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Grading quality of evidence and strength of recommendations
GRADE Working Group
Clinical guidelines are only as good as the evidence and judgments they are based on. The GRADE approach aims tomake it easier for users to assess the judgments behind recommendations Users of clinical practice guidelines and other recommendationsneed to know how much confidence they can place in therecommendations. Systematic and explicit methods of makingjudgments can reduce errors and improve communication. Wehave developed a system for grading the quality of evidence andthe strength of recommendations that can be applied across awide range of interventions and contexts. In this article wepresent a summary of our approach from the perspective of aguideline user. Judgments about the strength of a recommenda-tion require consideration of the balance between benefits andharms, the quality of the evidence, translation of the evidenceinto specific circumstances, and the certainty of the baseline risk.
It is also important to consider costs (resource utilisation) beforemaking a recommendation. Inconsistencies among systems for ing the complex judgments that go into clinical practice grading the quality of evidence and the strength of guidelines or other healthcare recommendations, either recommendations reduce their potential to facilitate critical implicitly or explicitly. To achieve simplicity in our presentation appraisal and improve communication of these judgments. Our we do not discuss all the nuances or provide detailed guidance system for guiding these complex judgments balances the need that guideline panels would need to apply our approach. This for simplicity with the need for full and transparent can be obtained from the authors (www.GradeWorking- consideration of all important issues.
A systematic and explicit approach to making judgments Introduction
about the quality of evidence and the strength of recommenda-tions can help to prevent errors, facilitate critical appraisal of Judgments about evidence and recommendations are complex.
these judgments, and can help to improve communication of this Consider, for example, the choice between selective serotonin information. Since the 1970s a growing number of organisations reuptake inhibitors and tricyclic antidepressants for the have employed various systems to grade the quality (level) of evi- treatment of moderate depression. Clinicians must decide which dence and the strength of recommendations.1–28 Unfortunately, outcomes to consider, which evidence to include for each different organisations use different systems to grade the quality outcome, how to assess the quality of that evidence, and how to of evidence and the strength of recommendations. The same evi- determine if selective serotonin reuptake inhibitors do more dence and recommendation could be graded as II-2, B; C+, 1; or good than harm compared with tricyclics. Because resources are strong evidence, strongly recommended depending on which always limited and money that is spent on selective serotonin system is used. This is confusing and impedes effective commu- reuptake inhibitors cannot be used elsewhere, they may also need to decide whether any incremental health benefits are The GRADE Working Group began as an informal collabo- ration of people with an interest in tackling the shortcomings of It is not practical for individual clinicians and patients to present grading systems. Table 1 summarises these shortcomings make these judgments unaided for each clinical decision.
and the ways in which we have overcome them. The GRADE sys- Clinicians and patients commonly use clinical practice tem enables more consistent judgments, and communication of guidelines as a source of support—that is, recommendations that such judgments can support better informed choices in health have been systematically developed by panels of people with care. Box 1 shows the steps in developing and implementing access to the available evidence, an understanding of the clinical guidelines from prioritising problems through evaluating their problem and research methods, and sufficient time for reflection.
implementation. We focus here on grading the quality of Users of systematically developed guidelines need to know evidence and strength of recommendations.
how much confidence they can place in evidence andrecommendations. We describe the factors on which ourconfidence should be based and a systematic approach for mak- Members of GRADE Working group are listed at the end of this article BMJ VOLUME 328 19 JUNE 2004
Definitions
reuptake inhibitors and tricyclic antidepressants), for whom(moderately depressed adult patients), and in what setting We have used the following definitions: the quality of evidence indicates the extent to which one can be confident that anestimate of effect is correct. The strength of a recommendationindicates the extent to which one can be confident that Quality of evidence for each important outcome
adherence to the recommendation will do more good than A systematic review of available evidence should guide these judgments. Reviewers should consider four key elements: study Judgments about the quality of evidence require assessments design, study quality, consistency, and directness.
of the validity of the results of individual studies for importantoutcomes. Explicit criteria should be used in making these Study design
judgments.26 29–32 The steps in our approach, which follow these Study design refers to the basic study design, which we have judgments, are to make sequential judgments about: broadly categorised as observational studies and randomised tri- The quality of evidence across studies for each important out- als. Both logical arguments and empirical evidence support this.33–36 Although observational studies commonly have results Which outcomes are critical to a decision that are similar to those of randomised trials, this is not always The overall quality of evidence across these critical outcomes the case. One dramatic example of such a discrepancy is the dif- ferent results of observational studies that suggested hormone replacement therapy decreased the risk of coronary heart All of these judgments depend on having a clearly defined disease and subsequent randomised trials that found no question and considering all of the outcomes that are likely to be reduction in risk and even an increased risk.37 38 Unfortunately, it important to those affected. The question should identify which is not possible to know in advance whether observational studies options are being compared (for example, selective serotonin accurately predict the findings of subsequent randomised trials.
