performance and its variability. The charts can therefore assist medical staff and managers in distinguishing whether a process is stable or out of control.2-21 In this way, SPC can be used as an aid to improve process performance. The hospital infection control community is slowly embracing SPC; however, the use of the tool is still in its infancy in the field of infection control. The corresponding literature includes manuscripts combining theory and application,2-19 as well as more practical examples of intervention in the field of hospital infection control.20-21
In an industrial setting, the SPC charts traditionally and most frequently used are the so-called Shewhart charts.2 These charts are traditionally based on the consecutive plotting of the frequency, proportion, or mean value of a quality indicator for a production sample; this plotting is done on a regular basis (eg, daily, weekly, or monthly). The charts include horizontal lines representing the mean, with k (typically 3) SD control limits on either side of the mean. There exist easy rules for determining when a process is said to be out of control.1,2 These charts are simple to make and simple to use, and they do not require the user to have a substantial background in statistics. However, the standard types of Shewhart charts are not always the correct choice. Several papers have addressed the problem of choosing the correct SPC charts.7,12-19
The incidence rate of nosocomial infection is a possible indicator of the quality of care in a hospital. The presence of a nosocomial infection often constitutes a rare event, and the population at risk is taken into consideration. Indicators of this type (ie, rare events) are the main instances for which conventional charts for proportions or counts are inappropriate. Among the different charts applicable for use in a rare event such as a nosocomial infection in a setting with a low incidence of such infection, the chart based on the consecutive plotting of the number of days between observations, the so-called g chart, is commonly recommended.18,19
During the winter of 2001–2002, Norway experienced a nationwide outbreak of Pseudomonas aeruginosa infection.22 The health authorities alerted Norwegian hospitals about a suspected outbreak in February 2002. A case-control study showed that this outbreak, the largest-ever outbreak of P. aeruginosa infection in Norway, was caused by mouth swabs contaminated during the manufacturing process.22
In this article, we present an SPC-based quality-control system for detection of rare events, demonstrating that its use in a Norwegian hospital during the 2001–2002 outbreak of P. aeruginosa infection would have alerted the hospital of this outbreak several weeks earlier than did the alert from the national health authorities.
Methods
SPC
SPC techniques are frequently used to monitor the performance of a process.1,2 The main tools of SPC are the control charts. In a control chart, the observed values of an indicator (vertical axis) are plotted consecutively, usually against some measure of time (horizontal axis).
Frequently Used SPC Charts
In an industrial setting, the traditional use of SPC is based on production samples. For every sample, the value of a quality indicator (eg, the number of defects) is calculated, and this value is usually recorded at equally spaced time points. This value is then plotted consecutively in a control chart. In a standard type of Shewhart chart, the frequency (which is usually plotted in a c or u chart), proportion (p chart), or mean value (I chart or XbarS chart) of a quality indicator is usually recorded for a large number of production samples, to achieve symmetry and to monitor the performance process. An essential goal of using these charts—which is not always directly stated—is to approximate normality. As a result, the symmetric upper and lower control limits (±3 σ limits) and the symmetric upper and lower acceptance limits (±2 σ limits) are the fundament for detection rules, giving indication of a shift in the process or of a process out of control.1,2 The 4 most common detection rules are (1) a single value outside either the upper or lower control limit, (2) two of 3 successive values outside an acceptance limit, (3) eight successive values on the same side of the center line, and (4) seven values in a row steadily increasing or decreasing.
The g Chart
For processes that generate rare events, the g chart, which plots the time between events, is the recommended way of monitoring the performance process, because the g chart can be more sensitive to changes in the process than the c chart.18,19 In a g chart, consecutive events are plotted along the horizontal axis, and the time between events (eg, in hours, days, weeks, or months) is plotted on the vertical axis. A value of 0 means that 2 consecutive events were registered at the same time, whereas high values on the vertical axis indicate a low frequency of events.
Data on the time between rare events are geometrically distributed and are inherently skewed.23 Hence, inferences drawn from such data, or charts, cannot be based on the symmetric limits of acceptance or control. Furthermore, the upper limit is of no practical interest, because it does not indicate whether the particular process under study is out of control, whereas the lower limit will in most cases be 0. This calls for a revision of the detection rules. However, it is still possible to formulate detection rules that are based on the mean and that are similar to the aforementioned fourth rule. A simple alternative rule can be developed using the median center line proposed by Benneyan.19 In the following, we show that a detection rule based on the mean and on the number of consecutive points below this level is also a valid and robust rule for detection in a g chart.
