PRACTICE MANAGEMENT: THE ROAD AHEAD John I. Allen, Section Editor
Adverse Outcomes: Why Bad Things Happen to Good People Amnon Sonnenberg Division of Gastroenterology/Hepatology, Portland VA Medical Center, and Oregon Health and Science University, Portland, Oregon
This month’s Practice Management section follows a slightly different motif compared to other months. Dr Amnon Sonnenberg wrote a provocative article suggesting that complications in gastroenterology are inevitable occurrences by statistical probability, so errors should not be viewed as personal flaws. The editors of Clinical Gastroenterology and Hepatology found this article so interesting in its conclusions that two experts in quality improvement were invited to write a counterpoint, which follows this article. While we agree wholeheartedly with Dr Sonnenberg that errors should not be viewed as personal flaws, we had to highlight the enormous amount of work available pointing to sound methods to reduce errors using systematic and validated techniques focused on process improvement, patient safety catches, systems analysis, and clinical redesign. We hope that readers will consider both articles carefully and come to their own conclusions about how they might improve their own practices in pursuit of the Triple Aim of healthcare. John I. Allen, MD, MBA, AGAF Special Section Editor wo common situations in gastroenterology potentially are associated with a bad outcome, namely, the occurrence of colorectal cancer and difficult endoscopic procedures. Although curable in a large fraction of patients when timely detected, nevertheless, colorectal cancer still results in mortality and substantial morbidity. Similarly, endoscopic treatment of large right-sided polyps, gastrointestinal bleeding, intestinal strictures, and many forms of
T
Resources for Practical Application To view additional online resources about this topic and to access our Coding Corner, visit www.cghjournal.org/content/ practice_management.
Clinical Gastroenterology and Hepatology 2015;13:820–823
pancreatobiliary disease may be unsuccessful or result in adverse events. As a general strategy to avoid adverse events, gastroenterologists undergo prolonged and continued training, try to adhere to professional guidelines, exert good clinical judgment, consult with peers, and may be overly cautious in peforming procedures. It is hoped that following these measures will help them keep the numbers of adverse events low or even prevent them altogether. Based on simple statistics, the example of colorectal cancer is used to show that even with the best intentions and prophylactic measures in place adverse events are unavoidable.
Missing a Crucial Consult Request A gastroenterology section may receive 7500 requests for consult per year. The majority of consults are for a screening colonoscopy and work-up of potential gastrointestinal bleeding or abdominal pain. A small (eg, 1%) fraction of patients already may harbor colorectal cancer at the time of the consult request. These patients are difficult to pre-identify based on the short description provided by the referring physician in their consult request. General practitioners use the terms hematochezia and melena in loose and imprecise way. Minor complaints and symptoms often are exaggerated to coax the gastroenterology service into seeing the patient. Repeat endoscopy often is requested for patients who have undergone a recent negative work-up. In assessing the individual consult request, it is difficult separate the wheat from the chaff. A common strategy by the reviewing gastroenterologist is to accept most requests except for the most inappropriate ones. This may decrease the error rate of missing a patient with colorectal cancer to 1%. An adverse outcome results from the joint occurrence of 2 separate events, namely colorectal cancer and physician error. The statistical behavior of rare events generally is modeled as a
© 2015 by the AGA Institute 1542-3565/$36.00 http://dx.doi.org/10.1016/j.cgh.2014.07.064
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued
Figure 1. Influence of error rate or patient number on the cumulative probability of 1 or more adverse events associated with (A) consult requests or (B) colonoscopies.
Poisson distribution. It relates to the number of events that occur in a fixed period of time, such as untoward effects, cancer diagnoses, or deaths. The occurrence of failure rates or physician errors generally are modeled as a binomial distribution. It is associated with situations involving 2 outcomes, such as failure and success or error and none.1 The superimposition of a Poisson and binomial distribution results in a joint distribution for the occurrence of adverse outcomes, which itself behaves similar to a Poisson distribution.2 The mean value of the joint Poisson distribution is the product of patient number cancer rate error rate. One easily can look up the probability values for the Poisson distribution in published statistical tables or calculate them by using the built-in function of Excel spreadsheets (Microsoft, Redmond, WA).2–4 With a mean value of 7500 1% 1% ¼ 0.75, for instance, the probability of no adverse events (n ¼ 0) is F ¼ 47.2%. Accordingly, the complementary probability of missing one or more colorectal cancers among the 7500 consult requests is 1 F ¼ 52.8%. If the error rate increases to 5%, the probability of missing 1 or more colorectal cancers becomes almost certain (Supplementary Table 1). An individual gastroenterologist may review 1500 patients per year. With an error rate of 1% or 5%, the individual gastroenterologist’s probability of missing at least one cancer is 13.9% or 52.8%, respectively. Figure 1A shows the probability of missing colorectal cancer in relationship to varying the error rate between 0% and 12% or the cumulative patient number between 0 and 90,000.
