CMAJ 1995 Basic Statistics for Clinicians

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assumes a straight-line fit between the independent and dependent variable, and the dependent variable is continuous, we refer to the analysis as "linear regression." In our next example, the dependent variable is dichotomous. Investigators sometimes use the term "logistic regression" to refer to such models because they are based on logarithmic equations. PREDICTING CLINICALLY IMPORTANT GASTROINTESTINAL BLEEDING We have recently considered whether we could predict which critically ill patients were at risk of clinically important gastrointestinal bleeding.7 In this example, the dependent variable was whether patients had had a clinically important bleed. When the dependent variable is dichotomous we use a logistic regression. The independent variables included whether patients were breathing independently or required ventilator support and the presence or absence of coagulopathy, sepsis, hypotension, hepatic failure and renal failure. In the study we followed 2252 critically ill patients and determined which of them had clinically important gastrointestinal bleeding. Table 1, which contains some of the results, shows that in univariate logistic regression analyses many of the independent variables were significantly associated with clinically important bleeding. For several variables, the odds ratio (discussed in a previous article in this series), which indicates the strength of the association, was large. However, when we constructed a multiple logistic regression equation, only two of the independent variables - ventilator support and coagulopathy - were significantly and independently associated with bleeding. All of the other variables that had predicted bleeding in the Risk factors Respiratory failure Coagulopathy Hypotension Sepsis Hepatic failure Renal failure Enteral feeding Administration of steroids Transplantation of an organ Therapy with anticoagulants *NS = not significant. univariate analysis were correlated with either ventilation or coagulopathy and were not statistically significant in the multiple regression analysis. Of the patients who were not supported by a ventilator, 0.2% (3/1597) had an episode of clinically significant bleeding, whereas 4.6% (30/655) of those being supported by a ventilator had such an episode. Of those with no coagulopathy 0.6% (10/1792) had an episode of bleeding, whereas of those with coagulopathy 5.1% (23/455) had such an episode. Our main clinical interest was identification of a subgroup with a risk of bleeding low enough that prophylaxis could be withheld. In an analysis separate from the regression analysis, but suggested by its results, we divided the patients into two groups, those who were neither supported by a ventilator nor had coagulopathy, in whom the incidence of bleeding was only 0.14% (2/1405), and those who were either supported by a ventilator or had coagulopathy, of whom 3.7% (31/847) had an episode of bleeding. Prophylaxis may reasonably be withheld from patients in the former group. CONCLUSION Correlation examines the strength of the relation between two variables, neither of which is necessarily considered the target variable. Regression examines the strength of the relation between one or more predictor variables and a target variable. Regression can be very useful in formulating predictive models such as the risk of myocardial infarction in patients presenting with chest pain,8 the risk of cardiac events in patients undergoing noncardiac surgery,9 or the risk of gastrointestinal bleeding in critically ill patients. Such predictive models can help us make clinical decisions. Whether you are considering a correlation between vari- Simple regression analysis 25.5 (< 0.0001) 9.5 (< 0.0001) 5.0 (0.03) 7.3 (
