Referral bias in aneurysmal subarachnoid hemorrhage

Transcription

1 J Neurosurg 78: , 1993 Referral bias in aneurysmal subarachnoid hemorrhage JACK P. WHISNANT~ M.D., SARA E. SACCO, M.D., W. MICHAEL O'FALLON, PH.D., NICOLEE C. FODE, R.N., M.S., AND THORALF M. SUNDT, JR., M.D. Departments of Health Sciences Research and Neurologic Surgery, Mayo Clinic and Mayo Foundation, Rochester, Minnesota v- The objective of this study was to assess the effect of referral bias on survival in patients with subarachnoid hemorrhage (SAH). The characteristics of 49 patients with aneurysmal SAH from a single community were compared with those of 328 patients referred from outside the community, all treated in the same medical care setting. In addition, referral patients who received surgery were compared by differential survival analysis with those still awaiting surgery at Days 1 to 3, Days 4 to 10, and Days 11 to 15. There was a dramatic difference in the 30-day survival rate between referral patients (83%) and community patients (59%), but most of the difference had occurred by the 2nd day after SAH. In the referral patients, the variables present at first medical attention that were found to have an independent effect on survival were clinical grade, presence of coma, number of days from SAH to referral, diastolic blood pressure, and patient age. There was a higher survival rate at 1 year for patients who were surgically treated compared with those awaiting surgery for each of the three time periods. Patients who underwent early surgical treatment had a l- year survival rate almost identical to that of patients with late surgery. Referral patients had a better early survival rate than did community patients because the referral group did not include patients who died and some who were in poor clinical condition before the opportunity for referral. The differential survival analysis described provides a new method for estimating survival for treated and untreated patients with SAH. KEY WORDS ~ referral bias 9 subarachnoid hemorrhage 9 surgical treatment 9 survival outcome M OST of the information about subarachnoid hemorrhage (SAH), including its frequency, distribution, prognosis, and management, is derived from studies performed at large referral-based medical centers. 1'2'13'16"17'2~ Each center has its own selection bias for patient referral based on the distance of the referral, the condition of the patient, the particular interests of the physicians at the referral center, and other variables that may affect the outcome reported for SAH patients. This, in turn, may affect what is reported as the natural history of the disease. 22 If referral factors affect the reported natural history, then conclusions as to what is considered a successful treatment option may not be valid. Sundt and Whisnant 32 first noted that survival following SAH in patients at the Mayo Clinic varied greatly as a function of whether the patient was a resident of Rochester, Minnesota, or was referred from elsewhere. There have been few studies dealing with the natural history of SAH in a population, 3'4"7:~ and no studies have directly compared a sample of referred patients with a population-based study of SAH treated in the same medical center. The Mayo Clinic is unique in that it includes a large referral practice and also is the foundation for a resource that provides information from all medical facilities giving medical care to residents of Rochester, Minnesota. The same physicians provide the medical and surgical care for both groups of patients, and the same staff neurosurgeons with experience in aneurysm surgery perform the operations in both groups. It is the primary aim of this paper to compare the characteristics of the patients with SAH from a single community with those of a large referral practice to assess the nature of the bias in the sample of patients from the referral practice. A differential survival analysis to assess outcome following SAH in referral patients is also presented. Clinical Material and Methods Patient Population The Mayo Clinic has a large referral base of patients and also has access to information from all medical 726 J. Neurosurg. / Volume 78/May, 1993

2 Referral bias in aneurysmal subarachnoid hemorrhage facilities providing medical care for residents of Rochester, Minnesota. Through a central computer database, ts all cases of first SAH proven or presumed due to aneurysm rupture were identified. The patients were divided into two groups: 1) patients referred to the Mayo Clinic from outside Rochester, Minnesota, and Olmsted County, hereafter referred to as the "referral group" and 2) patients from the defined population of Rochester, hereafter referred to as the "community group." Patients from Olmsted County who were not residents of Rochester were not included in the study. The referral cases were ascertained from January 1, 1980, to December 31, 1984, and patients must have suffered their first SAH within 31 days before their first evaluation at our institution. Because of the small numbers, the community group included the cases of first SAH for the time period January 1, 1975, to December 31, This study includes a different analysis of some of the patients reported by Chyatte, et al. 5 All cases of SAH were confirmed by lumbar puncture, computerized tomography (CT), operation, angiography, or autopsy. Patients in whom trauma was the likely cause of hemorrhage and patients with a primary intracerebral hemorrhage and secondary communication with the subarachnoid space were excluded. The distance of the patient's home from the Mayo Clinic was estimated from zip codes using a computer program. 