Adverse Events of Endoscopy A single gastroenterology section may perform 5000 colonoscopies per year. In approximately 5% of cases, the endoscopist may encounter technical difficulties.
Such difficulties may concern a tortuous large bowel that is hard to straighten out or a large sessile polyp in the right colon. Other examples abound. Secondary to these difficulties an error may occur with a rate of 1%. Such errors may lead to missed cancers, perforated colons, or delayed postpolypectomy bleeding, just to name a few. The occurrence of adverse events again can be treated similar to a Poisson variable with a mean value of 5000 5% 1% ¼ 2.5 and a probability of at least 1 bad outcome of 1 F ¼ 91.8%. Increasing the error rate to 5% increases the probability to 100%, that is, certainty of at least 1 bad outcome per year. An individual gastroenterologist may perform 1000 colonoscopies per year. With error rates of 1% or 5%, his/her probability of at least 1 bad outcome is 39.3% or 91.8%, respectively (Supplementary Table 1). Figure 1B shows the probability of adverse events in relationship to varying the error rate between 0% and 4% or the colonoscopy number between 0 and 20,000. Even if an individual endoscopist manages to stay free of any adverse events in a given year, eventually, an ever-increasing number of colonoscopies during multiple consecutive years will render a bad outcome a certainty.
Adverse Events Are Unavoidable A relatively simple statistical analysis shows that for a gastroenterology section or group as a whole, as well as on the level of an individual gastroenterologist, adverse events can be expected to occur with a high probability. Their occurrence is a function of the number of patient encounters and the probability of making mistakes. It is a statistical misconception to believe that their rare occurrence would make it possible for an individual gastroenterologist to dodge the bullet. It is another statistical misconception to assume that by exerting 821
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued extreme caution a gastroenterologist also could avert adverse events. Even with a low error rate of 1%, adverse events are unavoidable. The only means to truly reduce adverse events is to avoid patient encounters altogether. The occurrence of patients with colorectal cancer or endoscopically challenging colons follows a random and unpredictable Poisson process. Even if the error rate could be reduced through extensive training and extreme precaution, ultimately, the cumulative probability of multiple consecutive years for any individual gastroenterologist reaches certainty. It thus remains only a question of time until a bad outcome happens to the individual gastroenterologist. The present 2 examples dealt only with consults and colonoscopies, but similar considerations apply to other types of patient encounters and endoscopic procedures. The frequency of patient encounters with serious medical problems and their involvement in procedural interventions trying to treat pre-existing illness puts gastroenterologists at a heightened risk of being blamed for all kinds of bad disease outcomes.