Derivation of a Simple Detection Rule for g Charts
A c chart is based on a Poisson distribution, which will be reasonably symmetric for large samples. Because of the symmetric properties of many control charts, including the c chart, the probability of an observation being below the mean is 0.5 (50%). In contrast, this is not true for the g chart. For each baseline rate expressed in a g chart, the probability of an observation below the mean can be calculated explicitly. The detection rule, formulated as “a process out of control if k consecutive observations are below the mean,” depends on this probability. These calculations and the development of the detection rule are outlined in the Appendix. Table 1 displays the probability of k consecutive observations being below the mean for different values of k and the mean of the data at hand. This table shows how the probability of a false alarm varies as the infection rate decreases. When the mean number of days between infections exceeds 10, the probability of a false alarm (ie, a given number of consecutive observations below the mean) changes marginally. The rightmost column of this table could also have been calculated by the exponential approximation for low mean values, in which P(X ⩽ x̄) ≈ 0.632.
We observe that the number of consecutive values needed to reach a given significance level is relatively unaffected by the infection rate, if the rate is low. This fact can be used to formulate easy detection rules that are valid for a wide range of cases.
Types of Observations for Best Detection
A g chart can be based on some specific baseline rate or a rate estimated from historical data. In the later case, how the rate is estimated can affect the chart's overview of the performance of a process. For the best detection of deviations from recent historical baseline rates, it can be argued that the mean should not include the following observations: (1) very old observations, because they might not represent the current behavior of the process but rather the past behavior; and (2) very recent observations, because these could possibly include and, at the same time, conceal an as-yet-undetected outbreak. In conclusion, it would be preferable to calculate the mean on the basis of recent, but not the most recent, observations. This can be called a delayed moving window estimate of the mean. There is no set convention for how many historical data to include or how large a delay to use. The window width (ie, the number of observations used to calculate the mean) should be wide enough to give a stable estimate of the mean. This number will depend on the underlying infection rate and the distribution of the time between infections.
Evaluation of Stability of the Detection Rule
Our detection rule for the g chart is based on a delayed moving window estimate of the mean. Because there is no set convention for how large a delay should be or how many observations to use, we explored the stability of such a rule. We used 0, 5, 10, and 20 observations for the delay and 5, 10, 15, 30, and 50 observations for the width, with a total of 20 possible combinations. We used cluster analysis24 to test which of the 20 combinations would give similar results. The results of a cluster analysis can be visualized in a dendrogram. In a dendrogram, elements or groups of elements that are similar are linked together near the bottom of the graph, whereas elements or groups of elements that are less similar are linked together near the top of the graph.
National Outbreak of P. aeruginosa Infection in Norway as the Data Set
P. aeruginosa is a multiresistant pathogen that prefers a moist environment and causes severe infection in critically ill patients and immunocompromised patients. P. aeruginosa has been linked to several hospital-acquired outbreaks associated with contaminated equipment and tap water.25,26 The incidence of infection with this organism may be used as indicator in hospital infection control. During the winter of 2001–2002 in Norway, there was a national outbreak of P. aeruginosa infection. In late February 2002, the Norwegian Institute of Public Health (NIPH) alerted all secondary care hospitals in Norway about a suspected increase in the number of P. aeruginosa infections. The alert was based on reports from several Norwegian hospitals to the NIPH; these reports included data on the monthly incidence rates of nosocomial infections and on the monoclonality of strains.27 In March 2002, the NIPH declared the outbreak to be monoclonal and national.28 A total of 231 patients from 24 hospitals were identified as having the outbreak strain; 39 of these patients had positive blood culture results, and 71 died while hospitalized. In early April 2002, contaminated mouth swabs were identified as the cause of the outbreak.29
Data from the national outbreak of P. aeruginosa infection in Norway during the winter of 2001–2002 were collected at Asker and Bærum Hospital, a 250-bed secondary care hospital, and served as the data set for our case study. We implemented macros in Excel (Microsoft) to construct the SPC charts. The analysis of the detection rule was performed in R.24
Results
A standard-type Shewhart c chart2 plotting the number of P. aeruginosa infections per month at Asker and Bærum Hospital during January 1999–July 2002 is shown in Figure 1. Standard detection rules for such charts indicated an outbreak during January 2002. This would have been noticed in February 2002 as soon as the monthly reports for the hospital were made available.