Once the results of high quality randomised trials are available,few people would argue for continuing to base recommenda-tions on non-randomised studies with discrepant results.
Box 1: Sequential process for developing guidelines
On the other hand, randomised trials are not always feasible and, in some instances, observational studies may provide better First steps
1. Establishing the process—For example, prioritising problems,
evidence, as is generally the case for rare adverse effects. Moreo- selecting a panel, declaring conflicts of interest, and agreeing on ver, the results of randomised trials may not always be applicable—for example, if the participants are highly selectedand motivated relative to the population of interest. It is Preparatory steps
2. Systematic review—The first step is to identify and critically
therefore essential to consider study quality, the consistency of appraise or prepare systematic reviews of the best available results across studies, and the directness of the evidence, as well as the appropriateness of the study design. So, for example, well 3. Prepare evidence profile for important outcomes—Profiles are designed case series may provide high quality evidence for com- needed for each subpopulation or risk group, based on the plication rates from surgery or procedures, such as intraopera- results of systematic reviews, and should include a quality tive deaths or perforations after colonoscopy, which is more directly relevant than evidence from randomised trials. Similarly, Grading quality of evidence and strength of
cohort studies can provide high quality evidence for rates of recommendations
recall or procedures precipitated by false positive screening 4. Quality of evidence for each outcome—Judged on information results, such as biopsy rates after mammography.
summarised in the evidence profile and based on the criteria intable 25. Relative importance of outcomes—Only important outcomes Study quality
should be included in evidence profiles. The included outcomes Study quality refers to the detailed study methods and execution.
should be classified as critical or important (but not critical) to a Reviewers should use appropriate criteria to assess study quality for each important outcome.26 29–32 For randomised trials, for 6. Overall quality of evidence—The overall quality of evidence example, reviewers might use criteria such as the adequacy of should be judged across outcomes based on the lowest quality of allocation concealment, blinding, and follow up. Reviewers evidence for any of the critical outcomes.
should make explicit their reasons for downgrading a quality rat- 7. Balance of benefits and harms—The balance of benefits andharms should be classified as net benefits, trade-offs, uncertain ing. For example, they may state that failure to blind patients and trade-offs, or no net benefits based on the important health physicians reduced the quality of evidence for an intervention’s impact on pain severity and that they considered this a serious 8. Balance of net benefits and costs—Are incremental health benefits worth the costs? Because resources are always limited, it isimportant to consider costs (resource utilisation) when making a Consistency
Consistency refers to the similarity of estimates of effect across 9. Strength of recommendation—Recommendations should beformulated to reflect their strength—that is, the extent to which studies. If there is important unexplained inconsistency in the one can be confident that adherence will do more good than results, our confidence in the estimate of effect for that outcome decreases. Differences in the direction of effect, the size of thedifferences in effect, and the significance of the differences guide Subsequent steps
10. Implementation and evaluation—For example, using effective
the (inevitably somewhat arbitrary) decision about whether implementation strategies that address barriers to change, important inconsistency exists. Separate estimates of magnitude evaluation of implementation, and keeping up to date of effect for different subgroups should follow when investiga-tors identify a compelling explanation for inconsistency. For BMJ VOLUME 328 19 JUNE 2004
Table 1 Comparison of GRADE and other systems
Other systems
Advantages of GRADE system*
Implicit definitions of quality (level) of evidence and Makes clear what grades indicate and what should Implicit judgments regarding which outcomes are Clarifies each of these judgments and reduces risks important, quality of evidence for each important of introducing errors or bias that can arise when outcome, overall quality of evidence, balance between benefits and harms, and value ofincremental benefits Not considered for each important outcome.
