Nguyen D. Nguyen, John A. Eisman and Tuan V. Nguyen

Garvan Institute of Medical Research, Sydney, Australia

Indirect comparison of anti-vertebral fracture efficacy among available drugs: A Bayesian meta-analysis

Treatment of Osteoporosis

• Several drugs currently available for the treatment of osteoporosis.

• Which treatment appropriate?

– efficacy

– safety

– cost considerations.

Which drug is better?

• Decision makers need more head-to-head comparison trials.

• Reluctance of industry

– Uncertainty of result

– Sample size and costs

• Issues of head-to-head comparison trial

– Active control: which one?

– Margin of non-inferiority

– Parameter of comparison

Required sample size for a noninferiority comparative trial

Fracture Ratio of efficacy for new drug

in standard compared to standard drug

drug (%) 1.1 1.3 1.5

1.0 267453 34766 14413

2.0 131916 17202 8032

5.0 51179 6719 2763

8.0 30937 4031 1671

10.0 24205 3152 1307Sample size was based on 5% significant level with power of 80%

(de Boo and Zielhuis, Statist. Med., 2004)

Current status

• No head-to-head comparative trial in the field of osteoporosis.

• Indirect comparison based on meta-analysis, a useful approach to make simultaneous inference on the relative efficacy of various drugs.

Indirect comparison

Placebo

Drug A

Direct comparison Direct comparisonIndirect comparison

Direct comparison

Placebo

Drug B

PlaceboDrug C

RRA RRB

RRC

RRA

RRB

RRA

RRC

RRB

RRC

RR: relative risk

Traditional and Bayesian approaches

Treatment Placebo

Collect data (D)

P(D|given hyphothesis)

Traditional Bayesian

Treatment Placebo

Existing knowledge: effect/no effect/ no idea

Treatment Pplacebo

Collect data (D)

P(Hyphothesis|given D)

Prob. of observing data D given no effect Prob. of an effect given observed data D

Treatment Placebo

Hypothesis: effect

Treatment Placebo

Hypothesis: no effect

Traditional and Bayesian approaches Traditional Bayesian

1

• Point estimate

• Rely on p-value

significantdifference

notsignificantdifference

Relative risk

Favours treatment Favours placebo

0.2 0.6 1.0 1.4 1.8 2.2

0.6

Favours treatment Favours placebo

• Posterior distribution

• Not rely on p-value, comprehensive information

Relative risk

confidence interval

credible interval

Ln(ORA/ORB)-1.0 -0.5 0.0 0.5 1.0

Equivalent (p=0.26)

-1.0 -0.5 0.0 0.5 1.0

Acceptable (p=0.77)

-1.0 -0.5 0.0 0.5 1.0

Superior (p=0.65)

Favours A Favours B Favours A Favours B Favours A Favours B

Analysis of “noninferiority”

OR values between (0.9 -1.1) : A = BOR values to the left of 1.1 : A = acceptableOR values to the left of 1.0 : A > BOR values to the right of 1.0 : A < B

Tolerence limit 10%(LnOR between -0,1 & 0.1or OR between 0.9 & 1.1)

(Diamond GA and Kaul S, 2007)

To compare the anti-vertebral fracture efficacy among therapies by using Bayesian approach.

Search strategy and study inclusion

• A systematic search, electronic resource: PubMed, Ovid, and Cochrane Controlled Trials.

• Inclusion criteria

– Published randomized placebo-control trials (RCT) in English.

– Postmenopausal women receiving osteoporotic therapy.

– Vertebral fracture outcome.

Characteristics of studies

ID Drug Study (n) Sample (n) Duration (y)

1 Alendronate 6 8115 2 - 4

2 Etidronate 9 1162 2 - 4

3 Risedronate 5 2923 3

4 Ibandronate 1 2086 2 - 3

5 HRT 7 3376 1 - 4

6 Strontium ranelate 1 1803 3

7 Raloxifene 5 6951 1 - 3

8 Calcitonin 2 956 1 - 3

9 Fluoride 5 822 1 - 3

10 PTH 1 1431 2

All drugs 42 29625

Efficacy of individual drugs on vertebral fracture reduction

Odds-ratio

Favours treatment Favours placebo Drug OR (95% CrI)

Alendronate 0.50 (0.35, 0.74)

Etidronate 0.52 (0.29, 0.85)

Risedronate 0.57 (0.40, 0.85)

Ibandronate 0.50 (0.25, 0.96)

HRT 0.48 (0.27, 0.84)

Strontium ranelate 0.54 (0.30, 1.00)

Raloxifene 0.55 (0.34, 0.80)

Calcitonin 0.66 (0.36, 1.14)

Fluoride 0.59 (0.35, 0.96)

PTH 0.30 (0.15, 0.58)

OR, odds-ratioCrI, credible interval

Posterior distribution Point estimation

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Probability that a drug reduces fracture risk at least 30% (Coefficient of Efficacy)

Co

effic

ien

t o

f E

ffic

acy

0.99 0.950.88 0.86 0.85 0.83 0.79 0.75 0.71

0.53

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Indirect comparison the antivertebral fracture efficacy between Raloxifene and Etidronate

Ln(ORZ/ORA)

Favours Ralox. Favour Etid. Favours Ralox. Favour Etid. Favours Ralox. Favour Etid.

