Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis,...

Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis, Treatment

Thresholds Revisited

6 November 2008

Michael A. Kohn, MD, MPP

Using Randomized Trials to Quantify Treatment Effects

EBM is about using research studies to help in two related areas:

Diagnosis: Evaluate a test and then use it to determine whether a patient has a given disease. (Chs. 2, 3, 4, 5, 8)

Treatment: Determine if a treatment is beneficial in patients with a given disease, and if so, whether the benefits outweigh the costs and risks. (Chs. 9, 10)

In screening programs (Ch. 6), diagnosis and treatment are the most closely intertwined. Prognostic testing (Ch. 7) requires longitudinal studies and evaluation of calibration as well as discrimination.

Quantifying the Benefit of a Treatment: Take Home Points

• RCT Checklist

• Need baseline incidence of bad outcome*.

• Number Needed to Treat =NNT= 1/ARR

• Number Needed to (treat to) Harm = NNH = 1/ARI

• Back-of-the-envelope CEA: Treatment cost per bad outcome prevented = Treatment Cost x NNT

*Unless the RR is 1 and RRR is 0.

RCT Checklist

Design and conduct• Randomization to address issues of confounding • Blinding of patients and clinicians to prevent differential

co-interventions• Blinding of outcome assessors to prevent bias• Patient-Oriented Effect Measures (POEMs) vs. surrogate

outcomes• Decompose composite outcomes• Good follow-up to eliminate differential losses to follow-

up

*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; 2002. (Or try http://www.cche.net/usersguides/therapy.asp#Valid )

RCT Checklist for Study Validity*

http://www.cche.net/usersguides/therapy.asp#Valid

Analysis

• Intention-to-treat analysis (once randomized always analyzed)

• Compare entire randomization groups, not subgroups

• Between groups rather than within groups comparison


RCT Checklist for Study Validity*


Randomization, Intention-to-Treat Analysis, and Follow-up: Hip Replacement vs. Screws

• Pt is a 81-year-old woman with a hip fracture• Pt’s son is a physician. He asks about hip

replacement vs. screws.

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):1150-1155.

Displaced Femoral Neck Fracture = Hip Fracture

Internal Fixation = Screws

Hemiarthroplasty = Hip Replacement

Randomization, Intention-to-Treat Analysis, and Follow-up: Parker MH et al. Bone Joint

Surg Br. 84(8):1150-1155.

Randomized controlled trial of the effects of hip replacement vs. screws on re-operation and other outcomes in > 70-year-old patients with displaced, hip fractures.

Randomization: Parker MH et al. Bone Joint Surg Br. 84(8):1150-1155.

Why do a randomized experiment?

Why not do an observational study comparing mortality, re-operation rates, etc. between patients who had hip replacements and patients who had screws?

Intention-to-Treat: Parker MH et al. Bone Joint Surg Br. 84(8):1150-1155.

Some patients randomized to the hip replacement group ended up getting screws.

Why not include these patients’ outcomes in the screws group or at least exclude them from the hip replacement group?

Losses to Follow-Up: Parker MH et al. Bone Joint Surg Br. 84(8):1150-1155.*

If each treatment group had 20% loss to follow-up, there could still be bias.

What if those in the screws group were lost to follow-up because they got better and those in the hip replacement group were lost because they died?

*In fact, there were no losses to follow-up in this study.

Patient Oriented Endpoints, Blinding

• Pt is a 34-year-old man who dislocated his shoulder while surfing at Ocean Beach.

• He asks about early arthroscopic stabilization versus immobilization and PT.

Pubmed search 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):507-514

Endpoints, Blinding: Arthroscopy vs. immobilization for 1st 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):507-514.

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 1st Anterior Shoulder Dislocation (Arthroscopy. 1999 Jul-Aug;15(5):507-14. )**Western Ontario Shoulder Disability Index

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)

Blinding

• Blinding of Patients and Clinicians– Eliminates differential co-interventions

• Blinding of Outcome Assessment– Eliminates biased outcome assessment

Blinding

Blinding less important when opportunity for cointerventions that affect outcomes is minimal, and outcome is not subjective.

• Hip Replacement vs Screws 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.

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):2292-2300.