Systematic and explicit consideration of study Ensures these factors are considered appropriately Judgments about quality of evidence are often design, study quality, consistency, and directness of evidence in judgments about quality of evidence Explicit consideration of imprecise or sparse data, reporting bias, strength of association, evidence ofa dose-response gradient, and plausibleconfounding Implicitly based on the quality of evidence for Based on the lowest quality of evidence for any of Reduces likelihood of mislabelling overall quality of the outcomes that are critical to making a decision evidence when evidence for a critical outcome islacking Explicit judgments about which outcomes are Ensures appropriate consideration of each outcome critical, which ones are important but not critical, when grading overall quality of evidence and and which ones are unimportant and can be Explicit consideration of trade-offs between Clarifies and improves transparency of judgments important benefits and harms, the quality of evidence for these, translation of evidence intospecific circumstances, and certainty of baselinerisks Explicit consideration after first considering whether Ensures that judgments about value of net health Consistent GRADE evidence profiles, including Ensures that all panel members base their quality assessment and summary of findings judgments on same information and that thisinformation is available to others Seldom used by more than one organisation and International collaboration across wide range of Builds on previous experience to achieve a system organisations in development and evaluation that is more sensible, reliable, and widely applicable *Most other approaches do not include any of these advantages, although some may incorporate some of these advantages.
instance, differences in the effect of carotid endarterectomy on who have had a myocardial infarction as a surrogate for mortal- high and lower grade stenoses should lead to separate estimates ity,41 changes in lipoproteins as a surrogate for coronary heart disease,37 and bone density in postmenopausal women as a sur-rogate for fracture reduction.42 Directness
The accuracy of a diagnostic test is also a surrogate for Directness refers to the extent to which the people, interventions, important outcomes that might be affected by accurate and outcome measures are similar to those of interest. For exam- diagnosis, including improved health outcomes from appropri- ple, there may be uncertainty about the directness of the ate treatment and reduced harms from false positive results. Dif- evidence if the people of interest are older, sicker, or have more ferent criteria must be used when considering study design for comorbidity than those in the studies.39 To determine whetherimportant uncertainty exists, we can ask whether there is a com- studies of diagnostic accuracy. However, consideration of the pelling reason to expect important differences in the size of the directness of evidence is based on how confident we are of the effect. Because many interventions have more or less the same relation between being classified correctly (as a true positive or relative effects across most patient groups, we should not apply negative) or incorrectly (as a false positive or negative) and overly stringent criteria in deciding whether evidence is direct.
important consequences of this. For example, there is consistent For some therapies—for example, behavioural interventions in evidence from well designed studies that there are fewer false which cultural differences are likely to be important—more strin- negative results with non-contrast helical computed tomography than with intravenous pyelography in the diagnosis of suspected Similarly, reviewers may identify uncertainty about the acute urolithiasis.43 However, there is major uncertainty about directness of evidence for drugs that differ from those in the whether this has important health consequences.44 Because of studies but are within the same class. Similar issues arise for other this, the quality of this evidence could be considered low for types of interventions. For instance, can you generalise results to a less intense counselling intervention than that used in a study, Another type of indirect evidence arises when there are no or to an alternative surgical technique? These judgments can be direct comparisons of interventions and investigators must make difficult,40 and it is important for investigators to explain the comparisons across studies. For example, this would be the case rationale for the conclusions that they draw.
if there were randomised trials that compared selective serotonin On the other hand, studies using surrogate outcomes gener- reuptake inhibitors with placebo and tricyclics with placebo, but ally provide less direct evidence than those using outcomes that no trials that compared selective serotonin reuptake inhibitors are important to people. It is therefore prudent to use much with tricyclics. Indirect comparisons always leave greater more stringent criteria when considering the directness of uncertainty than direct comparisons because of all the other dif- evidence for surrogate outcomes. Examples of indirect evidence ferences between studies that can affect the results.45 based on surrogate outcomes that subsequent trials showed to bemisleading include suppression of cardiac arrhythmia in patients BMJ VOLUME 328 19 JUNE 2004
factors that were not adjusted for in studies comparing mortalityrates of for-profit and not-for-profit hospitals would have Box 2: Criteria for assigning grade of evidence
reduced the observed effect.48 Thus, the evidence that for-profit Type of evidence
hospitals have a higher risk of mortality is more convincing.) These considerations act cumulatively. For example, if randomised trials have both serious limitations and there is uncertainty about the directness of the evidence, the grade of Decrease grade if:
evidence would drop from high to low.