27 There were 328 patients with first SAH proven or presumed due to aneurysm rupture who were referred to the Mayo Medical Center from outside Olmsted County between January 1, 1980, and December 31, Their ages ranged from 12 to 91 years (median age 54.5 years); 61% were female. For the Rochester population, there were 49 cases of first SAH from January 1, 1975, to December 31, 1984; 70% were female. The age- and sex-specific distributions were similar for the two groups, although there was a trend toward more patients from the community in the oldest age group. There were 36 patients in the referral group and six in the community group who did not undergo angiography or autopsy but who had a high probability of having an aneurysm. Terminology Each patient was assigned a grade (I through VI) according to a modification of the criteria of Hunt and Hess 9 on the basis of clinical evaluation on arrival at the Mayo Clinic. The addition of Grade VI allowed inclusion of patients who died before receiving medical attention. The level of consciousness, determined at the time of first medical attention, was graded as follows: 0, normal level of consciousness; 1, somnolent but could be awakened and would respond to command; 2, unconscious and no response to command but purposeful response to pain; and 3, coma with no purposeful response to pain. The type of treatment given, including surgery, was recorded and the outcome was judged only in regard to mortality. The community patients were followed through review of medical records. The referral group was followed by medical visits, correspondence, and telephone conversations. Persons lost to follow-up study were censored (removed from the denominator) at the time they were last known to be alive for survival analysis. Aneurysm surgery was considered definitive if the procedure included aneurysm clipping (259 cases) or wrapping of the aneurysm if it was not completely clipped (five cases). Carotid artery ligation was not considered a definitive procedure, but only two patients underwent this procedure. Survival Analysis The probability of survival was estimated by the Kaplan-Meier product-limit method t4 and comparison was made with expected survival for the 1980 West North Central United States white population by means of a one-sample log-rank test. Because the proportionalhazards assumption was not satisfied for the full period of observation, Cox proportional-hazards analysis 6 was used to identify variables that predicted survival after admission to the Mayo Clinic, given survival for 7 days; logistic regression 33 was used to determine the variables that were associated with 7-day survival after admission to the Mayo Clinic. The variables assessed were patient age, sex, level of consciousness at first medical attention at the Mayo Clinic, clinical grade at admission to the Mayo Clinic, presence of focal neurological deficit at onset, seizure at onset, systolic and diastolic blood pressure at admission to the Mayo Clinic, presence of intraparenchymal hemorrhage on initial CT scan, distance from the patient's home to the Mayo Clinic, and time between onset of SAH and admission to the Mayo Clinic. Each variable was assessed individually and those found to be significant (p < 0.05) were used for further analysis. Interaction terms were also assessed. A similar analysis was performed for the community patients who were treated between 1975 and A separate analysis was performed to evaluate the effect of surgery on survival in the referral group. Patients were divided into three groups depending on how soon definitive aneurysm surgery was performed after their first SAH: Days 1 to 3, Days 4 to 10, and Days 11 to 15. By Day 15, 75% of the surgical procedures had been performed. For each of these time periods, a separate survival curve was estimated by the Kaplan- Meier product-limit method. 14 A comparison of survival rates using the log-rank test was made for those who underwent surgery and for those who had not yet had surgery at the given time period. For patients in the surgically treated group, time 0 for survival analysis was the time of operation. Patients who underwent surgery were included in only one surgery group according to the time of operation. Patients who had surgery in a time period after the one being analyzed were included in the no-surgery group for survival analysis and were censored (removed from the denominator) at the time of operation. For example, a patient who underwent surgery on Day 5 would be included in the no-surgery group for the survival analysis of the Day 1 to 3 surgery group until Day 5, at which time the patient would be censored. The patient would then be included in the next group as a surgical J. Neurosurg. / Volume 78/May,