Sub-group Analysis: ISIS II*

30-day mortality

*Lancet 1988;2(8607):349-360.

Overall Geminis and Libras

Other signs

Aspirin 9.4% 11.1% 9.0%

Placebo 11.8% 10.2% 12.1%

Sub-group Analysis: ISIS II*

30-day mortality

*Lancet 1988;2(8607):349-360.

Aspirin Placebo

Died Total % Died Total %

Gemini/Libra 150 1359 11.0% 147 1442 10.2%

All other signs 654 7228 9.0% 868 7157 12.1%

Composite Endpoints

Major Cardiac Event

Yes No

Bypass Graft

Irradiation 19 41 60 32%

Placebo 38 22 60 63%

Irradiation to prevent re-blockage after cleaning out a blocked coronary artery bypass graft.

“At 12 months, … the rate of major cardiac events was 49 percent lower (32 percent vs. 63 percent, P<0.001). “

Waksman, R., A. E. Ajani, et al. (2002). "Intravascular gamma radiation for in-stent restenosis in saphenous-vein bypass grafts." N Engl J Med 346(16): 1194-9.

Composite Endpoints

“Major Cardiac Event” =

Death or MI or Revascularization Procedure

Irradiation Group: 19 “Events”

4 deaths, 1 MI, 17 Revasc Proc

Placebo Group: 38 “Events”


Composite Endpoints

Could have been:

Irradiation Group: 19 “Events”


Placebo Group: 38 “Events”



DONE: RCT Checklist for Study Validity*• Randomization to address issues of confounding • Blinding of patients and clinicians to prevent differential

co-interventions• Blinding of outcome assessors to prevent bias• Patient-Oriented Effect Measures (POEMs) vs.

surrogate outcomes• Take care with composite outcomes• Good follow-up to eliminate differential losses to follow-

up• Intention-to-treat analysis (once randomized always

analyzed)• Between groups rather than within groups comparison• Compare entire randomization groups, not subgroups


RCTs1. 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):1150-1155.

2. 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):507-514

3. ISIS-2 (1988). "Randomised trial of intravenous streptokinase, oral aspirin, both, or neither among 17,187 cases of suspected acute myocardial infarction: ISIS-2. ISIS-2 (Second International Study of Infarct Survival) Collaborative Group." Lancet 2(8607): 349-60.

4. Waksman, R., A. E. Ajani, et al. (2002). "Intravascular gamma radiation for in-stent restenosis in saphenous-vein bypass grafts." N Engl J Med 346(16): 1194-9.

Effect Size(Dichotomous Outcomes*)

RR

RRR

ARR

NNT

ARI

NNH

* Not going to discuss continuous outcomes today

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):1150-1155.

Reduced Re-operation

Re-operation No Re-operation Risk

Hip Replacement 12 217 229 12/229 = 5.2%

Internal Fixation with Screws 90 136 226 90/226 = 39.8%

Risk Ratio (RR): 5.2%/39.8% = 0.13

Relative Risk Reduction (RRR): 1 - RR = 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 hip replacement instead of screws to prevent one patient requiring re-operation.)

Measures of Treatment Effect

RR= Risk Ratio =

RR < 1 means treatment is beneficial

RRR = Relative Risk Reduction = 1-RR

)/(

)/(

dcc

baa

Bad Outcome

No Bad Outcome

Totals

Treatment a b a + b

Control c d c + d

Totals a + c b + d N = a + b + c + d

Beware of the Odds Ratio

RR = Risk Ratio =

(a/b) (a/c)

OR = Odds Ratio = ------- = -------- = ad/bc

(c/d) (b/d)

)/(

)/(

dcc

baa

Bad Outcome

No Bad Outcome

Totals

Treatment a b a + b

Control c d c + d


In the hip replacement vs. screws example, the baseline risk of reoperation (with screws) is 40%,

so the baseline odds are 67%. The risk (or odds) with replacement is about 5% , so RR ≈ 5/40 ≈

1/8; but the OR ≈ 5/67 ≈ 1/13.

Atraumatic vs. Standard Spinal Needle and Occurence of Headache

Needle HA No HA Risk Odds

Atraumatic 50 239 289 17% 0.21

Standard 92 206 298 31% 0.45

142 445 587

RR 0.56

Reported This

OR 0.47Straus, S. E., K. E. Thorpe, et al. (2006). JAMA 296(16): 2012-22.

