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Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis, Testing Thresholds Revisited 26 October 2006 Michael.

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Presentation on theme: "Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis, Testing Thresholds Revisited 26 October 2006 Michael."— Presentation transcript:

1 Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis, Testing Thresholds Revisited 26 October 2006 Michael A. Kohn, MD, MPP Using Randomized Trials to Quantify Treatment Effects

2 Quantifying the Benefit of a Treatment: Take Home Points RCT Checklist: Importance of patient-oriented effect measures (POEMs), randomization, intention-to-treat analysis, good follow-up, blinding, and between-groups comparisons. The Relative Risk or Relative Risk Reduction associated with an intervention is of minimal use* without a baseline prevalence of bad outcomes. You need to have an absolute risk reduction to calculate number needed to treat. (NNT = 1/ARR) For undesired effects of treatment, calculate the absolute risk increase (ARI), and the number needed to harm (NNH = 1/ARI) Back-of-the-envelope CEA: Cost per bad outcome prevented = Treatment Cost x NNT *Unless the RR is 1 and RRR is 0.

3 RCT Checklist

4 Patient-Oriented Effect Measures (POEMs) vs. surrogate outcomes Randomization to address issues of confounding Intention-to-treat analysis (once randomized always analyzed) Good follow-up to eliminate differential losses to follow- up Blinding of patients and clinicians to prevent differential co-interventions Blinding of outcome assessors to prevent bias Between groups rather than within groups comparison Compare entire randomization groups, not subgroups *For checklist on study validity, see Chapter 1B1 “Therapy”, in Guyatt and Rennie (eds.), Users Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice; AMA Press; (Or try )http://www.cche.net/usersguides/therapy.asp#Valid RCT Checklist for Study Validity*

5 RCTs of Orthopedic Treatments 1.Kirkley A, Griffin S, Richards C, Miniaci A, Mohtadi N. Prospective randomized clinical trial comparing the effectiveness of immediate arthroscopic stabilization versus immobilization and rehabilitation in first traumatic anterior dislocations of the shoulder. Arthroscopy. Jul-Aug 1999;15(5): Parker MJ, Khan RJ, Crawford J, Pryor GA. Hemiarthroplasty versus internal fixation for displaced intracapsular hip fractures in the elderly. A randomised trial of 455 patients. J Bone Joint Surg Br. Nov 2002;84(8):

6 Endpoints: Arthroscopy vs. immobilization for 1 st shoulder dislocation Kirkley A, Griffin S, Richards C, Miniaci A, Mohtadi N. Prospective randomized clinical trial comparing the effectiveness of immediate arthroscopic stabilization versus immobilization and rehabilitation in first traumatic anterior dislocations of the shoulder. Arthroscopy. Jul-Aug 1999;15(5):

7 Outcomes Affected by Treatments* Dichotomous (e.g. recurrent dislocation) Continuous (e.g. WOSI**) Endpoints Patient relevant (e.g., ability to return to sports) Surrogate (e.g., MRI findings) * Example: Arthroscopy vs. conservative tx for 1 st Anterior Shoulder Dislocation (Arthroscopy Jul-Aug;15(5): ) **Western Ontario Shoulder Disability Index

8 Outcomes Affected by Treatments Dichotomous (e.g. recurrent dislocation) Continuous (e.g. WOSI) Endpoints Patient relevant (e.g., ability to return to sports) Surrogate (e.g., MRI findings)

9 Randomization, Intention-to-Treat Analysis, and Follow-up: Arthroplasty vs. Internal Fixation? Pt is a 81-year-old woman with a displaced, intracapsular femoral neck fracture. Pt’s son is a physician. He asks about hemiarthroplasty vs. internal fixation. Pubmed search  Parker MJ, Khan RJ, Crawford J, Pryor GA. Hemiarthroplasty versus internal fixation for displaced intracapsular hip fractures in the elderly. A randomised trial of 455 patients. J Bone Joint Surg Br. Nov 2002;84(8):

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13 Randomization, Intention-to-Treat Analysis, and Follow-up: Parker MH et al. Bone Joint Surg Br. 84(8): Randomized controlled trial of the effects of hemiarthroplasty vs. internal fixation on re- operation and other outcomes in > 70- year-old patients with displaced, intracapsular femoral neck fractures.