Practical Implications and Outlook Bad clinical outcomes usually lead to peer-reviews, tort claims, and law suits. In all of these instances, the bad outcome is being dealt with as a singular event or system failure rather than a statistical phenomenon. The overall numbers of consults or endoscopic procedures, from which the particular case was singled out by its associated adverse event, are ignored and the physician rarely is given credit for innumerous other patient encounters with good outcomes. The bad outcome is considered potentially reflective of professional failure or flawed performance. The process ultimately is geared toward showing avoidable mistakes and assigning guilt. The occurrence of an error, even at its lowest rate, generally is not accepted as a viable reason, although under different circumstances the same reviewers would be willing to accept the lessthan-perfect sensitivity or specificity of all diagnostic tests. There has been a prevailing tendency among gastroenterologists to extol the benefits of screening colonoscopy or other endoscopic procedures and describe in glowing terms their improvements through continued quality assurance. We have to develop with similar vigor matrices of reasonable failure rates to be expected during common gastrointestinal procedures and free ourselves from the illusion that perfection will become achievable through limitless quality assurance. Gastrointestinal 822
services need to clearly communicate that bad outcomes will happen despite the presence of best doctors, technology, and processes. Bad outcomes are certain to occur once in every 3000 to 10,000 procedures, depending on the error rate and case mix. Similar to any diagnostic test, physician encounters are characterized by their a and b errors. We should treat errors associated with consultation and endoscopy as statistical phenomena rather than personal flaws. Because adverse events will continue to occur, gastroenterology sections and private practices alike need to develop strategies on how to effectively protect their members from unjustified liability claims. The article has focused on the statistics underlying the occurrence of adverse events in gastroenterology. Obviously, there are other issues associated with adverse events that were not addressed by the present analysis, such as the distinction between preventable and nonpreventable adverse events, human factors in their occurrence and management, system design to ensure patient safety and minimize staff errors, means of quality assurance, and performance measurement.5–8 Highlighting the statistical nature of adverse events is not meant to belittle the need for continued efforts at improving patient safety and increasing the quality of health care delivery. Responses to adverse events that are seen as unjust can impede safety investigations, promote fear rather than mindfulness among physicians, make health care more bureaucratic rather than more careful, and cultivate professional secrecy, evasion, and self-protection.9 In a “just culture” of safety and accountability, the occurrence of any error would become an opportunity for learning and improvement rather than retribution or punishment. In addition to learning and improvement, ideally, the system that manages tort claims is also centered on helping and restituting the harmed patients rather than on punishing the offender.
Supplementary Material Note: To access the supplementary material accompanying this article, visit the online version of Clinical Gastroenterology and Hepatology at www.cghjournal.org, and at http://dx.doi.org/10.1016/j.cgh.2014.07.064.
References 1. 2.
Rumsey D. Probability for dummies. Indianapolis, IN: Wiley, 2006:151–166, 235–250. Higgins JJ, Keller-McNulty S. Concepts in probability and stochastic modeling. Belmont, CA: Duxbury Press, 1995:386–392.
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued 3.
Ingelfinger JA, Mosteller F, Thibodeau LA, et al. Biostatistics in clinical medicine. New York: McMillan, 1983:295–298.
4.
Beyer WH. CRC standard mathematical tables. Boca Raton, FL: CRC Press, 1981:542–546.
5.
Kohn LT, Corrigan JM, Donaldson MS, eds. To err is human: building a safer health system. Washington, DC: Institute of Medicine, National Academy Press, 2008.
6.
Ransom ER, Joshi MS, Nash DB, et al, eds. The healthcare quality book: vision, strategy, and tools. 2nd ed. Chicago, IL: Health Administration Press, 2008.
7.
Wachter RM. Understanding patient safety. 2nd ed. New York: McGraw Hill Medical, 2012.
8.
Nash DB, Janice Clarke JL, Skoufalos A, et al. Health care quality: the clinician’s primer. Tampa, FL: American College of Physician Executives, 2012.
9.
Dekker S. Just culture: balancing safety and accountability. Hampshire, England: Ashgate Publishing, 2007.
Reprint requests Address requests for reprints to: Amnon Sonnenberg, MD, MSc, Portland VA Medical Center, P3-GI, 3710 SW US Veterans Hospital Road, Portland, Oregon 97239. e-mail: [email protected]; fax: (503) 220-3426. Conflicts of interest The author discloses no conflicts.
823
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued Supplementary Table 1. Examples of Adverse Events in 4 Different Scenarios Variable
Scenario 1 Scenario 2 Scenario 3 Scenario 4
Consults Patients 7500 CRC 1/100 p(error) 0.01 m 0.75 1-F 52.8% Colonoscopies Patients 5000 Difficult 5/100 p(error) 0.01 m 2.5 1-F 91.8%
7500 1/100 0.05 3.75 97.6%
1500 1/100 0.01 0.15 13.9%
1500 1/100 0.05 0.75 52.8%
5000 5/100 0.05 12.5 100.0%
1000 5/100 0.01 0.5 39.3%
1000 5/100 0.05 2.5 91.8%
CRC, colorectal cancer; difficult, frequency of difficult colonoscopies; 1 - F, cumulative probability of 1 or more adverse events; p(error), rate of physician error; m, patients CRC p(error) or m ¼ patients difficult p(error).