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

Treatment a b a + b

Control c d c + d


Q: What does the 34% reduction mean?

Nimotop® Ad Graph

22% 33%

• RR = 21.8%/33% = .66• RRR = 1-0.66 = 34%• ARR = 33% - 21.8% = 11.2%

Original figure

11%

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

To scale

Why is NNT = 1/ARR?

67 no stroke anyway

22 strokes with Nimotop®

11 strokes prevented

22 strokes with with treatment

33 strokes with no treatment

100 SAH patients treated

Why is NNT 1/ARR?

Treat 100 SAH patients; prevent 11 strokes.

100/11 = 1/11% = 1/ARR = 9 patients treated per stroke prevented.

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):507-514. Numbers rounded for purposes of exposition.

NNT Practice

ISIS- 2*. Aspirin therapy (one month of 160 mg/day) in patients with acute myocardial infarction (AMI) reduced 30-day cardiovascular mortality from 11.8% in the placebo group to 9.3% in the aspirin group.

*Lancet 1988;2(8607):349-360.

NNT PracticeHow many AMI patients do we need to treat with

aspirin to prevent one CV death at 30 days?

Death at 30 Days

Died Lived

Aspirin 804 7783 8587 9.3%

Placebo 1016 7584 8600 11.8%

-2.5%

*Lancet 1988;2(8607):349-360.

NNT Practice

RCT of re-insertion of stylette to reduce post-LP headache.

Of 300 patients who had stylette re-inserted, only 15 (5%) got headaches.

Of 300 patients who did not have stylette re-inserted, 49 (16%) got headaches.

How many stylettes do you have to re-insert to prevent one post-LP headache?

J. Neurol. 1998 Sep;245(9):589-92

NNT Practice

Stylette Reinserted HA No HA Total Risk

Yes 15 285 300 0.05

No 49 251 300 0.16

ARR 0.11

NNT 9

The risk ratio (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 Reduction

*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, then the treatment is beneficial; 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.

Irradiation to prevent re-blockage after cleaning out a blocked coronary artery bypass graft.

“At 12 months, the rate of revascularization of the target lesion was 70 percent lower in the iridium-192 group than in the placebo group”


After cleaning out blocked bypass graft, how many do we have to treat with iridium to prevent one revascularization procedure (of the target lesion)?


“At 12 months, the rate of revascularization of the target lesion was 70 percent lower in the iridium-192 group than in the placebo group”


After cleaning out blocked bypass graft, how many do we have to treat with iridium to prevent 1 revascularization procedure in the next 12 months?


The baseline risk (i.e., risk in the placebo group) was 57%

Baseline 12-month risk of revascularization = 57%RRR = 0.70

ARR = RRR × Riskcontrol

ARR = 0.70 × 0.57 = 0.40NNT = 1/0.40 = 2.5Need to treat 2.5 unclogged grafts with radiation to

prevent 1 from needing revascularization of the target lesion in the next 12 months.


Need Baseline Risk

ARR = RRR × Riskcontrol

Analysis and Presentation of Results

• Relative risk most relevant for assessing causation

• Absolute risk reduction (ARR) most relevant for clinical decisions

• 1/(ARR) = Number Needed to Treat (NNT) per outcome prevented

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 3 2003;348(14):1322-1332. 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.

No Flu Shot?

How about Tamiflu?

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

grandmother (in her 70s) who lives 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; 285:748-754.

Prophylactic Oseltamivir: Index Case Flu+*

Household Contacts

Flu No Flu Risk

Oseltamivir 3 206 209 3/209 = 1.4%

Placebo 26 180 206 26/206 = 12.6%

29 386 415

Risk Ratio (RR): 1.4%/12.6% = 0.11

Relative Risk Reduction (RRR): 1 - RR = 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; 285:748-754.

Prophylactic Oseltamivir: Index Case Flu+*

Household Contacts

Flu No Flu Risk

Oseltamivir 3 206 209 3/209 = 1.4%

Placebo 26 180 206 26/206 = 12.6%

29 386 415

Risk Ratio (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; 285:748-754.