3 J. P. Whisnant, et al. TABLE 1 Level of consciousness at admission in patients with aneurysmal SAH* Level of Referral Community Consciousness Group Group no. of cases normal 52% 53% 1 22% 14% 2 13% 14% 3 13% 19% * Abbreviation: SAH = subarachnoid hemorrhage. For description of levels of consciousness, see text. patient with time 0 on Day 5 and would be excluded from analysis in the Day 11 to 15 surgery group. For patients in the no-surgery group, time 0 was assigned as the midpoint of the period: Day 2 for the first group, Day 7 for the second group, and Day 13 for the third group. Patients who died before the assigned day were not included in the analysis for that time period. For example, a patient who died on Day 6 would be included in the no-surgery group for the first analysis but would not be included in the analysis of the Days 4 to 10 surgery group because death occurred prior to the assigned day. The purpose of this differential survival analysis was to compare similar patients at each point in time. Optimum study results would have been available if the survival analysis was performed for each day rather than for a range of days, but there were not enough patients who had definitive surgery each day to perform such analyses. Results The level of consciousness at admission in the referral and community groups is noted in Table I. Thirtyseven percent of the patients in the referral group and 33% in the community group had a history of hypertension. Computerized Tomography Scans Computerized tomography scans of the head were obtained for 316 (96%) of the 328 patients in the re- TABLE 2 Clinical grade at admission in patients with aneurysmal SAH* Clinical Referral Group Community Group Grade No. Percent No. Percent I or II III IV or V VI total * Abbreviation: SAH = subarachnoid hemorrhage. Grading system is a modification of the Hunt and Hess classification; 9 clinical Grade VI was added to include those who died before receiving medical attention. ferral group and were normal in 53 (17%). In addition to SAH, CT revealed intraventricular hemorrhage in 83 patients (26%), intraparenchymal hemorrhage in 76 (24%), and an aneurysm in 34 (11%). A CT scan of the head was obtained for 31 (63%) of the 49 patients in the community group. The scan was normal in 13%, and revealed an intraventricular hemorrhage in 19% and an intraparenchymal hemorrhage in 45% in addition to SAH. Clinical Grade There were relatively more patients in Grades I through III in the referral group than in the community group (Table 2) (p = ). In the referral group, the patients with the "better" grades (Grades I to III) were younger (p < ), with a mean age of 49 years for patients with Grades I and II, 55 years for patients with Grade III, and 59 years for patients with Grades IV and V. We could not demonstrate a correlation between patient age and grade at presentation for patients in the community group; however, the mean age of patients in clinical Grades I and II (47 years) was similar to that in the referral group. Referral Distance The distance that referral patients traveled to the Mayo Clinic varied from 14 to more than 2000 miles, FIG. 1. Graphs showing the probability of survival for 5 years (left) and for the first 120 hours (right) after the onset of first aneurysmal subarachnoid hemorrhage (SAH) in referral patients and in community patients (n = number of patients). 728 J. Neurosurg. / Volume 78/May, 1993

4 Referral bias in aneurysmal subarachnoid hemorrhage FIG. 2. Graph demonstrating the probability of survival for 5 years after the onset of first aneurysmal subarachnoid hemorrhage (SAH) in patients with clinical Grades I to III in the referral group and in the community group (n = number of patients). with a median distance of 107 miles. Patients arrived at the Clinic from 0 to 31 days after the onset of their first SAH, with a median time of 4 days. Patients who were admitted more than 31 days after onset of SAH were not included in the study. The median time from onset to first medical attention at the Mayo Clinic for patients from Rochester was 1 hour. The referral patients with better grades (Grades I to III) on arrival were more likely to have traveled farther (p < ) and to have arrived a greater number of days after their first SAH (p < ). Aneurysm Surgery Definitive aneurysm surgery was performed on 264 (80%) of the 328 patients in the referral group. Eleven patients underwent additional procedures such as shunt or ventricular drainage placement at the time of definitive aneurysm surgery. In the community group, among the 43 patients who received medical attention before death, 23 had definitive aneurysm surgery. Survival Rates The survival rate from onset of SAH for the referral group was significantly higher than that for the community group (p = 0.005) (Fig. I left). The expected survival rate was the same for both groups, indicating similar patient age and sex distributions. The survival rates at 5 years for the referral and community groups were 63% and 53%, respectively. The survival rates at 30 days after onset of SAH were 83% in the referral group and 