- Email: [email protected]
Statistical analysis of spikes in bioburden
Radiation Physics and Chemistry 81 (2012) 1241–1243
Contents lists available at SciVerse ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Statistical analysis of spikes in bioburden Barry P. Fairand a,n, Vu Le b, Zabrina Tumaitis b a b
SteriPro, Division Sterigenics International, 3350 Kendelmarie Way, Dublin, OH 43017, USA SteriPro, Division Sterigenics International, 344 Bonnie Circle, Corona, CA 92880, USA
a r t i c l e i n f o
abstract
Article history: Received 22 June 2011 Accepted 15 February 2012 Available online 24 February 2012
A spike in a set of bioburden data can be considered a bioburden number or numbers that are several times greater in value than the average value of the data set. A spike is not considered a manifestation of a quality issue, but a consistent component of product bioburden that should be taken into account in establishing the minimum acceptable dose in the radiation sterilization process. Rather than a subjective approach, statistical techniques were used to determine when a bioburden number or numbers represent spikes in a set of bioburden data. Bioburden data taken from a cross section of different products over a few months were analyzed. Results of the study identified spikes when the spike bioburden was approximately three or more times the average bioburden for the data set. In those cases where bioburden spikes were identified, use of the spike bioburden rather than the average bioburden increased the sterilization dose by up to 10%. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Bioburden spikes Statistical techniques Radiation sterilization Sterilization dose
1. Introduction
2. Approach for analysis of bioburden data with spikes
Dose setting methods that are used to establish the minimum dose in radiation sterilization are based on product bioburden. Determination of the bioburden that is used in selecting the dose for the verification dose experiment is based on an average value calculated from 10 product items randomly selected from a manufactured batch of product. In those cases where multiple batches of product are manufactured, it is standard practice to take 10 product items from three batches of manufactured product and calculate the average biobuden for each of the three random samples (ANSI/AAMI/ISO 11137-2, 2006). An issue that is sometimes encountered in the analysis of bioburden data involves what is referred to as spikes in the bioburden data. A spike can be considered a bioburden number or numbers in the data set that are several times greater in value than the average value of the data set. A spike should not necessarily be considered a manifestation of a quality issue, rather a repetitious, but low probability event that is a consistent component of the product bioburden. Understanding in the medical device industry traditionally had defined a spike in a qualitative manner as a value that is two or more times the sample batch average. Rather than a qualitative assessment, the data was analyzed using statistical techniques, which offers a quantitative approach for determining if a bioburden number is simply an extreme manifestation of statistical variability in the data or in fact should be considered a spike and treated in a separate manner.
The average bioburden on a product is based on random samples that are taken from different batches of manufactured product. In this regard, it is standard practice to collect at least 10 samples for each data set. The averaging process assumes that all data in the data set are from the same population. The dispersion of values about the average value can be characterized using standard statistical techniques where the sample standard deviation is the cogent parameter for describing the dispersion of values about the average value and the distribution of data can be fit to a mathematical model. A Student-t probability distribution, which offers a mathematical fit to the bioburden data, was used in the analysis. The t-distribution is an appropriate statistical model when one is dealing with a limited number of degrees of freedom, i.e., number of comparisons, and the distribution in bioburden numbers is approximately symmetric. It is noted in ISO 11737-1 that the distribution could tend to be skewed with a long tail to the right (ANSI/AAMI/ISO 11737-1, 2006). Each of the individual random samples of bioburden was evaluated to see if the distribution was skewed to the right and in which case a lognormal distribution may be more appropriate for analysis of the bioburden data than a t-distribution. The analysis involved a visual inspection of the bioburden data and comparison of the mean and median values. Except for random samples with low average bioburdens, which showed some degree of skewness, that is about a 20% difference between the average and median values, the distributions were approximately symmetric wherin the mean and median buoburden numbers were not significantly different and use of a t-distribution in the analysis of the bioburden data
n
Corresponding author. E-mail address: [email protected] (B.P. Fairand).
0969-806X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radphyschem.2012.02.020
1242
B.P. Fairand et al. / Radiation Physics and Chemistry 81 (2012) 1241–1243
was considered appropriate. It is possible the observed skewness in the distributions with low average bioburden could be attributed to factors related to limitations in the sensitivity of the test method that is used to determine bioburden.
Table 1 Bioburden data.