14 Randomization: Parker MH et al. Bone Joint Surg Br. 84(8): Why do a randomized experiment? Why not do an observational study comparing mortality, re-operation rates, etc. between hemiarthroplasty patients and internal fixation patients?

15 Intention-to-Treat: Parker MH et al. Bone Joint Surg Br. 84(8): Some patients randomized to the hemiarthroplasty group ended up getting internal fixation. Why not include these patients’ outcomes in the internal fixation group or at least exclude them from the hemiarthroplasty group?

16 Losses to Follow-Up: Parker MH et al. Bone Joint Surg Br. 84(8): * If each treatment group had 20% loss to follow-up, there could still be bias. What if those in the internal fixation group were lost to follow-up because they got better and those in the hemi-arthroplasty group were lost because they died? *In fact, there were no losses to follow-up in this study.

17 Blinding Blinding of Patients Addresses placebo effect Blinding of Patients and Clinicians Eliminates differential co-interventions Blinding of Outcome Assessment Eliminates biased outcome assessment

18 Blinding Blinding less important when opportunity for cointerventions that affect outcomes is minimal, and outcome is not subjective. Arthroplasty vs Internal Fixation for hip fracture, with endpoints of mortality and re-operation: patients, clinicians, and outcome assessors not blinded. Arthroscopy vs. non-operative management of shoulder dislocation, with endpoints of re-dislocation, and WOSI*: patients not blinded, but clinicians and outcome assessors (therapists) were blinded. *Western Ontario Shoulder Disability Index ** Moseley JB, et al. A controlled trial of arthroscopic surgery for osteoarthritis of the knee. N Engl J Med 2002;347(2):81-88.

19 Between-groups Comparison Nissen SE, Tsunoda T, Tuzcu EM, Schoenhagen P, Cooper CJ, Yasin M, et al. Effect of recombinant ApoA-I Milano on coronary atherosclerosis in patients with acute coronary syndromes: a randomized controlled trial. Jama 2003;290(17):

20 Sub-group Analysis: ISIS II* 30-day mortality *Lancet 1988;2(8607): OverallGeminis and Libras Other signs Aspirin9.4%11.1%9.0% Placebo11.8%10.2%12.1%

21 Patient-Oriented Effect Measures (POEMs) vs. surrogate outcomes Randomization to address issues of confounding Intention-to-treat analysis (once randomized always analyzed) Good follow-up to eliminate differential losses to follow- up Blinding of patients and clinicians to prevent differential co-interventions Blinding of outcome assessors to prevent bias Between groups rather than within groups comparison Compare entire randomization groups, not subgroups *For checklist on study validity, see Chapter 1B1 “Therapy”, in Guyatt and Rennie (eds.), Users Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice; AMA Press; (Or try )http://www.cche.net/usersguides/therapy.asp#Valid DONE: RCT Checklist for Study Validity*

22 Effect Size (Dichotomous Outcomes) RR RRR ARR NNT ARI NNH

23 This study was properly randomized but not blinded, used an intention-to-treat analysis, and had NO losses to follow-up. Results follow… Parker MH et al. Bone Joint Surg Br. 84(8):

24 Reduced Re-operation Re-operationNo Re-operationRisk Hemiarthroplasty /229 =5.2% Internal Fixation /226 =39.8% Relative Risk (RR):5.2%/39.8% =0.13 Relative Risk Reduction (RRR):1 - RR =0.87 Absolute Risk Reduction (ARR):39.8% - 5.2% =34.6% Number Needed to Treat (NNT)1/ARR =3 (Need to treat 3 patients with hemirarthoplasty instead of internal fixation to prevent one patient requiring re-operation.)

