Understanding Risk

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SCIENCE"

'UNDERSTANDING

,

UNDERSTANDING RISK Salim Daya, MB, FRCSC, Professor, Departments of Obstetrics and Gynaecology, and Clinical Epidemiology and Biostatistics, McMaster University ABSTRACT

The most valid evidence upon which therapeutic decisions can be based comes [rom randomized controlled trials. The results of such trials should be reported using both relative and absolute estimators of the effect of treatment. These measures convey information about the magnitude of the treatment effect and the therapeutic effort required in relation to the therapeutic yield, thereby allowing the physician to make more informed treatment decisions. Clinically important information is provided by the relative risk and its complement, the relative risk reduction and by the absolute risk reduction and its reciprocal, the number needed to treat. The odds ratio is intuitively more difficult to understand thon the relative risk and, therefore, does not provide a clinically meaningful estimate of the effect size. However, it is particularly useful for statistical analysis and combination of data, and is commonly used in multivariate analyses. RESUME

Les donnees les plus valables sur lesquelles on peut fander des decisions therapeutiques proviennent d' essais randomises et contr6les. Les resultats de ces essais devraient etre communiques a Ia fois au moyen d' estimateurs relatifs et absolus de l' effet du traitement. Ces mesures comportent des renseignements au sujet de l' ampleur de l' effet du traitement et de l' effort therapeutique necessaire en fonction du rendement therapeutique, ce qui permet au m€decin de prendre des decisions plus eclairees a l' egard du traitement. Des renseignements d'importance clinique sont foumis par le risque relatif et son complement, Ia reduction du risque relatif, et par Ia reduction du risque absolu et son inverse, le nombre necessaire pour traiter. Le risque relatif est intuitivement plus difficile a comprendre que le risque relatif, et il ne foumit donc pas une estimation cliniquement significative de l'importance de l' effet. Cependant, il est particulierement utile ades fins d' analyse statistique et de combinaison de donnees et on l'utilise [requemment dans les analyses multivariees. J SOC OBSTET GYNAECOL CAN 1997;19:1275-82 KEYWORDS

Relative risk, absolute risk reduction, odds ratio, number needed to treat, treatment effect estimators. Received on July 31st, 1996. Revised and accepted on October 2nd, 1996.

prescriptions filled because they were unsure of the benefits of the therapy. Although the reported rates of commencement and maintenance of post-menopausal honnone replacement therapy (HRT) are variable, these figures are quite representative of the findings in this area of our specialty and are worrisome, particularly in light of the fact that as the post-baby boom generation ages, an increasing proportion of women in our society is

INTRODUCTION

In a health survey of post-menopausal women aged 45 to 55 years it was found that 20 percent of those receiving honnone therapy for the first time stopped taking the drug within nine months of commencing treatment. 1 Furthermore, ten percent took the medication only intennittently and almost one-third never had their

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• ESTRACE contains 100% 17ß-estradiol, the same estrogen produeed by the ovary .1t .i~ ESTRACE 17ß-estradiol is mieronized . ",.~r ~ to be readily absorbed from the ". ; if:" gastrointestinal trad. 1 • ESTRACE 17ß-estradiol is biologieally adive no metabolie conversion is required. • ESTRACE is ettedive in relieving menopausal symptoms. 2 • ESTRACE ean provide the protedive benefits of ERT against eardiovaseular disease. 5 • The only oral non-conjugated estrogen for the prevention of osteoporosis. • ESTRACE otters protedion against osteoporosis at a starting dose of 0.5 mg per day.3*