2.1. Single spike in data set Spikes in a random sample of bioburden data typically appear as a single value in a set of ten numbers. For the case of a single spike in the set of bioburden data, a statistical technique can be used to place a quantitative bound on when a bioburden number in the data set should be considered a spike rather than an extreme manifestation of statistical variability in the data. This approach is based on calculation of a t-statistic and comparison of that number with a critical t-value, which is related to the degree of risk one is willing to accept that a bioburden value should be considered a spike rather than an extreme manifestation of statistical variability in the data (ASTM E178-08). The test statistic is given by the following expression: ð1Þ
where t is the test statistic, Ci is the bioburden number considered outlier that is spike, Cavg is the average bioburden number for 10 samples, and ss is the sample standard deviation. If the value of t that is calculated from the above expression exceeds a critical t-value, i.e., t*, the bioburden number under study should be considered a spike. The risk of designating a biobuden number as a spike, when in fact it should have been retained in the data set, was set equal to 2% or one chance in 50, which is more conservative than a value of 5% that is commonly used for reporting results of research in many fields of science. Because the only concern is the largest bioburden number in the data set, a one sided t-distribution was used in the selection of the critical t-value. The 2% number is equal to the area in the upper tail of the probability curve. The critical t* value for 9 degrees of freedom, i.e., 10 observations, and a 2% risk is 2.398.
y¼(Ci/Cavg)
0 1.211 1.288 1.451 1.496 1.512 1.591 1.772 1.878 1.901 1.901 2.035 2.121 2.144 2.147 2.193 2.408 2.442 2.482 2.748
1 1.68 1.291 1.582 1.325 1.762 1.75 1.601 2.414 2 2.405 2.564 2.286 2.5 2.593 2.222 2.549 2.886 3.333 3.812
4.0
Ratio Peak to Average Bioburden
t ¼ ðC i 2C avg Þ=ss
t-Value
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
0.5
3. Results 3.1. Bioburden data The analysis was based on random samples that were taken from microbiological data collected from a spectrum of different medical devices over a few months. The average bioburdens ranged from about 10 CFU to more than 3000 CFU. Each random sample of ten bioburden numbers was independent of other random samples. 3.2. Statistical analysis A sampling of bioburden information that was used in the analysis of a possible single spike in a data set is given in Table 1. The data is presented in terms of two dimensionless parameters; the ratio of peak bioburden number to average bioburden number and the corresponding test statistic. As the ratio of peak bioburden number to average bioburden number approaches 1, the value of t approaches 0. This set of intercept data also is included in Table 1. The data in Table 1 is plotted in Fig. 1. As seen from Fig. 1, all of the data could fit a single function. The cohesiveness of the data shown in Fig. 1, which is plotted as a function of the t-value, is consistent with selection of a t-distribution for statistical analysis of the data. Non-linear regression analysis was used to fit the data to a third order polynomial that is given by Eq. (2). The resultant
1.0
1.5
2.0
2.5
3.0
t-Value Fig. 1. Ratio (peak/average) bioburden number versus t-value.
curve is shown in Fig. 1 y ¼ ðC i =C avg Þ ¼ 0:999 þ 0:262t20:069t 2 þ 0:122t 3
ð2Þ
When a critical t-value (t*) of 2.398 is substituted into Eq. (2), the ratio of peak bioburden number to average bioburden number is 2.9 or approximately three. This multiple in peak-to-average bioburden is not inconsistent with the multiple of two that is noted in Ref. Bryans (1996). As seen from the data in Table 1 and plot of the data in Fig. 1, bioburden spikes were identified in four cases.
4. Proposed application of spike information Once a bioburden spike is identified, it should be considered in the selection of the sterilization dose. This would depend on the method that is used to establish the sterilization dose. For example, when Method 1 is used to establish the sterilization dose, it is proposed that selection of the verification dose be based on the average bioburden and the spike bioburden number should be used in selecting the sterilization dose. The bioburden data for the four spikes that were identified in Table 1 are given in Table 2.