59% in the community group. At 12 hours after onset, the survival rates were 98% in the referral group and 80% in the community group (Fig. 1 right). The survival rate from onset of SAH for patients with clinical Grades I to IlI at admission in the referral group was compared to that in the community group (Fig. 2). The difference in survival data between the two groups was significant at 30 days (log-rank chi-squared test, p = 0.02), but the 5-year probability of survival was identical in the two groups. The survival rates of patients in the referral group were also evaluated by comparing those who had received definitive aneurysm surgery with those who did not. Patients with clinical Grade V at admission were excluded to prevent the bias of including in the nosurgery group those patients who were highly unlikely to ever be considered as surgical candidates. The survival rates for patients who underwent surgery at the various time periods were compared with that of patients who had not yet had surgery. There was a significantly higher survival rate at 1 year for patients who had surgery compared with those who did not for each of the three time periods (Fig. 3). The survival rate at 1 year for patients who had early surgery was virtually identical to that for patients who underwent later surgery, and the difference in survival rates for those who had surgery and for those awaiting surgery was similar for each time period (Table 3). Logistic Regression and Proportional-Hazards Analysis Logistic regression revealed that patient age, distance from the patient's home to the Mayo Clinic, presence of intraparenchymal hemorrhage, days from onset of SAH to admission to the Mayo Clinic, level of consciousness, clinical grade at admission, and diastolic blood pressure were significantly related to 7-day survival. These variables were then used in a multivariate analysis with the addition of interaction terms. The final model of independently significant variables is FIG. 3. Graphs showing the probability of survival for 30 days for patients who had definitive aneurysm surgery compared with that for patients awaiting surgery at specified times after first medical attention for subarachnoid hemorrhage: surgery performed 1 to 3 days (left); 4 to 10 days (center); and 11 to 15 days (right). Patients with clinical Grade V were excluded. J. Neurosurg. / Volume 78/May,

5 TABLE 3 Survival rates in relation to aneurysm surgery at three time periods in referral SAH patients* J. P. Whisnant, et al. Time of Day 1-3 Post-SAH Day 4-10 Post-SAH Day Post-SAH Analysis With Awaiting With Awaiting With Awaiting (days) Surgery Surgery Surgery Surgery Surgery Surgery no. of cases % % 92 96% % 56 98% % 30 92% 75% 96% 77% 93% 65% % 47% 89% 48% 90% 49% p value 0.02t 0.04t 0.007'f * Abbreviation: SAH = subarachnoid hemorrhage. Survival analysis excludes patients with clinical Grade V at admission. "~ Log-rank test at 1-year follow-up monitoring. shown in Table 4. A poor clinical grade had the highest odds ratio. For the community patients, presence of coma at admission had the highest odds ratio at 22 (95% confidence interval ). This variable is closely related to high clinical grade but each was an independently significant predictor of survival after admission to the Mayo Clinic in the referral patients. Proportional-hazards regression was used to assess the predictors of survival, given a 7-day survival. Significant predictors used for the multivariate analysis were patient age, level of consciousness, clinical grade, and systolic and diastolic blood pressure. The final model is shown in Table 5. For the referral patients, presence of coma was still the most important predictor of survival after admission to the Mayo Clinic, with an odds ratio of 3.28 (95% confidence interval ). In referral patients, an increased level of diastolic blood pressure was associated with improved survival during the first 7 days, whereas the reverse was the case after the initial 7 days. Selection Bias Discussion Each referral center has its own patient selection biases depending on geographic location, distance from referring physicians, and particular interests of consul- TABLE 4 Logistic regression model for 7-day survival in 327 referral SAH patients* # 95% Variable Coefficient'~ p Odds Confidence (mean _+ SEM) Value Ratio Interval grade (IV or V)~ _ ~ coma _ diastolic BP _ w days from onset _ to admission to Mayo Clinic * Abbreviations: SAH = subarachnoid hemorrhage; BP = blood pressure; SEM = standard error of the mean. i A negative value indicates a decreased probability of early death related to increasing values for the variable. Grading according to a modified Hunt and Hess classification) w For 10 mm Hg difference. rants at the referral center. Population-based studies are likely to produce more uniform data. There was a dramatic difference in the 30-day survival rate between the referral patients (83%) and the community patients (59%) (Fig. 1 left). This difference was quite prominent, even at 12 hours after the onset of SAH (98% vs. 80%) (Fig. 1 right). After the first 2 days, the difference in the rate of change of survival for the two groups was much less