823.e1
Adverse Outcomes: Why Bad Things Happen to Good People Amnon Sonnenberg Division of Gastroenterology/Hepatology, Portland VA Medical Center, and Oregon Health and Science University, Portland, Oregon
This month’s Practice Management section follows a slightly different motif compared to other months. Dr Amnon Sonnenberg wrote a provocative article suggesting that complications in gastroenterology are inevitable occurrences by statistical probability, so errors should not be viewed as personal flaws. The editors of Clinical Gastroenterology and Hepatology found this article so interesting in its conclusions that two experts in quality improvement were invited to write a counterpoint, which follows this article. While we agree wholeheartedly with Dr Sonnenberg that errors should not be viewed as personal flaws, we had to highlight the enormous amount of work available pointing to sound methods to reduce errors using systematic and validated techniques focused on process improvement, patient safety catches, systems analysis, and clinical redesign. We hope that readers will consider both articles carefully and come to their own conclusions about how they might improve their own practices in pursuit of the Triple Aim of healthcare. John I. Allen, MD, MBA, AGAF Special Section Editor wo common situations in gastroenterology potentially are associated with a bad outcome, namely, the occurrence of colorectal cancer and difficult endoscopic procedures. Although curable in a large fraction of patients when timely detected, nevertheless, colorectal cancer still results in mortality and substantial morbidity. Similarly, endoscopic treatment of large right-sided polyps, gastrointestinal bleeding, intestinal strictures, and many forms of
T
Resources for Practical Application To view additional online resources about this topic and to access our Coding Corner, visit www.cghjournal.org/content/ practice_management.
Clinical Gastroenterology and Hepatology 2015;13:820–823
pancreatobiliary disease may be unsuccessful or result in adverse events. As a general strategy to avoid adverse events, gastroenterologists undergo prolonged and continued training, try to adhere to professional guidelines, exert good clinical judgment, consult with peers, and may be overly cautious in peforming procedures. It is hoped that following these measures will help them keep the numbers of adverse events low or even prevent them altogether. Based on simple statistics, the example of colorectal cancer is used to show that even with the best intentions and prophylactic measures in place adverse events are unavoidable.
Missing a Crucial Consult Request A gastroenterology section may receive 7500 requests for consult per year. The majority of consults are for a screening colonoscopy and work-up of potential gastrointestinal bleeding or abdominal pain. A small (eg, 1%) fraction of patients already may harbor colorectal cancer at the time of the consult request. These patients are difficult to pre-identify based on the short description provided by the referring physician in their consult request. General practitioners use the terms hematochezia and melena in loose and imprecise way. Minor complaints and symptoms often are exaggerated to coax the gastroenterology service into seeing the patient. Repeat endoscopy often is requested for patients who have undergone a recent negative work-up. In assessing the individual consult request, it is difficult separate the wheat from the chaff. A common strategy by the reviewing gastroenterologist is to accept most requests except for the most inappropriate ones. This may decrease the error rate of missing a patient with colorectal cancer to 1%. An adverse outcome results from the joint occurrence of 2 separate events, namely colorectal cancer and physician error. The statistical behavior of rare events generally is modeled as a
© 2015 by the AGA Institute 1542-3565/$36.00 http://dx.doi.org/10.1016/j.cgh.2014.07.064
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued
Figure 1. Influence of error rate or patient number on the cumulative probability of 1 or more adverse events associated with (A) consult requests or (B) colonoscopies.
Poisson distribution. It relates to the number of events that occur in a fixed period of time, such as untoward effects, cancer diagnoses, or deaths. The occurrence of failure rates or physician errors generally are modeled as a binomial distribution. It is associated with situations involving 2 outcomes, such as failure and success or error and none.1 The superimposition of a Poisson and binomial distribution results in a joint distribution for the occurrence of adverse outcomes, which itself behaves similar to a Poisson distribution.2 The mean value of the joint Poisson distribution is the product of patient number cancer rate error rate. One easily can look up the probability values for the Poisson distribution in published statistical tables or calculate them by using the built-in function of Excel spreadsheets (Microsoft, Redmond, WA).2–4 With a mean value of 7500 1% 1% ¼ 0.75, for instance, the probability of no adverse events (n ¼ 0) is F ¼ 47.2%. Accordingly, the complementary probability of missing one or more colorectal cancers among the 7500 consult requests is 1 F ¼ 52.8%. If the error rate increases to 5%, the probability of missing 1 or more colorectal cancers becomes almost certain (Supplementary Table 1). An individual gastroenterologist may review 1500 patients per year. With an error rate of 1% or 5%, the individual gastroenterologist’s probability of missing at least one cancer is 13.9% or 52.8%, respectively. Figure 1A shows the probability of missing colorectal cancer in relationship to varying the error rate between 0% and 12% or the cumulative patient number between 0 and 90,000.