ables or a regression analysis, you should consider not only the statistical significance of the relation but also its magnitude or strength, in terms of the proportion of variation explained by the model or the extent to which groups with very different risks can be specified. We thank Derek King, BMath, for conducting the original analyses reported in this article and for preparing the figures. . 3~~~~~~~~~~~~~~~. ...... ........ ... . .. ..... I. McGavin CR, Gupta SP, McHardy GJR: Twelve-minute walking test for assessing disability in chronic bronchitis. BMJ 1976; 1: 822-823 2. Guyatt GH, Berman LB, Townsend M: Long-term outcome after respiratory rehabilitation. Can Med Assoc J 1987; 137: 1089-1095 3. Guyatt GH, Keller J, Singer J et al: A controlled trial of res- *C.onfe.rences co4nt.ed from page 493 Apr. 3-5, 1995: Current Treatments Conference: Diagnostic and Treatment Problems in Primary Care Victoria Coastal Conferences Ltd., 1459 Jamaica Rd., Victoria BC V8N 2C9; tel 604 477-7559, fax 604 595-9594 Apr. 6-7, 1995: Therapeutic Camps for Children and Adolescents (sponsored by the Recreation Discipline and the Children's Outpatient Department, Royal Ottawa Hospital) Ottawa Robert Wilson, conference facilitator, Wilcom Services Inc., 59 Horner Dr., Nepean ON K2H 5G1; tel 613 596-6064, fax 613 596-0711 Apr. 10-11, 1995: 5th Annual Palliative Care Conference - Palliative Care . . . Towards Consensus in Practice (in collaboration with the Canadian Association of Nurses in AIDS Care, the Canadian Association of Nurses in Oncology, the Community Hospice Association of Ontario, the Metropolitan Toronto Palliative Care Council, the Ontario Medical Association, Section of Palliative Care, and the Ontario Palliative Care Association) Toronto Humber College, Business and Industry Services, 205 Humber College Blvd., Etobicoke ON M9W 5L7; tel 416 675-5077, fax 416 675-0135 Apr. 20-22, 1995: 6th International Congress on Dermatology and Psychiatry: Getting in Touch Amsterdam, the Netherlands Bureau PAOG Amsterdam, Tafelbergweg 25, 1105 BC Amsterdam, the Netherlands; tel 011 20 566-4801, fax 011 20 696-3228 Apr. 23-27 1995: An Update on Geriatrics Alzheimer's disease, depression, therapeutics and medical ethics Jerusalem, Israel Study credits available. Dr. A. Mark Clarfield, Sarah Herzog Hospital, c/o Ortra Ltd., 2 Kaufman St., PO Box 50432, Tel Aviv 61500, Israel; tel 011 972 3 517-7888, fax 011 972 3 517-4433 Apr. 23-27, 1995: Probing the Future: Canadian Society of Clinical Chemists and Canadian Association of Medical Biochemists 39th Annual Scientific Congress Whistler, BC CSCC-CAMB 39th Annual Conference, PO Box 1570, 190 Railway St., Kingston ON K7L 5C8; tel 613 531-8899, fax 613 531-0626 Du 23 au 27 avr. 1995: ((Probing the Future)): 39e congres annuel de la Soci6te canadienne des clinico-chimistes et de l'Association canadienne des m6dico-biochimistes Whistler, C-B Congres annuel de la SCCC-AMBC, CP 1570, 190, rue Railway, Kingston ON K7L 5C8; tel 613 531-8899, fax 613 531-0626 Page 27 of 27 piratory muscle training in chronic airflow limitation. Thorax 1992; 47: 598-602 4. Goldstein RS, Gort EH, Stubbing D et al: Randomized controlled trial of respiratory rehabilitation. Lancet 1994; 344: 1394-1397 5. Godfrey K: Simple linear regression. N Engl J Med 1985; 313: 1629-1636 6. Morgan AD, Peck DF, Buchanan DR et al: Effect of attitudes and beliefs on exercise tolerance in chronic bronchitis. BMJ 1983; 286: 171-173 7. Cook DJ, Fuller HD, Guyatt GH et al: Risk factors for gastrointestinal bleeding in critically ill patients. N Engl J Med 1994; 330: 377-381 8. Pozen MW, D'Agostino RB, Selker HP et al: A predictive instrument to improve coronary-care-unit admission practices in acute ischemic heart disease. N Engl J Med 1984; 3 10: 1273-1288 9. Detsky AS, Abrams HB, McLaughlin JR et al: Predicting cardiac complications in patients undergoing non-cardiac surgery. J Gen Intern Med 1986; 1: 211-219 Apr. 24-25, 1995: Approaching the Dream: Clinical and Cultural Perspectives Paris, France Ontario Council for Leadership in Educational Administration, 252 Bloor St. W, Ste. 12-115, Toronto ON M5S 1V5; tel 416 944-2652, fax 416 944-3822 Apr. 26-29, 1995: Canadian Association of Speech-Language Pathologists and Audiologists Ottawa Linda J. Garcia, CASLPA Conference '95, Programme d'audiologie et d'orthophonie, University of Ottawa, 545 King Edward Ave., Ottawa ON KlN 6N5; tel 613 564-9918, fax 613 564-9919 Apr. 28-29, 1995: 8th Annual Scientific Conference on Lyme Borreliosis and Other Tick- Borne Diseases Vancouver Lyme Disease Foundation, Inc., 1 Financial Plaza, Hartford CT 06103; tel 203 525-2000 or 800 886-LYME, fax 203 525-TICK Apr. 30, 1995: 7th Annual Symposium on Treatment of Headaches and Facial Pain New York Dr. Alexander Mauskop, director, New York Headache Center, 301 E 66th St., New York NY 10021; tel 212 794-3550 continued on page 529 504 CAN MED ASSOC J * 15 FtVR. 1995; 152 (4) For prescribing information see page 594 -*
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