Number Needed To HarmNausea No Nausea Risk

Oseltamivir 27 467 494 27/494 = 5.5%

Placebo 12 449 461 12/461 = 2.6%

Risk Ratio (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.

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.

Ratio of Undesired to Desired Effects

“Harms” / Bad Outcome Prevented =

ARI/ARR =

NNT/NNH

Or

Bad Outcomes Prevented / Harm Caused =

ARR/ARI =

NNH/NNT

Number Needed to HarmTransfusion No Transfusion

Hip Replacement 44 179 223 44/223 = 19.7%


Risk Ratio (RR): 19.7%/1.8% = 11.00


Number Needed to Harm (NNH) ????

Number Needed to HarmTransfusion No Transfusion

Hip Replacement 44 179 223 44/223 = 19.7%


Risk Ratio (RR): 19.7%/1.8% = 11.00


Number Needed to Harm (NNH) 1/ARI = 6

(Need to treat 6 patients with hip replacement instead of screws to cause one patient requiring transfusion.)

Ratio of Desired to Undesired Effects

Bad Outcomes Prevented / Harm Caused = ARR/ARI = NNH/NNT*Hip Replacement vs. Screws for Hip FxRisk Difference for re-operation:

∆ Risk Re-Op = 5.2% - 39.8% = -34.6%Risk Difference for transfusion:

∆ Risk Trx = 19.7% - 1.8% = +17.9% Re-operations prevented/Transfusion Caused: -

34.6/17.9 = -1.93 ≈ -2

*Easier here to divide ∆ re-operation by ∆ transfusion, rather than use NNH or NNT.

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

BOTE CEA

Back-of-the-Envelope Cost Effectiveness Analysis

(In book, this is referred to a “treatment cost per bad outcome prevented.)

Back-of-the-Envelope Cost Effectiveness Analysis

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 .

BOTE CEA: Oseltamivir

Index Case Flu +• NNT = 9 (Treat 9 household contacts,

prevent 1 flu case)

• NNT x Treatment Cost* = 9 x $45 = $405/flu case prevented

•Cost of Tamiflu 75 mg #10 = $79.99 www.drugstore.com $79.99 1/7/08

http://www.drugstore.com/

BOTE CEA: Aspirin after MI

• NNT = 1/0.025 = 40 (Treat 40 MI patients to prevent 1 death at 30 days)

• At Rite Aid, a bottle (#120) of 81 mg aspirin tablets costs $5.00, but you only need 60.

• NNT x Treatment Cost* = 40 x $2.50 = $100/death prevented

Death at 30 Days

Died Lived

Aspirin 804 7783 8587 9.3%

Placebo 1016 7584 8600 11.8%

-2.5%

*Lancet 1988;2(8607):349-360.

BOTE CEA Example

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

Drug cuts risk of breast-cancer relapse

Findings so promising, study halted so scientists could release news

By Sabin RussellChronicle Medical Writer

Front Page, San Francisco Chronicle 10/10/03

RCT of Letrozole (Femara®), after tamoxifen, to prevent breast cancer recurrence

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.”

Femara Trial Results

Recurrence No Recurrence

Letrozole 75 2500 2575

Placebo 132 2450 2582

Risk(Letrozole) = 75/2575 = 2.9%Risk(Placebo) = 132/2582 = 5.1%RR = 2.9/5.1 = 0.57RRR = 1- 0.57 = 43%

N Engl J Med. 2003 Nov 6;349(19):1793-802.

Femara Trial Results

ARR = 5.1% - 2.9% = 2.2%

NNT = 1/2.2% = 45

Treatment Cost = $266/month* x 12 months/year x 2.5 years = $7980

Femara Cost per Recurrence Prevented =

$7980 x 45 ≈ $360,000

*2.5mg tablets are available from www.drugstore.com $266/30 day supply (30 tablets) 1/7/2008.