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, , , entering the post-menopausa1 phase. lt has been estimated that at least 350 Canadian women reach the menopause on any given day. The improvements in hea1th care and living conditions have resu1ted in an increased life expectancy, the consequence being that women will now spend almost one-third of their 1ives in the post-menopausa1 state. Apart from the physica1 manifestations from hypo-estrogenie symptoms, for examp1e, hot flushes and dyspareunia, which can be quite devastating and affect the individua1's quality oflife, the cost to society in terms of hea1th care and 10ss of productivity from osteoporosis and cardiovascu1ar disease is signifieant, and will continue to rise un1ess preventative strategies become more efficient. Post-menopausa1 estrogen use is associated with a general improvement in weH being and a signifieant reduction in both cardiac mortality and osteoporosis whieh is often associated with signifieant debility and death from the resulting fractures. In women who have undergone a hysterectomy, the evidence c1early supports the use of HRT. For post-menopausa1 women with intact reproductive tracts, the bulk of the evidence is also in favour ofHRT use. The decision to use HRT is easy for women who are troub1ed by such symptoms as hot flushes, inabi1ity to sleep, irritability, and vaginal dryness. Asymptomatic or mi1d1y symptomatic women, however, often have doubts about the benefits of HRT and are more 1ikely to be concerned about an increased risk for cancer. Because there are no immediate effects from HRT in such women, the 10ng term benefit is not readi1y apparent and they are 1ess willing to initiate and/or continue with treatment. A major influence in the use of HRT is the view of the attending physician. It has been shown that physician recommendation is one of the strongest factors 1eading to the use of HRT. 2 The explosion in the amount of information that is availab1e and the increasing demands on physicians' time have 1ed to great diffieu1ties in the evaluation of the quality of evidence to guide physicians in making appropriate decisions. This process is complicated further by reports in the lay media of the controversies surrounding various interventions. The busy physician is then left with having to make decisions ftom information contained in the most readily availab1e review artic1es, most of which are opinion-based rather than evidence-based. The practising c1inician needs to understand the yardsticks

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which are used to measure and compare the benefits and risks of various hea1th care approaches, so that the discussion with the patient of the advantages and disadvantages can be more informed and meaningful. A1though there are severa1 yardsticks availab1e describing the extent of c1inieal benefit, the advantages and deficiencies of the more common1y used ones will be discussed by illustrating their use in post-menopausa1 HRT assessment. In order to provide a c1ear pieture of the differences between the various measures of benefit, the effect of HRT in reducing the likelihood of osteoporosis-related hip fractures will be considered. A1though the most valid evidence upon which therapeutic decisions can be based comes from randomized controlled trials, such evidence is presently unavai1ab1e. Consequently, a hypothetica1 examp1e will be used in whieh the data were produced using the risk estimates obtained from the Framingham study, which inc1uded a cohort of 2,873 women examined periodieally and followed for more than 20 years. J In the hypothetiea1 examp1e, fractures were observed in 124 of 226 women in the contro1 group and in 42 of 222 women in the experimental (treated) group (Tab1e 1). RISK VERSUS ODDS

Risk is a concept that expresses the probability that an adverse health outcome (or event) will occur, whereas, odds refers to the probability that an event will occur

TABLE 1 EFFECT OF POST-MENOPAUSAL HORMONE REPLACEMENT THERAPY ON THE PREVENTION OF OSTEOPOROSIS-RELATED HIP FRACTURES Hip Fractures

Allocation group

Yes Hormone replacement

42 124

.~bJ

102

caJ

~

(no treatment)

282

162

Total

222

180

[Al

therapy Control

Total

No

a±fl

li±6l

226 '~

448 Ib+dl

ia±b±c~

Control group event rate (CER) (risk)-clc + d- 124/226- 0.55 Experimental group event rate (EER) (risk)- a/a +b- 421222- 0.19 Relative risk (RR)- EER/CER- O.34 Odds of event in controlgroup - cld - 124/102- 1.22 Odds of event in experimental group - alb- 421180- 0.23 Odds ratio (OR) (- relative odds) - (alb)/(cld)- adlbc- O.19 Relatrve risk reduction (RRR)- (CER - EER)/CER - O.64 (64%) (also, RRR - l - RR) Absolute risk reduction (ARR) (- absolute risk difference)- CER- EER- O.36 Number needed to treat (NND- l/(CER - EER)- 1/ARR- 3 (also, NNT- lI[RRR x CER}- 3)

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, , , compared to the probability that it will not occur. Using the format in Table 1, risk can be calculated as follows: Risk of event (in the experimental group) = Risk of event (in the control graup)