25 Measures of Treatment Effect RR= Relative Risk or Risk Ratio = RR 1 means tx is associated with increased risk, as is usually the case for a side effect. RRR = Relative Risk Reduction = 1-RR Bad Outcome No Bad Outcome Totals Treatmentaba + b Controlcdc + d Totalsa + cb + dN = a + b + c + d

26 Beware of the Odds Ratio RR= Relative Risk or Risk Ratio = (a/b) (a/c) OR = Odds Ratio = = = ad/bc (c/d) (b/d) Bad Outcome No Bad Outcome Totals Treatmentaba + b Controlcdc + d Totalsa + cb + dN = a + b + c + d

27 Measures of Treatment Effect ARR = Absolute Risk Reduction = c/(c+d) - a/(a+b) NNT = Number Needed to Treat (to prevent 1 bad outcome) = 1/ARR Bad Outcome No Bad Outcome Totals Treatmentaba + b Controlcdc + d Totalsa + cb + dN = a + b + c + d

28 NNT Practice In patients < 30 years old with first-time acute anterior shoulder dislocation, prompt arthroscopic surgery (vs. standard conservative therapy) reduces the 2-year re-dislocation rate by almost 33% in absolute terms (from about 50% to about 17%).* How many first-time dislocation patients do we need to treat with arthroscopy to prevent one having re-dislocation at 2 years? *Kirkley A, et al. Arthroscopy. Jul-Aug 1999;15(5): Numbers rounded for purposes of exposition.

29 The relative risk (RR) or relative risk reduction (RRR = 1-RR) associated with a treatment is of minimal use without knowing the baseline level of risk*. Problem with the Relative Risk *The RR is not completely useless without the baseline risk. If RR=1, the tx is useless regardless of the baseline risk. If RR > 1, the treatment is harmful. Also, if you already know the baseline risk in your own population, the RR may be all you need.

30 The selective estrogen receptor modulator raloxifene (Evista®) at a dose of 60 mg /d for 3 years reduces vertebral fracture risk by 33% in women with osteoporosis.* How many women with osteoporosis do we need to treat with raloxifene to prevent a vertebral fracture? Problem with the Relative Risk *JAMA Aug 18;282(7): Numbers rounded for exposition.

31 The selective estrogen receptor modulator raloxifene (Evista®) at a dose of 60 mg /d for 3 years reduces vertebral fracture risk by 33% in women with osteoporosis. Baseline 3-year risk of vertebral fracture = 10% How many women with osteoporosis do we need to treat with raloxifene to prevent a vertebral fracture? Problem with the Relative Risk Need Baseline Risk

32 Baseline 3-year risk of vertebral fracture = 10% RRR = 0.33 ARR = 0.1 x 0.33 =.033 NNT = 1/0.033 = 30 Need to treat 30 osteoporotic women with raloxifene for 3 years to prevent a vertebral fracture. Problem with the Relative Risk Need Baseline Risk

33 Effect of Flu Vaccination on All-Cause Mortality During the Flu Season The study population included almost 300,000 subjects at least 65 years old, of whom about 58% were vaccinated. Among vaccinated and unvaccinated subjects, 1.2% and 2.0% respectively died during the flu season. Nichol et al. N Engl J Med. Apr ;348(14): This was NOT an RCT, lots of confounding to address, but it’s related to the flu. Pooled computerized data from 3 large managed care organizations.

34 No Flu Shot? How about Tamiflu?

35 Mechanism of Action of Neuraminidase Inhibitors Moscona A. Neuraminidase inhibitors for influenza. N Engl J Med 2005;353(13):

36 Flu Prophylaxis? Pt is a 14-year-old girl with fever, myalgias, cough and sore throat X 1 day Should you rx prophylactic Tamiflu® for the pt’s grandparents (in their 70s) who live in the same household and didn’t get the flu shot this year? Pubmed search  Welliver R et al. Effectiveness of Oseltamivir in Preventing Influenza in Household Contacts: A Randomized Controlled Trial. JAMA 2001; 285:

37 Prophylactic Oseltamivir: Index Case Flu+* Household Contacts FluNo FluRisk Oseltamivir /209 =1.4% Placebo /206 =12.6% Relative Risk (RR):1.4%/12.6% =0.11 Relative Risk Reduction (RRR):1 - RR =0.89 Absolute Risk Reduction (ARR):12.6% - 1.4% =11.2% Number Needed to Treat (NNT)???? *Welliver R et al. Effectiveness of Oseltamivir in Preventing Influenza in Household Contacts: A Randomized Controlled Trial. JAMA 2001; 285:

38 Prophylactic Oseltamivir: Index Case Flu+* Household Contacts FluNo FluRisk Oseltamivir /209 =1.4% Placebo /206 =12.6% Relative Risk (RR):1.4%/12.6% =0.11 Relative Risk Reduction (RRR):1 - RR =0.89 Absolute Risk Reduction (ARR):12.6% - 1.4% =11.2% Number Needed to Treat (NNT)1/ARR =9 *Welliver R et al. Effectiveness of Oseltamivir in Preventing Influenza in Household Contacts: A Randomized Controlled Trial. JAMA 2001; 285:

39 Number Needed To Harm NauseaNo NauseaRisk Oseltamivir /494 =5.5% Placebo /461 =2.6% Relative Risk (RR):5.5%/2.6% =2.1 Absolute Risk Increase (ARI):5.5% - 2.6% =2.9% Number Needed to Harm (NNH):1/ARI =35 NNH is really number needed to treat to cause one undesired effect.

40 Number Needed to Harm Not an apt term for number needed to treat to cause one bad outcome. Would prefer NNTc (“Number Needed to Treat to cause”) vs. NNTp (“Number Needed to Treat to prevent”), but NNH is well established.

41 Ratio of Undesired to Desired Effects “Harms” / Bad Outcome Prevented = ARI/ARR = NNT/NNH Or Bad Outcomes Prevented / Harm Caused = ARR/ARI = NNH/NNT

42 Number Needed to Harm TransfusionNo Transfusion Hemiarthroplasty /223 =19.7% Internal Fixation /223 =1.8% Relative Risk (RR):19.7%/1.8% =11.00 Absolute Risk Increase (ARI):19.7% - 1.8% =17.9% Number Needed to Harm (NNH)????

43 Number Needed to Harm TransfusionNo Transfusion Hemiarthroplasty /223 =19.7% Internal Fixation /223 =1.8% Relative Risk (RR):19.7%/1.8% =11.00 Absolute Risk Increase (ARI):19.7% - 1.8% =17.9% Number Needed to Harm (NNH)1/ARI =6 (Need to treat 6 patients with hemirarthoplasty instead of internal fixation to cause one patient requiring transfusion.)

44 Ratio of Desired to Undesired Effects Bad Outcomes Prevented / Harm Caused = ARR/ARI = NNH/NNT* Arthroplasty vs. Internal Fixation for Hip Fx Risk Difference for re-operation: ∆ Risk Re-Op = 5.2% % = -34.6% Risk Difference for transfusion: ∆ Risk Trx = 19.7% - 1.8% = +17.9% Re-operations prevented/Transfusion Caused: -34.6/17.9 = ≈ -2 *Easier here to divide ∆ re-operation by ∆ transfusion, rather than use NNH or NNT.

45 Ratio of Undesired to Desired Effects Cases of Nausea / Flu Case Prevented = 2.9%/ 11% = 0.25 Or Flu Cases Prevented / Nausea Caused = 11%/2.9% = 4

46 BOTE CEA Back-of-the-Envelope Cost Effectiveness Analysis

47 How many patients do I need to treat (at the treatment cost) to prevent 1 bad outcome? Number Needed to Treat (NNT) = 1/ARR Cost of preventing one bad outcome = NNT x Treatment Cost* *This is just ∆$Cost /∆Risk.

48 BOTE CEA: Oseltamivir Index Case Flu + NNT = 9 (Treat 9 household contacts, prevent 1 flu case) NNT x Treatment Cost* = 9 x $35 = $315/flu case prevented Cost of Tamiflu 75 mg #10 = $ /4/2004www.drugstore.com $ /25/06

49 BOTE CEA Example Raloxifene vs. placebo in women with osteoporosis

50 Raloxifene vs. Placebo Raloxifene (Evista®) 60 mg/d x 30 d = $87* 36 months of treatment = 36 x $87 = $3132 Need to treat 30 patients to prevent 1 fx 30 x $3132 ≈ $93,960 per vertebral fx prevented. *Drugstore.com 10/25/06