pronounced (Fig. 1 right). Therefore, after the first 2 days following SAH, the bias in survival estimates determined by referral is not so apparent. The selection bias for referral patients is determined by the fact that this group did not include patients who died and some who were in poor clinical condition before the opportunity for referral. The relative lack of such patients in the referral group accounts for the difference in survival rates between the referral and the community patients in the Kaplan-Meier survival analyses. Our data support the idea that patients in better clinical condition are more likely to be referred, because there was a significantly greater proportion of patients with better clinical grades (Grades I to III) in the referral group. In this study, there was a higher percentage of patients with SAH documented by CT in the referral group. Six patients in the community group died prior to receiving medical attention and one died in the emergency room; therefore, seven would not have had the opportunity to have a CT examination performed. If these patients are excluded, 74% of the patients in TABLE 5 Proportional-hazards model for death, given 7-day survival, in 287 referral SAH patients* r 95% Variable Coefficient p Odds Confidence (mean _+ SEM) Value Ratio Interval diastolic BP _ # coma patient age z~ * Abbreviations: SAH = subarachnoid hemorrhage; BP = blood pressure; SEM = standard error of the mean. t For 10 mm Hg difference. For 10-year difference. 730 J. Neurosurg. / Volume 78/May, 1993

6 Referral bias in aneurysmal subarachnoid hemorrhage the community group underwent CT. There was a larger percentage of patients with intraparenchymal hemorrhage found on CT scans in the community group, which is consistent with the finding of a greater number of persistent focal neurological deficits in this group. Patients with intraparenchymal hemorrhage on CT may be underrepresented in the referral group because such patients may have been in worse condition and less likely to be referred. There was a greater percentage of aneurysms located in the posterior fossa in the referral group, reflecting a particular referral preference for one or more of our neurosurgeons. In the referral group, there was no difference in survival rates based on location of the aneurysm. Among the patients in the referral group, 264 (80%) of 328 had definitive aneurysm surgery compared with only 23 (53%) of 43 in the community group. A higher incidence of early death obviously influenced the lower frequency of definitive aneurysm surgery in the community group. In addition to clinical grade at admission, other factors have been shown to influence survival in a population-based sample of patients. In community studies, a decreased survival rate was shown to be associated with a history of hypertension, presence of parenchymal hematoma, 26 level of consciousness, and increasing age." In the referral group, we examined all of these variables except pre-existing hypertension, which we were unable to assess uniformly. Decreased level of consciousness and high clinical grade had the greatest effect on 7-day survival rates after admission to the Mayo Clinic in the referral group (Table 4), whereas only decreased level of consciousness greatly affected 7-day survival rates in the community group. Decreased level of consciousness also had the greatest effect on survival after 7 days in the referral group (Table 5), whereas high clinical grade had the greatest effect after 7 days in the community group. Decreased level of consciousness and clinical grade are obviously closely related. Patients in poor clinical condition were likely to have been transferred more quickly but from shorter distances. Schievink, et al., 3~ also demonstrated this in a referral-based study, and Kassell, et al., x5 noted that a delay in admission to a referral center was associated with better survival. For referral patients, factors present at admission to the Mayo Clinic that independently affected 7-day survival rates included clinical grade, presence or absence of coma, diastolic blood pressure, and number of days from onset of SAH to day of referral. Although distance of referral was significant in a univariate analysis, it was not independently significant in the multivariate analysis. An early higher diastolic blood pressure was associated with better 7-day survival rates, but an elevated diastolic blood pressure was detrimental when considering survival after 7 days. Otherwise, only presence of coma and increasing age affected survival after 7 days (Table 5). The amount of subarachnoid blood demonstrated on CT scans has also been found to be a significant independent predictor of death or severe disability in a multiple logistic regression analysis of patients 4 weeks after SAH? We did not have enough uniform data on this variable to include it in our multivariate analysis. Early vs Late Surgery Differential survival analysis compared the survival rates for referral patients who underwent surgery during one of three different time periods after first medical attention to the rate for those who did not have surgery. This technique was used to compare