Ondansetron for Oral Rehydration

VomitedDidn't

Vomit

Ondansetron 15 92 107 14%

Placebo 37 70 107 35%

RR 0.41

ARR 21%

NNT 5

Pill Cost $18

N Engl J Med. 2006 Apr 20;354(16):1698-705

BOTE CEA Examples

• Oseltamivir to prevent flu in household contacts of flu+ individuals:$405 per case of flu prevented

• Aspirin after acute MI: $100 per death prevented at 30 days

• Letrozole after tamoxifen to prevent recurrent breast cancer: $360,000 per recurrence prevented at 2.5 years

• Ondansetron to prevent vomiting during oral rehydration: $90 to prevent emesis during oral rehydration in one patient.

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

BOTE vs. “Real” CEABack 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.

Quantifying the Benefit* of a Treatment: Take Home Points

• The Risk Ratio or Relative Risk Reduction associated with an intervention is of minimal use without a baseline incidence 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: Treatment cost per bad outcome prevented = Treatment Cost x NNT

*With regard to dichotomous outcomes

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

grandmother (in her 70s) who lives 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.)

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%

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 = ∞)

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 = ∞)

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

No Adjustment of NNH for Disease Prevalence?

Long-term aspirin tx for primary prevention of MI

Assuming baseline risks are 1%/yr for MI, 0.03%/year for hemorrhagic CVAAnd RR’s are 0.76 for MI and 2.0 for hemorrhagic CVA

Risk of: Aspirin Placebo DifferenceNNT

MI 0.0076 0.01 -0.0024 417

Hemorrhagic CVA 0.0006 0.0003 0.0003 3333

Ratio of the rate differences = (0.0024/0.0003) = 3333/417 = 8

“For every 8 heart attacks prevented by aspirin, it causes 1 hemorrhagic stroke”

No Adjustment of NNH for Disease Prevalence?

Long-term aspirin for primary prevention of MI

Sensitivity to changes in the baseline risk of MI:

Baseline risk of MI:Ratio of MI prevented/CVA caused1%/year 82%/year 160.1%/year 0.8 (or, 1.25 strokes/MI)

But, this assumes that the risk of stroke is independent of the risk of MI. Aren’t both the result of vascular disease?

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 = $59.99 www.drugstore.com 3/4/2004

http://www.drugstore.com/

Treatment Threshold Probability from Cost-Effectiveness Threshold

IF you can specify the amount you are willing to spend on prophylactic oseltamivir to prevent one case of the flu, you can calculate the treatment threshold probability Ptt

Cost-Effectiveness Threshold Example

Willing to spend $800 on prophylactic oseltamivir per case prevented.

Ptt = $45/(11.2%×$800) = 0.50

Using the Chapter 3 notation:

C = $45

B = (11.2% × $800) - $45 = $45

C/(C+B) = 45/(45+45) = .50

Treatment Threshold Probability from Threshold Cost Effectiveness Ratio

Assume it is worth $800 in oseltamivir to prevent one case of the flu. We can calculate the treatment threshold probability PTT:

NNT* x $45 = $800

NNT/ PTT = $800/$45 ≈ 18

NNT/17.8 = PTT

9/18 = 0.5 = PTT

Estimating B (using only treatment costs)

V = Value of preventing ONE case (“worth $800 in oseltamivir to prevent one flu case”)

C = Cost of treating one D- individual unnecessarily (household contact of a Flu- individual) ($45)

B = Cost of failing to treat one D+ individual (household contact of a Flu+ individual)

B = ARR × V – C

V = $800 (worth $800 in oseltamivir to prevent one case of the flu)

C = $45 (cost of txing one pt with oseltamivir)

ARR = 11.2%

B = 11.2% x $800 - $45 = $45

Estimating B (using only treatment costs)

Treatment Threshold Probability

from B and C

C = $45

B = $45

B/C = 1:1 = Threshold Odds

B/(B+C) = 1/2 = Threshold Prob = PTT

Assumptions

• Only considers drug/treatment costs, not side effects of treatment

• Treatment does not reduce outcome risk among D- patients

• Can specify the amount willing to spend in treatment costs to prevent one outcome

Review: Testing Thresholds (Chapter 3)

Probability of Disease

Treat none; no test

Treat based on test results

Treat all; no test

No Treat-Test Threshold

Test-Treat Threshold

Treatment Threshold

Absolute Risk Reduction, Number Needed to Treat, Back-of-the-Envelope Cost Effectiveness Analysis,...

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