B.P. Fairand et al. / Radiation Physics and Chemistry 81 (2012) 1241–1243
1243
5. Conclusions
Table 2 Data for bioburden spikes. Spike ID t-value
Bioburden number (CFU)
Verification dose (kGy)
Sterilization dose (kGy)
t ¼ 2.408
Ci ¼65 Cavg ¼ 25.5
N/A 6.3
20.5 19.1
t ¼ 2.442
Ci ¼852 Cavg ¼ 295.2
N/A 9.4
24.7 22.9
t ¼ 2.482
Ci ¼88 Cavg ¼ 26.4
N/A 6.4
21.0 19.1
t ¼ 2.748
Ci ¼260 Cavg ¼ 68.2
N/A 7.5
22.7 20.6
The doses that are given in Table 2 were taken from Table 5 (Method 1) in ANSI/AAMI/ISO 11137-2. As seen from Table 2, use of the spike bioburden number in the selection of the sterilization dose increased its value from use of the average bioburden number by about 7–10%. A ratio of spike bioburden number to average bioburden number that is much greater than 3 may be indicative of a quality issue that is traceable to a manufacturing material problem or possibly laboratory contamination rather than a low probability event that is a consistent component of product bioburden. Statistical analysis of the bioburden data may offer insight as to whether one is dealing with a spike that is a consistent component of product bioburden or in fact is related to a quality issue. In that regard, the relationship of the resultant data to the curve that is shown in Fig. 1 may be helpful in ascertaining if one is dealing with a bioburden spike or quality issue. One would expect this situation to occur on a very infrequent basis.
As seen from the preceding treatise, statistical techniques can be used for analysis of spikes in the bioburden data and provide quantitative results that can be used in the selection of sterilization parameters. Results from the cited examples are not inconsistent with present methods for analysis of bioburden data, but represent a quantitative approach for analysis of the bioburden data that is not subjective in its interpretation. Statistical techniques also offer the possibility of evaluating bioburden data to test for outliers that may be attributable to quality issues and should not be considered spikes in the bioburden data. It is proposed that a statistical approach for analysis of bioburden data be considered and tested on a wider scale of data to assess its applicability in the radiation sterilization process.
Acknowledgement The authors would like to thank Sterigenics International for support in this study. References ANSI/AAMI/ISO 11137-2, Sterilization of Health Care Products—Part 2: Establishing the Sterilization Dose, 2006. ANSI/AAMI/ISO 11737-1, Sterilization of Health Care Products-Microbiological Methods—Part 1: Determination of the Population of Microorganisms on Product, 2006. ASTM E178-08, Standard Practice for Dealing with Outlying Observations. Bryans, T., 1996. Using Bioburden Spikes in Radiation Dose Setting, vol. 3 (1). The Validation Consultant.
Contents lists available at SciVerse ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Statistical analysis of spikes in bioburden Barry P. Fairand a,n, Vu Le b, Zabrina Tumaitis b a b
SteriPro, Division Sterigenics International, 3350 Kendelmarie Way, Dublin, OH 43017, USA SteriPro, Division Sterigenics International, 344 Bonnie Circle, Corona, CA 92880, USA
a r t i c l e i n f o
abstract
Article history: Received 22 June 2011 Accepted 15 February 2012 Available online 24 February 2012
A spike in a set of bioburden data can be considered a bioburden number or numbers that are several times greater in value than the average value of the data set. A spike is not considered a manifestation of a quality issue, but a consistent component of product bioburden that should be taken into account in establishing the minimum acceptable dose in the radiation sterilization process. Rather than a subjective approach, statistical techniques were used to determine when a bioburden number or numbers represent spikes in a set of bioburden data. Bioburden data taken from a cross section of different products over a few months were analyzed. Results of the study identified spikes when the spike bioburden was approximately three or more times the average bioburden for the data set. In those cases where bioburden spikes were identified, use of the spike bioburden rather than the average bioburden increased the sterilization dose by up to 10%. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Bioburden spikes Statistical techniques Radiation sterilization Sterilization dose
1. Introduction
2. Approach for analysis of bioburden data with spikes
Dose setting methods that are used to establish the minimum dose in radiation sterilization are based on product bioburden. Determination of the bioburden that is used in selecting the dose for the verification dose experiment is based on an average value calculated from 10 product items randomly selected from a manufactured batch of product. In those cases where multiple batches of product are manufactured, it is standard practice to take 10 product items from three batches of manufactured product and calculate the average biobuden for each of the three random samples (ANSI/AAMI/ISO 11137-2, 2006). An issue that is sometimes encountered in the analysis of bioburden data involves what is referred to as spikes in the bioburden data. A spike can be considered a bioburden number or numbers in the data set that are several times greater in value than the average value of the data set. A spike should not necessarily be considered a manifestation of a quality issue, rather a repetitious, but low probability event that is a consistent component of the product bioburden. Understanding in the medical device industry traditionally had defined a spike in a qualitative manner as a value that is two or more times the sample batch average. Rather than a qualitative assessment, the data was analyzed using statistical techniques, which offers a quantitative approach for determining if a bioburden number is simply an extreme manifestation of statistical variability in the data or in fact should be considered a spike and treated in a separate manner.