Figure 1. A c chart of the monthly incidence rate of Pseudomonas aeruginosa infection during the period from November 1997 to July 2002. Included in the figure are the average and the upper and lower control and acceptance limits (3 σ and 2 σ, respectively). The calculations of the mean and the limits were based on 30 observations from 1999 to 2001.
A g chart plotting the number of days between new infections is shown in Figure 2. The figure shows 82 consecutive days between observations of infection during the period from March 2001 to March 2002, with a delayed moving window estimate of the mean based on 30 observations and a delay of 10. With a detection rule of 7 observations below the mean, the outbreak would have been detected on January 11, 2002. This date is more than 3 weeks before the date of detection that was reported by using the traditional approach and c charts, and it is more than 9 weeks before NIPH declared the outbreak to be national.
Figure 2. A g chart of 83 consecutive observations of the number of days between Pseudomonas aeruginosa infections during the period from March 2001 to March 2002. The calculations of the mean and the limits were based on 30 observations, with a delay of 10 observations. Observation 62 occurred on January 11, 2002.
Evaluation of the Stability of the Detection Rule
The delayed moving window estimate of the mean based on 30 observations and a delay of 10 that was applied above was chosen on the basis of the analysis presented in this section. A selection of 4 different combinations of delays and window widths is shown in Figure 3. Short widths resulted in huge fluctuations in the mean, making it unpredictable and thus useless for infection control. Too wide a range, on the other hand, could bury important patterns in the data, such as slowly increasing or decreasing trends. Also, because the organization of hospitals and the flow of patients are dynamic features, it is not always apparent that the underlying “steady state” of a process is fixed and permanent over time. We also observed that if the window width is wide enough, little stability is gained by increasing it. These are arguments for choosing a restricted value for the width. In the case of a long delay (in particular, for short ranges), a restricted width value becomes essential for detection of an outbreak (data not shown). On the basis of data from the present study, we recommend that the delay be greater than the number of observations needed in the detection rule. If it is not, the mean might be too influenced by the falling trend and thus obscure the outbreak. We have chosen a delay of 10 (Table 1).
Figure 3. The g charts of the number of days between Pseudomonas aeruginosa infection (Figure 2) with a delayed moving window estimate of the mean. The 4 different mean lines represent 4 different choices of delay (d) and window widths (w).
However, by detecting a process out of control in our study, we found that several combinations of width and delay behaved in a similar fashion. These combinations were shown both by an extended version of Figure 3 (data not shown) and cluster analysis (Figure 4). The dendrogram in Figure 4 shows which combinations of width and delay behave similarly. We observed that there were 2 main clusters. One of them consisted solely of combinations of both small widths and low delays (Figure 4). There is, as such, a subsubstantial difference between combinations of both low widths and low delays, compared with the remaining combinations. A more thorough investigation of the data and of the 20 different combinations revealed that, during the period of interest, there were possibly 2 different outbreaks. Six of the combinations did not detect the first outbreak, and most of these belonged to the right cluster of the dendrogram. A delay of at least 10 was needed to ensure detection of both outbreaks. We further observed that, if too short a range was used, the second outbreak was defined as 2 separate outbreaks (Figure 4), implying that a range of at least 15 is advisable to ensure stability. Statistical rules for the stability of calculations of the mean imply that it would most likely be advisable to go beyond 25 for the range.30 We have chosen range 30 and delay 10 in all of our SPC charts for the delayed moving window estimate of the mean.
Figure 4. Dendrogram of the degree of similarity between detection rules based on different combinations of window widths (w = 5, 10, 15, 30, and 50) and delays (d = 0, 5, 10, and 20) for estimation of the mean. Combinations that are similar with respect to detection of outbreaks are linked together near the bottom of the figure. Combinations that are less similar with respect to detection of outbreaks are linked together near the top of the figure. The shaded area (right) marks those combinations that did not detect both outbreaks. The gray square (left) marks those combinations defining the second outbreak as 2 separate outbreaks.
Discussion
In the present work, we have demonstrated how the use of a g chart for the monitoring of nosocomial infections could have detected the Norwegian outbreak several weeks before the alert from the NIPH.
For SPC techniques to be effective, they need to be generally applicable, they need to give a quick overview of a given process, and they need to be able to detect shifts in the performance process very quickly. As a result, simplicity is a desirable characteristic of the SPC techniques and charts. In contrast to previous c chart examples, the present work shows how a g chart with a detection rule based on consecutive observations below the mean can be used as a relatively robust tool for detecting rare hospital events.2-7,9,10,12,16,17,20,21 The g chart might detect a shift in process more quickly (ie, it might be more sensitive), compared with the c chart. Thus, our results are in agreement with those of Benneyan,18,19 who described the improved shift-detection sensitivity in g charts, compared with conventional charts. The present work also includes an analysis of the moving average as well as the delay.