In the osteoporosis example, the relative risk ofhip fractures with HRT is (42/222)/024/226)=0.34. The complement of the relative risk (i.e. 1 - relative risk) is the relative risk reduction (RRR) which expresses the praportionate risk difference. Thus, a relative risk of 0.34 represents a 66 percent reduction in the event rate (i.e. fractures) in the experimental (i.e treated) graup compared to controls. The relative risk reduction, therefore, is the reduction in adverse events achieved by treatment, expressed as a praportion of the contral rate. In numerical terms, it is the absolute difference in event rates between the contra 1and experimental graups, divided by the event rate in the contral group.

a

a+b c c+d

In our osteoporasis example, the risk ofhip fractures in the experimental graup is 42/222=0.19 and in the control group it is 124/226=0.55. Using the format in Table 1, odds can be calculated as follows: Odds of event (in the experimental group) =

a

b c

Odds of event (in the contral group)

i.e. Relative risk reduction =

d

Control group event rate - experimental group event rate

Thus, the odds of fractures occurring in the experimental group is 42/180=0.23 and in the contral graup it is 124/102=1.22. There is a simple mathematical relationship between risk and odds that allows them to be interconvertible.

Contral graup event rate The main disadvantage of using the relative risk reduction in clinical decision making is that it does not reflect the magnitude of the baseline risk (i.e. the risk without treatment). Furthermore, when adverse events without treatment are very rare or very common it is possible that the absolute effect of therapy is overestimated or underestimated, respectively.

Risk=odds/O + odds) Thus, in the example, the risk of fractures in the contral group=1.22/0 + 1.22)=0.55.

ODDS RATIO

Likewise, odds=risk/O- risk).

The odds ratio (OR) is often used as an approximation to the relative risk in case-contral studies. It is also a valid measure of treatment effect in randomized trials because it expresses the association between exposure (i.e. treatment graup) and outcome. The odds ratio is an expression of the comparison between the odds of an event occurring in the experimental graup with the odds in the contral graup. I

Therefore, in the example, the odds of fractures in the control group=0.55/0 - 0.55)= 1.22. RELATIVE RISK

The relative risk (RR), which is also known as the risk ratio or the event rate ratio, is an expression of the prabability that an event will occur when two graups of subjects are compared. Mathematically, the relative risk can be calculated as follows:

Mathematically it is calculated as follows: Odds ratio =

Risk of event in experimental group Relative risk = - - - - - - - - - - - - - Risk of event in contral group Event rate in experimental group Event rate in contra1graup a/a+b

Odds of event in experimental group Odds of event in contral graup

(alb)

ad

(c/d)

bc

In our example, the odds ratio of hip fractures with HRT is (42/180)/024/102)=0.23/1.22=0.19. The

c/c+d

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, , , concrete terms that are readily understood by patients and physicians how much effort must be expended to prevent one event. This estimator of treatment effect can also be used to compare the effects of other interventions, and is an important factor in deciding how to balance therapeutic benefits against side effects and costs of treatment. For high event rates in the control group, the NNT will be low even for small amounts of relative risk reduction. For example, if a disease has a baseline risk of 90 percent and if treatment produces a relative risk reduction of 10 percent (Le. 90% with control and 81 % with treatment), then the NNT will be 1/9 = 11. In contrast, when the event rate in the control group is low, then the risk reduction will have to be quite large to produce a similarly low NNT. Therefore, if the baseline risk is 20 percent, the relative risk reduction would have to be at least 45 percent to produce an NNT of 11. The known therapeutic effect of HRT on reducing the likelihood of fractures can be represented in similar terms. Long term (i.e. > 10 years) use of estrogens was associated with relative risk reductions of 73 percent for all hip fractures, 75 percent for wrist fractures, and 40 percent for all non-spinal fractures. 4 These figures translate into NNTs of 1.4, 1.3, and 2.5, respectively, indicating that for every four to five women treated with estrogen for > 10 years, fractures will be prevented in two to three women.