51 BOTE CEA Example Letrozole (Femara®) to prevent breast cancer recurrence after 5 years of tamoxifen therapy.

52 Drug cuts risk of breast-cancer relapse Findings so promising, study halted so scientists could release news By Sabin Russell Chronicle Medical Writer Front Page, San Francisco Chronicle 10/10/03 RCT of Letrozole (Femara®), after tamoxifen, to prevent breast cancer recurrence

53 RRR or ARR? “The trial was interrupted almost 2½ years after it began. Researchers had scheduled a midpoint peak at the data, and found letrozole was apparently working far better than expected. The women who took it had 43 percent fewer recurrences of their breast cancer compared to those assigned in the study to take a placebo, or dummy pill.”

54 Femara Trial Results RecurrenceNo Recurrence Letrozole Placebo Risk(Letrozole) = 61/2575 = 2.9% Risk(Placebo) = 106/2582 = 5.1% RR = 2.9/5.1 = 0.57 RRR = = 0.43 N Engl J Med Nov 6;349(19):

55 Femara Trial Results ARR = 5.1% - 2.9% = 2.2% NNT = 1/2.2 = 45 Treatment Cost = $252/month* x 12 months/year x 2.4 years = $7260 Femara Cost per Recurrence Prevented = $7260 x 45 = $327,000 *2.5mg tablets are available from the International Pharmacy for $252/30 day supply (30 tablets) (Price on 10/25/06 = $240/30 pills.)www.drugstore.com

56 BOTE CEA Examples Oseltamivir to prevent flu in household contacts of flu+ individuals: $315 per case of flu prevented Raloxifene to prevent vertebral fracture: $93,960/fracture prevented at 3 years. Letrozole after tamoxifen to prevent recurrent breast cancer: $327,000/recurrence prevented at 2.4 years

57 BOTE vs. “Real” CEA Estimates treatment costs per bad outcome prevented – including the bad outcome’s costs Treatment Costs Bad Outcome + Bad Outcome’s Costs “Real” Cost Effectiveness Analysis: Treatment Costs – Bad Outcome’s Costs Bad Outcome

58 BOTE vs. “Real” CEA Back of the envelope: Treatment Costs Bad Outcome + Bad Outcome’s Costs “Real”: Treatment Costs – Bad Outcome’s Costs Bad Outcome Note that “real” analysis LOWERS the cost per bad outcome prevented and makes treatment look better.

59 Quantifying the Benefit* of a Treatment: Take Home Points The Relative Risk or Relative Risk Reduction associated with an intervention is of minimal use without a baseline prevalence of bad outcomes. You need to have an absolute risk reduction to calculate number needed to treat. (NNT = 1/ARR) For undesired effects of treatment, calculate the absolute risk increase (ARI), and the number needed to harm (NNH = 1/ARI) Back-of-the-envelope CEA: Cost per bad outcome prevented = Treatment Cost x NNT *With regard to dichotomous outcomes

60 Flu Treatment? Pt is a 14-year-old girl with fever, myalgias, cough and sore throat X 1 day Should you prescribe Tamiflu for the patient herself? Pubmed search  Treanor JJ, et al. Efficacy and safety of the oral neuraminidase inhibitor oseltamivir in treating acute influenza: a randomized controlled trial. US Oral Neuraminidase Study Group. Jama 2000;283(8):

61 Continuous Outcomes Flu + Median Illness Duration Oseltamivir 70 hours Placebo100 hours Difference-30 hours Treatment Cost = $60 (75 mg bid x 5 days) $60/30 hours = $2 in drug cost per hour of symptoms x 24 hours/day ≈ $50/day of symptoms Treanor JJ, et al. Jama 2000;283(8):

62 Flu Prophylaxis? Pt is a 14-year-old girl with fever, myalgias, cough and sore throat X 1 day Should you rx prophylactic Tamiflu® for the pt’s grandparents (in their 70s) who live in the same household and didn’t get the flu shot this year? What if the 14-year-old doesn’t have the flu? The relative risk reduction is the same (89%), but the baseline risk for the grandparents is so low that prophylactic oseltamivir doesn’t do much. (ARR is negligible, NNT is enormous.)