The average bioburden on a product is based on random samples that are taken from different batches of manufactured product. In this regard, it is standard practice to collect at least 10 samples for each data set. The averaging process assumes that all data in the data set are from the same population. The dispersion of values about the average value can be characterized using standard statistical techniques where the sample standard deviation is the cogent parameter for describing the dispersion of values about the average value and the distribution of data can be fit to a mathematical model. A Student-t probability distribution, which offers a mathematical fit to the bioburden data, was used in the analysis. The t-distribution is an appropriate statistical model when one is dealing with a limited number of degrees of freedom, i.e., number of comparisons, and the distribution in bioburden numbers is approximately symmetric. It is noted in ISO 11737-1 that the distribution could tend to be skewed with a long tail to the right (ANSI/AAMI/ISO 11737-1, 2006). Each of the individual random samples of bioburden was evaluated to see if the distribution was skewed to the right and in which case a lognormal distribution may be more appropriate for analysis of the bioburden data than a t-distribution. The analysis involved a visual inspection of the bioburden data and comparison of the mean and median values. Except for random samples with low average bioburdens, which showed some degree of skewness, that is about a 20% difference between the average and median values, the distributions were approximately symmetric wherin the mean and median buoburden numbers were not significantly different and use of a t-distribution in the analysis of the bioburden data
n
Corresponding author. E-mail address: [email protected] (B.P. Fairand).
0969-806X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.radphyschem.2012.02.020
1242
B.P. Fairand et al. / Radiation Physics and Chemistry 81 (2012) 1241–1243
was considered appropriate. It is possible the observed skewness in the distributions with low average bioburden could be attributed to factors related to limitations in the sensitivity of the test method that is used to determine bioburden.
Table 1 Bioburden data.
2.1. Single spike in data set Spikes in a random sample of bioburden data typically appear as a single value in a set of ten numbers. For the case of a single spike in the set of bioburden data, a statistical technique can be used to place a quantitative bound on when a bioburden number in the data set should be considered a spike rather than an extreme manifestation of statistical variability in the data. This approach is based on calculation of a t-statistic and comparison of that number with a critical t-value, which is related to the degree of risk one is willing to accept that a bioburden value should be considered a spike rather than an extreme manifestation of statistical variability in the data (ASTM E178-08). The test statistic is given by the following expression: ð1Þ
where t is the test statistic, Ci is the bioburden number considered outlier that is spike, Cavg is the average bioburden number for 10 samples, and ss is the sample standard deviation. If the value of t that is calculated from the above expression exceeds a critical t-value, i.e., t*, the bioburden number under study should be considered a spike. The risk of designating a biobuden number as a spike, when in fact it should have been retained in the data set, was set equal to 2% or one chance in 50, which is more conservative than a value of 5% that is commonly used for reporting results of research in many fields of science. Because the only concern is the largest bioburden number in the data set, a one sided t-distribution was used in the selection of the critical t-value. The 2% number is equal to the area in the upper tail of the probability curve. The critical t* value for 9 degrees of freedom, i.e., 10 observations, and a 2% risk is 2.398.
y¼(Ci/Cavg)
0 1.211 1.288 1.451 1.496 1.512 1.591 1.772 1.878 1.901 1.901 2.035 2.121 2.144 2.147 2.193 2.408 2.442 2.482 2.748
1 1.68 1.291 1.582 1.325 1.762 1.75 1.601 2.414 2 2.405 2.564 2.286 2.5 2.593 2.222 2.549 2.886 3.333 3.812
4.0
Ratio Peak to Average Bioburden
t ¼ ðC i 2C avg Þ=ss
t-Value
3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
0.5
3. Results 3.1. Bioburden data The analysis was based on random samples that were taken from microbiological data collected from a spectrum of different medical devices over a few months. The average bioburdens ranged from about 10 CFU to more than 3000 CFU. Each random sample of ten bioburden numbers was independent of other random samples. 3.2. Statistical analysis A sampling of bioburden information that was used in the analysis of a possible single spike in a data set is given in Table 1. The data is presented in terms of two dimensionless parameters; the ratio of peak bioburden number to average bioburden number and the corresponding test statistic. As the ratio of peak bioburden number to average bioburden number approaches 1, the value of t approaches 0. This set of intercept data also is included in Table 1. The data in Table 1 is plotted in Fig. 1. As seen from Fig. 1, all of the data could fit a single function. The cohesiveness of the data shown in Fig. 1, which is plotted as a function of the t-value, is consistent with selection of a t-distribution for statistical analysis of the data. Non-linear regression analysis was used to fit the data to a third order polynomial that is given by Eq. (2). The resultant
1.0
1.5
2.0
2.5
3.0
t-Value Fig. 1. Ratio (peak/average) bioburden number versus t-value.