reciprocal of this figure represents the odds ratio of a favourable event (in this case, no hip fractures, Le. 1/0.19 =5.26). Therefore, for adverse outcome events, an efficacious treatment will produce an OR < 1. This is analagous to the relative risk for an adverse effect being less than one. Whereas for treatments that produce positive outcome events, an efficacious treatment will produce OR > 1. The odds ratio, like the relative risk reduction, does not reflect the magnitude of the risk without treatment and, therefore, has limited clinical usefulness. ABSOLUTE RISK REDUCTION

The absolute risk reduction (ARR), also referred to as the attributable risk reduction or the risk difference, is the difference in event rates between the experimental and control groups. Le. Absolute risk reduction = control group event rate - experimental group event rate. In the example, the absolute risk reduction in hip fractures with HRTwas 0.55 - 0.19=0.36, Le. treatment reduces the risk of the adverse outcome in absolute terms by 36 percent. The advantage of the absolute risk reduction, when compared to the relative risk reduction and odds ratio, is that it is an expression of the consequences of giving no treatment. Thus, it provides a clinically more meaningful indication of the effect of treatment.

RELATIVE RISK VERSUS ODDS RATIO NUMBER NEEDED TO TREAT

Both relative risk (risk ratio) and odds ratio are relative estimators of treatment effect. In contrast, the absolute risk reduction (or risk difference) and its derived quantity, the number needed to treat, are absolute estimators. The relative risk is a well recognized and established estimator of treatment effect that can be obtained from prospective trials, and provides a quantitative estimate for the clinical quest ion of the proportion of treated patients, relative to control, who experience an event. The odds ratio approximates the relative risk when the baseline risk of the outcome event is low (typically < 10%). Such a situation is often seen in case-control studies in which the relative risk cannot be calculated direcdy because the prevalence of the adverse outcome is usually not known. Also, such studies are used typically to investigate rare events. One has to rely instead on the odds ratio in these situations, either by comparing the odds of incurring an adverse event in the treated (or

The number needed to treat (NNT) is the number of patients who must be treated to prevent one adverse event. It is calculated as the reciprocal of the absolute risk reduction. Number needed to treat= I/absolute risk reduction. The NNT also can be expressed mathematically in terms of the relative risk reduction as follows: Number needed to treat= 1/(relative risk reduction x control group event rate). In our example, the NNTwith HRT to prevent one woman having a hip fracture is 1/0.36=3 (also 1/[0.64 x 0.55]=3). The NNT has the same advantage as the ARR in that, unlike the relative risk reduction and odds ratio, it expresses efficacy in a clinically meaningful way by incorporating both the baseline risk without treatment and the reduction in risk with treatment. It also expresses in more

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, , , exposed} group and the control group (Le. [a/b]/[c/d]=ad/bc) or by comparing the odds oE exposure in the event and non-event groups (i.e. [a/c]/[b/d]= ad/bc); both methods produce the same answer. The odds ratio will deviate markedly from the relative risk when the treatment effect is large and when the baseline risk is high. By convention, both the odds ratio and relative risk are expressed in quantities less than one when treatment prevents events and greater than one when treatment causes events-the odds ratio strays further from unity than the relative risk in both situations. Thus, the odds ratio magnifies the apparent siie of the treatment effect. As baseline risk increases, the odds ratio moves increasingly further from unity than the relative risk. The odds ratio has limited clinical applicability for several reasons. It is intuitively less easy to understand than the relative risk, probably because the concept of odds itself is not very clear. Neither the relative nor the absolute size oE the treatment effect are communicated by the odds ratio. Consequently, physicians are not very familiar with the use of odds in making clinical decisions, thereby reducing its value as an effect estimator. Furthermore, because many controlled trials focus on common adverse events, the approximation of the odds ratio to the relative risk is less accurate, and its use willlikely overestimate the benefit and harrn of treatment. When treatments produce a constant relative risk reduction for different event rates in the control group, the odds ratios are not constant but vary across these event rates and vice versa. For example, a relative risk reduction of 25 percent (Le. a relative risk of 0.75) corresponds to an odds ratio that varies from 0.73 to 0.23 when the event rate in the control group varies from 10 percent to 90 percent. Thus, an odds ratio derived from a trial perforrned in one population cannot be used to estimate the post-treatment event rate in patients with a substantially different baseline risk. The magnitude of the treatment effect from such an attempt either will be overestimated or underestimated depending on the baseline risk in the trial patients. Despite these properties that interEere with the clinical application of the odds ratio, it is very effective for the analysis of data from subgroups of patients to produce a single overall estimate of the effect of treatment. It is also commonly used in the analysis and reporting of systematic overviews of randomized trials that have dichotomous outcomes and in multivariate analyses that are performed to control for confounding factors.