For the present data set from Asker and Bærum Hospital, the c chart also detected the outbreak, but at a later date than did the g chart. In another hospital setting, it is quite possible that the time before detection would have been longer if a c chart had been used rather than a g chart and that a c chart would not have detected the minor outbreaks that the g chart detected. This information can be valuable for determining when interventions should be added to daily routines. The window width seemed to be the most important parameter for determining the robustness of our method, whereas the delay added to the method's ability to detect an outbreak. A detection rule based on a narrow range of observations (5 or 10 observations), with little or no delay (0 or 5 observations), suffered from being too short sighted and thus detected too few outbreaks. In general, we believe that a mean based on too narrow a width of observations is too unstable a basis for a detection rule, because it follows the observations too closely. According to our data, a delay of 10 or more and a range of approximately 30 gave consistently good results.
In an industrial setting, the consequences of a false alarm (ie, SPC incorrectly determining that a production process is out of control) are delays and economic losses, and it is usually highly important to avoid such false alarms. In a hospital setting, on the other hand, a false alarm will cause hospital staff to spend more time on extra efforts exploring the possible outbreak, but neglecting a true outbreak for a long time is most likely worse. SPC detection rules are based on probabilities, but a .05 significance level, which is commonly used by the medical community, is not always applicable to SPC nor, as an alternative, are calculations of the commonly used 80% or 90% power. When determining detection rules and probability limits, one must pragmatically take into account the clinical, economical, and administrative gains from early detection of an outbreak, considered against the consequences of a false alarm.
As a result of this experience, g charts were introduced as part of standard surveillance procedures in infection control at Asker and Bærum Hospital. Various nosocomial pathogens have been carefully selected in accord with the hospital profile (ie, pathogens from selected units and from the hospital as a whole). Data are currently updated weekly by infection control staff and presented quarterly on the hospital intranet. To avoid false alarms, the nosocomial aspect of each potential outbreak is analyzed by infection control staff before being processed further.
False alarms will always challenge daily use of SPC. This aspect has also been discussed by others.15 Thus, it is important to implement systems that minimize this challenge. The potential of wasting resources on false alarms may be offered as a reason against our implementation routines at Asker and Bærum Hospital; however, our experience is that, once established, the system is simple to operate. Another limitation of the present study is that the g chart is appropriate only if the baseline incidence is relatively low.15,18,19 However, because the costs associated with these rare events is often high, choosing the right SPC method is crucial for rapid detection of outbreaks; this fact has also been discussed by others.7,12-19
We conclude that SPC is a robust and valuable tool for quality management and should be used in hospital care. In particular, the present work shows that the g chart, with a detection rule based on consecutive observations below the mean, is a sensitive and robust tool for monitoring of nosocomial infections with a low infection rate. The benefits from correct use and follow-up of SPC charts include decreased economic expenses for the hospitals, better patient health, and even lives saved.
Acknowledgments
Potential conflicts of interest. All authors report no conflicts of interest relevant to this article.
Appendix
Probability Calculations
The calculations are mainly based on formulas presented by Benneyan.18,19
Let p denote the probability of an infection at a given day, and X the number of days between events. X can then take values of 0, 1, 2, 3, and so on. If we consider each day as independent, we get a series of so-called Bernoulli trials, each with 2 possible outcomes: “day with infection” or “day without infection.” The probability of the latter is (1−p). The number of days between events, X, will follow a geometric distribution,20 
The probability of, say, 4 days between infection is P(x = 4) = (1−p)4p, which corresponds to 4 days without infection and then an infection on the fifth day. The cumulative distribution is given by 
The probability p of an infection at a given day is unknown and must be estimated from the observed data. An estimate for p for a given time period is 
with [macx] denoting the mean number of days between events in that period.
The probability that the next value of X is below the mean, P(X ⩽ x̄), can be estimated from a cumulative geometric distribution inserting p = p̂.23 The probability of k consecutive events below the mean is 
The Excel macro is available on request by mail from the corresponding author.
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Address reprint requests to Mette Walberg, PhD, Microbiology Section, Laboratory Centre, Asker and Bærum Hospital, 1309 Rud, Norway (mette.
walberg@sabhf. no).