the survival rate of similar patients by time of surgery after SAH. We found a significantly higher survival rate at 1 year for patients undergoing surgery compared to those awaiting surgery for each of the three time periods (Fig. 3 and Table 3). The difference between those who had surgery and those awaiting surgery was nearly identical for each of the three time periods, as was the 1-year survival rate after surgery (Table 3). Therefore, we found no evidence of net benefit in terms of survival rates following either early or late surgery. This differential survival analysis would be more useful in studies with a large number of patients in order to estimate the effectiveness of the various surgical times, particularly if a survival analysis could be obtained for each day after SAH. Caution would be necessary in interpreting the analyses in the first 2 days after SAH because the number of hours after SAH is an important determinant of survival at that time. References 1. 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7 J. P. Whisnant, et al. Stroke 20: , Jane JA, Winn HR, Richardson AE: The natural history of intracranial aneurysms: rebleeding rates during the acute and long term period and implication for surgical management. Clin Neurosurg 24: , Kaplan EL, Meier P: Nonparametric estimation from incomplete observations. J Am Stat Assoc 53: , Kassell NF, Adams HP Jr, Torner JC, et al: Influence of timing of admission after aneurysmal subarachnoid hemorrhage on overall outcome. Report of the Cooperative Aneurysm Study. Stroke 12: , Kasseil NF, Boarini DJ, Adams HP Jr, et al: Overall management of ruptured aneurysm: comparison of early and late operation. Neurosurgery 9: , Kasseil NF, Tarrier JC: The International Cooperative Study on Timing of Aneurysm Surgery -- an update. Stroke 15: , Kurland LT, Molgaard CA: The patient record in epidemiology. Sci Am 245(4):54-63, Ljunggren B, S~iveland H, Brandt L, et al: Early operation and overall outcome in aneurysmal subarachnoid hemorrhage. J Neurosurg 62: , Locksley HB: Report on the Cooperative Study of Intracranial Aneurysms and Subarachnoid Hemorrhage. Section V, Part I. Natural history of subarachnoid hemorrhage, intracranial aneurysms and arteriovenous malformations. Based on 6368 cases in the Cooperative Study. J Neurosurg 25: , Locksley HB: Report on the Cooperative Study of Intracranial Aneurysms and Subarachnoid Hemorrhage. Section V, Part II. Natural history of subarachnoid hemorrhage, intracranial aneurysms and arteriovenous malformations. Based on 6368 cases in the Cooperative Study. J Neurosurg 25: , Melton LJ III: Selection bias in the referral of patients and the natural history of surgical conditions. Mayo Clio Proc 60: , 1985 (Editorial) 23. Nishioka H: Report on the Cooperative Study of Intracranial Aneurysms and Subarachnoid Hemorrhage. Section VII, Part I. Evaluation of the conservative management of ruptured intracranial aneurysms. J Neurosarg 25: , Nishioka H, Torner JC, Graf C J, et al: Cooperative Study of Intracranial Aneurysms and Subarachnoid Hemorrhage: a long-term prognostic study. I1. Ruptured intracranial aneurysms managed conservatively. Arch Neural 41:1142-I 146, Pakarinen S: Incidence, aetiology, and prognosis of primary subarachnoid haemorrhage. A study based on 589 cases diagnosed in a defined urban population during a defined period. Aeta Neural Scand Suppl 43 (Suopl 29): 1-128, Phillips LH II, Whisnant JP, O'Failon WM, et al: The unchanging pattern of subarachnoid hemorrhage in a community. Neurology 30: , Polissar L, Dahlberg S, Metch B, et al: Referral Patterns of Cancer Patients to Major Cancer Centers. Technical Report No. 70. Seattle, Wash: Department of Biostatistics, School of Public Health and Community Medicine, September, Rosen~rn J, Eskesen V, Schmidt K, et al: The risk of rebleeding from ruptured intracranial aneurysms. J Nearosurg 67: , Sacco RL, Wolf PA, Bharucha NE, et al: Subarachnoid and intracerebral hemorrhage: natural history, prognosis, and precursive factors in the Framingham Study. Neurology 34: , Schievink WI, van der Weft DJM, Hageman LM, et al: Referral pattern of patients with aneurysmal subarachnoid hemorrhage. Surg Neural 29: , Solomon RA, Fink ME: Current strategies for the management of aneurysmal subarachnoid hemorrhage. Arch Neural 44: , Sundt TM Jr, Whisnant JP: Subarachnoid hemorrhage from intracranial aneurysms. Surgical management and natural history of disease. N Engl J Med 299: , Walker SH, Duncan DB: Estimation of the probability of an event as a function of several independent variables. Biometrika 54: , Whisnant JP, Phillips LH II, Sundt TM Jr: Aneurysmal subarachnoid hemorrhage. Timing of surgery and mortality. Mayo Clin Proc 57: , Winn HR, Richardson AE, O'Brien W, et al: The longterm prognosis in untreated cerebral aneurysms: II. Late morbidity and mortality. Ann Neural 4: , 1978 Manuscript received June 23, Accepted in final form September 30, This study was supported in part by Research Grants NS and AR from the National Institutes of Health. Address reprint requests to: Jack P. Whisnant, M.D., Mayo Clinic, 200 First Street SW, Rochester, Minnesota J. Neurosurg. / Volume 78/May, 1993