63 Prophylactic oseltamivir works if the index case has the flu, but you don’t know whether she does. You know that 45% of similar patients have laboratory proven influenza. Probability of Flu + = 45%

64 NNT is calculated for patients with a particular condition “D”. P = probability of that condition “D” in your patients Your NNT* = NNT / P Note that NNT* goes up as P = probability of condition “D” goes down. Patient May Not Have The Condition That You’re Treating *Assumes that treatment for patients without condition D has no value. (For D- patients, ARR = 0, NNT = ∞)

65 NNT if index case flu + = 9. Probability of flu = 0.45 NNT* = 9 / 0.45 = 20 Probability of Flu + = 45% *Assumes that treatment when index case is flu - has no value (ARR = 0, NNT = ∞)

66 No Adjustment of NNH for Disease Prevalence Oseltamivir is no less likely to cause nausea in household contacts of Flu- patients than in those of Flu+ patients. Prevalence of Flu+ = P = 45% ARI for nausea is still: 5.5% - 2.6% = 2.9% But, ARR is now: 0.45(12.6 %-1.4%) = 5% Cases Flu Prevented for each case of nausea caused: 5%/2.6% ≈ 2

67 BOTE CEA: Oseltamivir Index Case Flu + NNT = 9 (Treat 9 household contacts, prevent 1 flu case) NNT x Treatment Cost* = 9 x $35 = $315/flu case prevented 45% Prob Flu+ NNT* = 9/0.45 = 20 NNT* x Treatment Cost = 20 x $35 = $700/flu case prevented * Cost of Tamiflu 75 mg #10 = $ /4/2004www.drugstore.com

68 Treatment Threshold Probability from Threshold Cost Effectiveness Ratio Assume it is worth $840 in oseltamivir to prevent one case of the flu. We can calculate the treatment threshold probability P TT : NNT* x $35 = $840 NNT/ P TT = $840/$35 = 24 NNT/24 = P TT 9/24 = = P TT

69 Treatment Threshold Probability from B and C B = 1/9 x $840 - $35 = $58.33 C = $35 B/C = 0.6 = Threshold Odds B/(B+C) = = Threshold Prob = P TT

70 When does it make sense to test the index patient? QuickVue Rapid Bedside Antigen Test* Sensitivity = 75% Specificity = 95% *Poehling KA, et al. Bedside diagnosis of influenzavirus infections in hospitalized children. Pediatrics 2002;110:83-8.

71 Review: Testing Thresholds for an Imperfect but Costless Test (Chapter 3) Probability of Disease  Treat none; no test Treat based on test resultsTreat all; no test No Treat-Test Threshold Test-Treat Threshold Treatment Threshold

72 Review: Calculate Testing Thresholds Treatment Threshold = P TT = Treatment Threshold Odds = 0.375/0.625 = 0.6 LR(+) = {Sens/(1-Spec)} = 0.75/(1-0.95) = 0.75/0.05 = 15 LR(-) = {(1-Sens)/Spec} = (1-0.75)/0.95 = 0.25/0.95 = 0.26 No Treat-Test Threshold Odds = 0.6/15 = 0.04 No Treat-Test Threshold Probability = 0.04/(1+0.04) = 0.04 Test-Treat Threshold Odds = 0.6/0.26 = 2.28 Test-Treat Threshold Probability = 2.28/(1+2.28) = 0.70

73 Testing Thresholds LR+ (15) LR- (.26) | >|< | | | |---| | | | | | | | | | | | |.5 | PROBABILITY

74 Interpret the Results If the prior probability of influenza is <4 % (the lower testing threshold), then even if the rapid antigen test is positive, the post-test probability will still be below 37.5% (the treatment threshold), and you would not treat the patient’s household contacts. If the prior probability is >70% (the higher testing threshold), then even if the antigen test is negative, the post-test probability will be above 37.5%, and you would treat the household contacts anyway.

75 Interpret the Results Between 4% and 70%, the test MAY be indicated, because it has at least the potential of affecting management. Note that so far, we have not considered costs or risks of the test (as opposed to those of the treatment)-- when these are factored in as well, the testing range will be narrower.


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