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the number needed to treat, expresses the absolute risk reduction in a manner that can be understood readily by physicians and patients, and can be used to evaluate any harm as well as benefit of therapy. Although these various measures convey different information, they should all be provided so that physicians are not misled by the apparent size of the treatment effect. In this way, more infonned treatment decisions can be made.

PHYSICIANS' PERCEPTIONS OF TREATMENT EFFECTIVENESS

Although measures of treatment effect include absolute and relative estimators, the perceptions by physicians of the effectiveness of treatment are more likely to be influenced by the magnitude of the relative risk reduction that they produce or by the number of patients needed to be treated. 5 Interestingly, the same result expressed either as a relative or absolute risk reduction will generate very different responses in support of the treatment. Physicians are more likely to provide a new intervention for their patients when the results are presented with the relative reduction rather than the absolute reduction in risk. 6 This fact was also observed in a study which evaluated the perceptions of drug effectiveness.7 When the same results were presented in different fonnats, physicians rated the treatment effectiveness as marginally better using a relative rather than an absolute estimator, and substantially lower using the number needed to treat. Thus, it is now quite clear that in presenting the results of studies, the choice of the estimator of the treatment effect will have an important influence on how physicians view the value of the treatment and incorporate this judgement into their management decisions. In all areas of medicine, including post-menopausal HRT, it is important to present the results of clinical trials using both the relative risk and its derived quantity, the relative risk reduction, and the absolute risk reduction and its derived quantity, the number needed to treat. This approach ensures that a complete description of the therapeutic effect and therapeutic effort is provided so that appropriate treatment decisions can be made.

REFERENCES 1. 2.

3.

4.

5. 6.

7.

Revanikar VA. Compliance with hormone therapy. Am J Obstet GynecoI1987;154:1332. Ferguson KJ, Hoegh C, Johnson S. Estrogen replacement therapy: a survey of women's knowledge and attitudes. Arch Int Med 1989;149:133. Kiel DP, Felson DT, Anderson JJ, Wilson PWF, Maskowitz MA. Hip fracture and the use of estrogens in postmenopausal women. The Framingham Study. N Engl J Med 1987;317:1169-74. Cauley JA, Seeley DG, Ensrud K, Ettinger B, Black D, Cummings SR. Estrogen replacement therapy and fractures in older women. Ann Intern Med 1995;122:9-16. Laupacis A, Sackett DL, Roberts RS. Therapeutic priorities of Canadian internists. Can Med Assoc J 1990;142:329-33. Forrow L, Taylor WC, Arnold RM. Absolutely relative: how research results are summarized can affect treatment decisions. Am J Med 1992;92:121-4. Naylor CD, Chen E, Strauss B. Measured enthusiasm: does the method of reporting trial results alter perception of therapeutic effectiveness? Ann Intern Med 1992;117:916-21.

CONCLUSION

The most valid estimates of the effect of treatment are obtained from randomized trials. The treatment effect can be expressed in various ways depending on whether treatment prevents an event or causes an event. In the case of the fonner, the estimator of the treatment effect can be expressed in relative or absolute tenns. The relative estimators are relative risk, odds ratio, and relative risk reduction, whereas the absolute estimators are the absolute risk reduction and the number needed to treat. The absolute risk reduction is superior to the relative risk reduction because it incorporates both the baseline risk and the magnitude of the risk reduction. lts reciprocal,

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