• Serious ( − 1) or very serious ( − 2) limitation to study quality The same rules should be applied to judgments about the quality of evidence for harms and benefits. Important plausible • Some ( − 1) or major ( − 2) uncertainty about directness harms can and should be included in evidence summaries by considering the indirect evidence that makes them plausible. For • High probability of reporting bias ( − 1) example, if there is concern about anxiety in relation to screen-ing for melanoma and no direct evidence is found, it may be Increase grade if:
appropriate to consider evidence from studies of other types of • Strong evidence of association—significant relative risk of > 2 ( < 0.5) based on consistent evidence from two or moreobservational studies, with no plausible confounders (+1)46 Judgments about the quality of evidence for important • Very strong evidence of association—significant relative risk of outcomes across studies can and should be made in the context > 5 ( < 0.2) based on direct evidence with no major threats to of systematic reviews, such as Cochrane reviews. Judgments about the overall quality of evidence, trade-offs, and recommen- • Evidence of a dose response gradient (+1) dations typically require information beyond the results of a • All plausible confounders would have reduced the effect (+1) Overall quality of evidence
Combining the four components
The quality of evidence for each main outcome can be
Other systems have commonly based judgments of the overall determined after considering each of the above elements: study quality of evidence on the quality of evidence for the benefits of design, study quality, consistency, and directness. Our approach interventions. When the risk of an adverse effect is critical for a initially categorises evidence based on study design into judgment, and evidence regarding that risk is weaker than randomised trials and observational studies (cohort studies, evidence of benefit, ignoring uncertainty about the risk of harm case-control studies, interrupted time series analyses, and is problematic. We suggest that the lowest quality of evidence for controlled before and after studies). We then suggest considering any of the outcomes that are critical to making a decision should whether the studies have serious limitations, important provide the basis for rating overall quality of evidence.
inconsistencies in the results, or whether uncertainty about the Outcomes that are important, but not critical, should be directness of the evidence is warranted (box 2). We suggest the included in evidence profiles and should be considered when following definitions in grading the quality of the evidence: making judgments about the balance between health benefits and High = Further research is very unlikely to change our confi-
harms but should not be taken into consideration when grading the overall quality of evidence. Deciding whether an outcome is Moderate = Further research is likely to have an important
critical, important but not critical, or not important is a value judg- impact on our confidence in the estimate of effect and may ment. So far as possible these judgments should take account of Low = Further research is very likely to have an important
impact on our confidence in the estimate of effect and is likely to Box 3: Imprecise or sparse data
Very low = Any estimate of effect is very uncertain.
There is not an empirical basis for defining imprecise or sparse Limitations in study quality, important inconsistency of results, or uncertainty about the directness of the evidence can • Data are sparse if the results include just a few events or lower the grade of evidence. For instance, if all available studies have serious limitations, the grade will drop by one level, and if • Data are imprecise if the confidence intervals are sufficientlywide that an estimate is consistent with either important harms all studies have very serious limitations the grade will drop by two levels. Fatally flawed studies may be excluded.
These different definitions can result in different judgments.
Additional considerations that can lower the quality of Although it may not be possible to reconcile these differences, we evidence include imprecise or sparse data (box 3) and high risk offer the following guidance when considering whether to of reporting bias. Additional considerations that can raise the downgrade the quality of evidence due to imprecise or sparse A very strong association (for example, a 50-fold risk of The threshold for considering data imprecise or sparse should poisoning fatalities with tricyclic antidepressants compared with be lower when there is only one study. A single study with a smallsample size (or few events) yielding wide confidence intervals selective serotonin reuptake inhibitors, see table 2) or strong spanning both the potential for harm and benefit should be association (for example, a threefold increased risk of head inju- ries among cyclists who do not use helmets compared with those • Confidence intervals that are sufficiently wide that, irrespective of other outcomes, the estimate is consistent with conflicting recommendations should be considered as imprecise or sparse Presence of all plausible residual confounding would have reduced the observed effect. (For example, plausible explanatory BMJ VOLUME 328 19 JUNE 2004
the values of those who will be affected by adherence to Net benefits = the intervention clearly does more good than
The decision regarding what is critical can be difficult. The Trade-offs = there are important trade-offs between the ben-
plausibility of adverse outcomes may influence the decision regarding whether they are critical. Weak evidence about Uncertain trade-offs = it is not clear whether the interven-
implausible putative harms should not lower the overall grade of evidence. Decisions about whether a putative harm is plausible No net benefits = the intervention clearly does not do more
may come from indirect evidence. For example, if there is impor- tant concern about serious adverse effects of a drug because of Those making a recommendation should consider four main animal studies, the overall quality of evidence may receive a lower grade based on whatever human evidence is available for The trade-offs, taking into account the estimated size of the that particular adverse effect. Sometimes lack of evidence for effect for the main outcomes, the confidence limits around those plausible putative harms may make it impossible to assess the net estimates, and the relative value placed on each outcome benefit of an intervention. In these circumstances a guideline panel may elect to recommend additional research.