curve is shown in Fig. 1 y ¼ ðC i =C avg Þ ¼ 0:999 þ 0:262t20:069t 2 þ 0:122t 3
ð2Þ
When a critical t-value (t*) of 2.398 is substituted into Eq. (2), the ratio of peak bioburden number to average bioburden number is 2.9 or approximately three. This multiple in peak-to-average bioburden is not inconsistent with the multiple of two that is noted in Ref. Bryans (1996). As seen from the data in Table 1 and plot of the data in Fig. 1, bioburden spikes were identified in four cases.
4. Proposed application of spike information Once a bioburden spike is identified, it should be considered in the selection of the sterilization dose. This would depend on the method that is used to establish the sterilization dose. For example, when Method 1 is used to establish the sterilization dose, it is proposed that selection of the verification dose be based on the average bioburden and the spike bioburden number should be used in selecting the sterilization dose. The bioburden data for the four spikes that were identified in Table 1 are given in Table 2.
B.P. Fairand et al. / Radiation Physics and Chemistry 81 (2012) 1241–1243
1243
5. Conclusions
Table 2 Data for bioburden spikes. Spike ID t-value
Bioburden number (CFU)
Verification dose (kGy)
Sterilization dose (kGy)
t ¼ 2.408
Ci ¼65 Cavg ¼ 25.5
N/A 6.3
20.5 19.1
t ¼ 2.442
Ci ¼852 Cavg ¼ 295.2
N/A 9.4
24.7 22.9
t ¼ 2.482
Ci ¼88 Cavg ¼ 26.4
N/A 6.4
21.0 19.1
t ¼ 2.748
Ci ¼260 Cavg ¼ 68.2
N/A 7.5
22.7 20.6
The doses that are given in Table 2 were taken from Table 5 (Method 1) in ANSI/AAMI/ISO 11137-2. As seen from Table 2, use of the spike bioburden number in the selection of the sterilization dose increased its value from use of the average bioburden number by about 7–10%. A ratio of spike bioburden number to average bioburden number that is much greater than 3 may be indicative of a quality issue that is traceable to a manufacturing material problem or possibly laboratory contamination rather than a low probability event that is a consistent component of product bioburden. Statistical analysis of the bioburden data may offer insight as to whether one is dealing with a spike that is a consistent component of product bioburden or in fact is related to a quality issue. In that regard, the relationship of the resultant data to the curve that is shown in Fig. 1 may be helpful in ascertaining if one is dealing with a bioburden spike or quality issue. One would expect this situation to occur on a very infrequent basis.
As seen from the preceding treatise, statistical techniques can be used for analysis of spikes in the bioburden data and provide quantitative results that can be used in the selection of sterilization parameters. Results from the cited examples are not inconsistent with present methods for analysis of bioburden data, but represent a quantitative approach for analysis of the bioburden data that is not subjective in its interpretation. Statistical techniques also offer the possibility of evaluating bioburden data to test for outliers that may be attributable to quality issues and should not be considered spikes in the bioburden data. It is proposed that a statistical approach for analysis of bioburden data be considered and tested on a wider scale of data to assess its applicability in the radiation sterilization process.
Acknowledgement The authors would like to thank Sterigenics International for support in this study. References ANSI/AAMI/ISO 11137-2, Sterilization of Health Care Products—Part 2: Establishing the Sterilization Dose, 2006. ANSI/AAMI/ISO 11737-1, Sterilization of Health Care Products-Microbiological Methods—Part 1: Determination of the Population of Microorganisms on Product, 2006. ASTM E178-08, Standard Practice for Dealing with Outlying Observations. Bryans, T., 1996. Using Bioburden Spikes in Radiation Dose Setting, vol. 3 (1). The Validation Consultant.