Adverse Events of Endoscopy A single gastroenterology section may perform 5000 colonoscopies per year. In approximately 5% of cases, the endoscopist may encounter technical difficulties.
Such difficulties may concern a tortuous large bowel that is hard to straighten out or a large sessile polyp in the right colon. Other examples abound. Secondary to these difficulties an error may occur with a rate of 1%. Such errors may lead to missed cancers, perforated colons, or delayed postpolypectomy bleeding, just to name a few. The occurrence of adverse events again can be treated similar to a Poisson variable with a mean value of 5000 5% 1% ¼ 2.5 and a probability of at least 1 bad outcome of 1 F ¼ 91.8%. Increasing the error rate to 5% increases the probability to 100%, that is, certainty of at least 1 bad outcome per year. An individual gastroenterologist may perform 1000 colonoscopies per year. With error rates of 1% or 5%, his/her probability of at least 1 bad outcome is 39.3% or 91.8%, respectively (Supplementary Table 1). Figure 1B shows the probability of adverse events in relationship to varying the error rate between 0% and 4% or the colonoscopy number between 0 and 20,000. Even if an individual endoscopist manages to stay free of any adverse events in a given year, eventually, an ever-increasing number of colonoscopies during multiple consecutive years will render a bad outcome a certainty.
Adverse Events Are Unavoidable A relatively simple statistical analysis shows that for a gastroenterology section or group as a whole, as well as on the level of an individual gastroenterologist, adverse events can be expected to occur with a high probability. Their occurrence is a function of the number of patient encounters and the probability of making mistakes. It is a statistical misconception to believe that their rare occurrence would make it possible for an individual gastroenterologist to dodge the bullet. It is another statistical misconception to assume that by exerting 821
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued extreme caution a gastroenterologist also could avert adverse events. Even with a low error rate of 1%, adverse events are unavoidable. The only means to truly reduce adverse events is to avoid patient encounters altogether. The occurrence of patients with colorectal cancer or endoscopically challenging colons follows a random and unpredictable Poisson process. Even if the error rate could be reduced through extensive training and extreme precaution, ultimately, the cumulative probability of multiple consecutive years for any individual gastroenterologist reaches certainty. It thus remains only a question of time until a bad outcome happens to the individual gastroenterologist. The present 2 examples dealt only with consults and colonoscopies, but similar considerations apply to other types of patient encounters and endoscopic procedures. The frequency of patient encounters with serious medical problems and their involvement in procedural interventions trying to treat pre-existing illness puts gastroenterologists at a heightened risk of being blamed for all kinds of bad disease outcomes.