Translation of the evidence into practice in a specific setting, If the evidence for all of the critical outcomes favours the taking into consideration important factors that could be same alternative, and there is high quality evidence for some, but expected to modify the size of the expected effects, such as prox- not all, of those outcomes, the overall quality of evidence might imity to a hospital or availability of necessary expertise still be considered high. For example, there is high quality Uncertainty about baseline risk for the population of interest.
evidence that antiplatelet therapy reduces the risk of non-fatal If there is uncertainty about translating the evidence into stroke and non-fatal myocardial infarction in patients who have practice in a specific setting, or uncertainty about baseline risk, had a myocardial infarction. Although the evidence for all-cause this may lower our confidence in a recommendation. For exam- mortality is of moderate quality, the overall quality of evidence ple, if an intervention has serious adverse effects as well as might still be considered high, even if all cause mortality wasconsidered a critical outcome.
Box 4: Values are not right or wrong
Recommendations
The following example shows how different people might make Does the intervention do more good than harm?
different recommendations because of differences in values, even Recommendations involve a trade-off between benefits and harms. Making that trade-off inevitably involves placing, Question: Should the general population be screened for
implicitly or explicitly, a relative value on each outcome. It is often difficult to judge how much weight to give to different out- Setting: Primary care in the United States
Baseline risk: General population (melanoma incidence in 1995
comes, and different people will often have different values. Peo- ple making judgments on behalf of others are on stronger Reference: Helfand et al. Screening for skin cancer. Systematic
ground if they have evidence of the values of those affected. For instance, people making recommendations about chemotherapy Rockville, MD: Agency for Healthcare Research and Quality.
for women with early breast cancer will be in a stronger position April 2001. (AHRQ Publication No 01-S002.) if they have evidence about the relative importance those women There is very low quality evidence for the accuracy of screeningand for the outcome of lethal melanoma. Potential harms from place on reducing the risk of a recurrence of breast cancer rela- screening include the consequences of false positive tests, but tive to avoiding the side effects of chemotherapy.
evidence regarding these is lacking. Based on this it is possible to We suggest making explicit judgments about the balance conclude that the overall quality of evidence is very low and that between the main health benefits and harms before considering there are uncertain net benefits from screening. Based on a costs. Does the intervention do more good than harm? Recom- single case-control study, the odds ratio for lethal melanoma was mendations must apply to specific settings and particular groups estimated to be 0.37 for screened versus not screened people.
of patients whenever the benefits and harms differ across settings The lifetime risk of dying of melanoma was estimated to be0.36% for white men.
or patient groups. For instance, consider whether we should rec- Based on this evidence, many people might make a ommend that patients with atrial fibrillation receive warfarin to recommendation of “don’t screen” because of placing a high reduce their risk of stroke, despite the increase in bleeding risk value on avoiding the potential but unknown harms of screening that will result. Recommendations, or their strength, are likely to healthy people relative to the uncertain benefits. However, some differ in settings where regular monitoring of the intensity of people might recommend “probably screen” because of placing a anticoagulation is available and settings where it is not. Further- high value on the small but potentially important benefits ofscreening relative to the unknown potential harms. Under these more, recommendations (or their strength) are likely to differ in circumstances, after taking into consideration costs, a panel patients at very low risk of stroke (those under 65 without any developing guidelines might elect not to make a comorbidity) and patients at higher risk (such as older patients recommendation for clinical practice and to make a specific with heart failure) because of differences in the absolute recommendation regarding the research that is needed to reduce reduction in risk. Recommendations must therefore be specific uncertainty and clarify the trade-offs.
to a patient group, and a practice setting. It is particularly impor- This example is typical of the value judgments that underlierecommendations about screening, but the same issues arise in tant to consider the circumstances of disadvantaged populations making recommendations about treatment for both acute and when making recommendations and, when appropriate, modify chronic conditions, where it is always necessary to balance the recommendations to take into consideration differences expected benefits against the expected harms in light of the between advantaged and disadvantaged populations.
relative values attached to each important outcome, and We suggest using the following definitions to categorise the BMJ VOLUME 328 19 JUNE 2004
Table 2 Quality assessment of trials comparing selective serotonin reuptake inhibitors (SSRIs) with tricyclic antidepressants for treatment of moderate
depression in primary care2
Quality assessment
Summary of findings
No of patients
modifying
Relative
No of studies
Consistency
Directness
factors*
Tricyclics
Absolute
Importance
Depression severity (measured with Hamilton Depression Rating Scale after 4 to 12 weeks)
Transient side effects resulting in discontinuation of treatment
Poisoning fatalities§
WMD = weighted mean difference, RRR = relative risk reduction.