Practical Implications and Outlook Bad clinical outcomes usually lead to peer-reviews, tort claims, and law suits. In all of these instances, the bad outcome is being dealt with as a singular event or system failure rather than a statistical phenomenon. The overall numbers of consults or endoscopic procedures, from which the particular case was singled out by its associated adverse event, are ignored and the physician rarely is given credit for innumerous other patient encounters with good outcomes. The bad outcome is considered potentially reflective of professional failure or flawed performance. The process ultimately is geared toward showing avoidable mistakes and assigning guilt. The occurrence of an error, even at its lowest rate, generally is not accepted as a viable reason, although under different circumstances the same reviewers would be willing to accept the lessthan-perfect sensitivity or specificity of all diagnostic tests. There has been a prevailing tendency among gastroenterologists to extol the benefits of screening colonoscopy or other endoscopic procedures and describe in glowing terms their improvements through continued quality assurance. We have to develop with similar vigor matrices of reasonable failure rates to be expected during common gastrointestinal procedures and free ourselves from the illusion that perfection will become achievable through limitless quality assurance. Gastrointestinal 822
services need to clearly communicate that bad outcomes will happen despite the presence of best doctors, technology, and processes. Bad outcomes are certain to occur once in every 3000 to 10,000 procedures, depending on the error rate and case mix. Similar to any diagnostic test, physician encounters are characterized by their a and b errors. We should treat errors associated with consultation and endoscopy as statistical phenomena rather than personal flaws. Because adverse events will continue to occur, gastroenterology sections and private practices alike need to develop strategies on how to effectively protect their members from unjustified liability claims. The article has focused on the statistics underlying the occurrence of adverse events in gastroenterology. Obviously, there are other issues associated with adverse events that were not addressed by the present analysis, such as the distinction between preventable and nonpreventable adverse events, human factors in their occurrence and management, system design to ensure patient safety and minimize staff errors, means of quality assurance, and performance measurement.5–8 Highlighting the statistical nature of adverse events is not meant to belittle the need for continued efforts at improving patient safety and increasing the quality of health care delivery. Responses to adverse events that are seen as unjust can impede safety investigations, promote fear rather than mindfulness among physicians, make health care more bureaucratic rather than more careful, and cultivate professional secrecy, evasion, and self-protection.9 In a “just culture” of safety and accountability, the occurrence of any error would become an opportunity for learning and improvement rather than retribution or punishment. In addition to learning and improvement, ideally, the system that manages tort claims is also centered on helping and restituting the harmed patients rather than on punishing the offender.
Supplementary Material Note: To access the supplementary material accompanying this article, visit the online version of Clinical Gastroenterology and Hepatology at www.cghjournal.org, and at http://dx.doi.org/10.1016/j.cgh.2014.07.064.
References 1. 2.
Rumsey D. Probability for dummies. Indianapolis, IN: Wiley, 2006:151–166, 235–250. Higgins JJ, Keller-McNulty S. Concepts in probability and stochastic modeling. Belmont, CA: Duxbury Press, 1995:386–392.
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued 3.
Ingelfinger JA, Mosteller F, Thibodeau LA, et al. Biostatistics in clinical medicine. New York: McMillan, 1983:295–298.
4.
Beyer WH. CRC standard mathematical tables. Boca Raton, FL: CRC Press, 1981:542–546.
5.
Kohn LT, Corrigan JM, Donaldson MS, eds. To err is human: building a safer health system. Washington, DC: Institute of Medicine, National Academy Press, 2008.
6.
Ransom ER, Joshi MS, Nash DB, et al, eds. The healthcare quality book: vision, strategy, and tools. 2nd ed. Chicago, IL: Health Administration Press, 2008.
7.
Wachter RM. Understanding patient safety. 2nd ed. New York: McGraw Hill Medical, 2012.
8.
Nash DB, Janice Clarke JL, Skoufalos A, et al. Health care quality: the clinician’s primer. Tampa, FL: American College of Physician Executives, 2012.
9.
Dekker S. Just culture: balancing safety and accountability. Hampshire, England: Ashgate Publishing, 2007.
Reprint requests Address requests for reprints to: Amnon Sonnenberg, MD, MSc, Portland VA Medical Center, P3-GI, 3710 SW US Veterans Hospital Road, Portland, Oregon 97239. e-mail: [email protected]; fax: (503) 220-3426. Conflicts of interest The author discloses no conflicts.
823
PRACTICE MANAGEMENT: THE ROAD AHEAD, continued Supplementary Table 1. Examples of Adverse Events in 4 Different Scenarios Variable
Scenario 1 Scenario 2 Scenario 3 Scenario 4
Consults Patients 7500 CRC 1/100 p(error) 0.01 m 0.75 1-F 52.8% Colonoscopies Patients 5000 Difficult 5/100 p(error) 0.01 m 2.5 1-F 91.8%
7500 1/100 0.05 3.75 97.6%
1500 1/100 0.01 0.15 13.9%
1500 1/100 0.05 0.75 52.8%
5000 5/100 0.05 12.5 100.0%
1000 5/100 0.01 0.5 39.3%
1000 5/100 0.05 2.5 91.8%
CRC, colorectal cancer; difficult, frequency of difficult colonoscopies; 1 - F, cumulative probability of 1 or more adverse events; p(error), rate of physician error; m, patients CRC p(error) or m ¼ patients difficult p(error).
823.e1