*Imprecise or sparse data, a strong or very strong association, high risk of reporting bias, evidence of a dose-response gradient, effect of plausible residual confounding.
†There was uncertainty about the directness of the outcome measure because of the short duration of the trials.
‡It is possible that people at lower risk were more likely to have been given SSRIs and it is uncertain if changing antidepressant would have deterred suicide attempts.
§There is uncertainty about the baseline risk for poisoning fatalities.
important benefits, a recommendation is likely to be much less monetary value of resources used—are important considerations certain when the baseline risk of the population of interest is in making recommendations, but they are context specific, change over time, and their magnitude may be difficult to We suggest using the following categories for recommenda- estimate. While recognising the difficulty of making accurate estimates of costs, we suggest that the incremental costs of “Do it” or “don’t do it”indicating a judgment that most well
healthcare alternatives should be considered explicitly alongside the expected health benefits and harms. When relevant and “Probably do it” or “probably don’t do it”indicating a judgment
available, disaggregated costs (differences in use of resources) that a majority of well informed people would make but a should be presented in evidence profiles along with important outcomes. The quality of the evidence for differences in use of A recommendation to use or withhold an intervention does resources should be graded by using the criteria outlined above not mean that all patients should be treated identically. Nor does it mean that clinicians should not involve patients in the decision,or explain the merits of the alternatives. However, because mostwell informed patients will make the same choice, theexplanation of the relative merits of the alternatives may be rela- How it works in practice
tively brief. A recommendation is intended to facilitate an Table 2 shows an example of the system applied to evidence appropriate decision for an individual patient or a population. It from a systematic review comparing selective serotonin reuptake should therefore reflect what people would likely choose, based inhibitors with tricyclic antidepressants conducted in 1997.49 on the evidence and their own values or preferences in relation After discussion we agreed that there was moderate quality to the expected outcomes. A recommendation to “probably do evidence for the relative effects of selective serotonin reuptake something” indicates a need for clinicians to more fully and care- inhibitors and tricyclic antidepressants on depression severity fully consider patients’ values and preferences when offering and poisoning fatalities and high quality evidence for transient side effects. We then reached agreement that the overall quality In some instances it may not be appropriate to make a recom- of evidence was moderate and that there were net benefits in mendation because of unclear trade-offs or lack of agreement (as favour of selective serotonin reuptake inhibitors (no difference in illustrated in box 4). When this is due to a lack of good quality evi- depression severity, fewer transient side effects, and fewer dence, specific research should be recommended that would pro- poisoning fatalities). Despite agreement that there seemed to be vide the evidence that is needed to inform a recommendation.
net benefits we concluded with a recommendation to “probably” Are the incremental health benefits worth the costs?
use selective serotonin reuptake inhibitors, reflecting uncertainty Because spending money on one intervention means less money because of the quality of the evidence. We did not have evidence to spend on another, recommendations rely, implicitly if not of the costs of using selective serotonin reuptake inhibitors com- explicitly, on judgments about the value of the incremental pared with tricyclics for this exercise. Had we considered costs health benefits in relation to the incremental costs. Costs—the this recommendation might have changed.
BMJ VOLUME 328 19 JUNE 2004
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44 Worster A, Haines T. Does replacing intravenous pyelography with noncontrast helical Correspondence to: Andrew D Oxman, Informed Choice Research Department, computed tomography benefit patients with suspected acute urolithiasis? Can Assoc Norwegian Health Services Research Centre, PO Box 7004, St Olavs Plass, 0130 BMJ VOLUME 328 19 JUNE 2004

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be less than 47 dB for coherent channel cable systems,when measured with modulated carriers and time Measuring averaged.” In other words, the visual carrier must be at least 51dB above any interfering signals, except (there isalways an “except”) in a system with harmonically cable system related carriers (HRC). In an HRC system, the visual carrier must be at least 47 dB abo

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The Graph of a Rational Function List of things to do to analyze the graph of a rational function f (x) = Find the domain there are places where denominator = 0 are prohibited, otherwise domain is R . Locate any intercepts solve p(x) = 0. The x intercepts are points of the form (r,0) where r is a root of p(x) but not a root of q(x). Vertical asymptotes reduce f(x) to l

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