Tolerance limit was defined as ± 10%

-1.5 -0.5 0.5 1.5

Equivalent (p=0.21)

-1.5 -0.5 0.5 1.5

Acceptable (p=0.48)

-1.5 -0.5 0.5 1.5

Superior (p=0.37)

Drug Probability (%) of the relative efficacy between two drugs

Alendronate (1) Etidronate (2) Risedronate (3)

Equivalent Etidronate (2) 23

Risedronate (3) 24 21

Ibandronate (4) 20 18 20

Acceptable Etidronate (2) 53

Risedronate (3) 40 43

Ibandronate (4) 53 53 66

Better Etidronate (2) 41

Risedronate (3) 27 31

Ibandronate (4) 43 44 56

Comparison efficacy of vertebral fracture reduction among drug treatments

No evidence that a drug was either much better or worse than the others.

Drug Probability (%) of the relative efficacy between two drugs

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Equivalent Strontium r. (6) 20 19 22 16 17

Raloxifene (7) 25 22 27 18 19 20

Calcitonin (8) 15 14 19 13 12 15 17

Fluoride (9) 20 18 23 16 16 18 22 20

PTH 10 10 7 11 12 9 8 5 7

Acceptable Strontium r. (6) 46 47 60 43 40

Raloxifene (7) 47 48 65 44 40 53

Calcitonin (8) 26 28 39 28 24 34 34

Fluoride (9) 37 39 53 37 32 44 47 64

PTH 92 91 96 86 87 91 94 96 95

Better Strontium r. (6) 35 37 50 35 31

Raloxifene (7) 34 37 51 35 30 43

Calcitonin (8) 18 20 29 21 17 26 24

Fluoride (9) 26 29 40 28 23 35 35 54

PTH 88 86 93 81 81 86 90 94 92(1), alendronate; (2), etidronate; (3), risedronate; (4), ibandronate; (5), HRT

Anti-vertebral fracture

• Most active therapies significantly reduced the risk of vertebral fx (vs. placebo), with variable magnitudes.

• Evidence of efficacy for calcitonin uncertain.

• No evidence for a drug either much better or worse than the others.

• Superiority for PTH vs. other drugs.

Bayesian approach

• Updating the existing knowledge or information.

• Comprehensive information.

• Clinically relevant inference of results.

Acknowledgements

• The Ho Chi Minh City Medical Association.

• Bridge Healthcare Co. Ltd., Australia for the untied sponsorship.

Thank you!

Anti-vertebral fracture• Most active therapies significantly reduced the

risk of vertebral fx (vs. placebo), with variable magnitudes: bisphosphonates, raloxifene, HRT, fluoride, strontium ranelate and PTH. 

• Evidence of effect for calcitonin uncertain.

• No evidence for a drug neither much better nor worse than the others.

• Superiority for PTH vs. other drugs.

• Probabilities that PTH better than alendronate: 0.88, etidronate: 0.86; risedronate: 0.93, HRT: 0.91, and raloxifene: 0.94.

Indirect comparison

– Not necessary, because “equivalence” depends on the tolerance limit.

Drug A Drug B

Drug C

=Drug B

=Drug ADrug C=?

Drug A Drug B

Drug C

>

Drug B >Drug A Drug C>?

– Not necessary, because of different populations.

Anti-vertebral fracture

• Current therapies were efficacious in reducing vertebral fracture risk and their effect sizes were comparable.

• However, PTH appears to have higher anti-vertebral efficacy that all other treatments.

Traditional and Bayesian approaches

A/placebo B/placebo

Hypothesis: no effect

A/placebo B/placebo

Collect data

P(D|given hyphothesis)

Traditional Bayesian

A/placebo B/placebo

Hypothesis: effect

A/placebo B/placebo

Collect data

P(Hyphothesis|given D)

Prob. of observing data D given no effect Prob. of an effect given observed data D

Bayesian approach: Updating information

P(H|D)Prior

informationCurrent likelihood (Observed data)= x

• Prior information:

Probability of effect based on existing knowledge.

Vague prior, or no difference/ no effect between drug and placebo or between two drugs.

Posterior distribution

Posterior distribution of efficacy of drug therapy on vertebral fracture reduction

Agent OR (95% CrI) Probability that OR ≤

0.9 0.8 0.7 0.6

Alendronate 0.50 (0.35, 0.74) 1.00 0.99 0.95 0.80

Etidronate 0.52 (0.29, 0.85) 0.97 0.94 0.85 0.68

Risedronate 0.57 (0.40, 0.85) 0.99 0.95 0.83 0.56

Ibandronate 0.50 (0.25, 0.96) 0.94 0.89 0.79 0.64

Zoledronic acid 0.28 (0.15, 0.50) 1.00 1.00 1.00 0.99

HRT 0.48 (0.27, 0.84) 0.98 0.95 0.88 0.74

Strontium ranelate 0.54 (0.30, 1.00) 0.93 0.87 0.75 0.58

Raloxifene 0.55 (0.34, 0.80) 0.99 0.95 0.86 0.64

Calcitonin 0.66 (0.36, 1.14) 0.83 0.71 0.53 0.33

Fluoride 0.59 (0.35, 0.96) 0.94 0.86 0.71 0.48

PTH 0.30 (0.15, 0.58) 1.00 1.00 0.99 0.97

Large sample size is required!

Consider a head-to-head comparison trial:

• Margin of inferiority = 20% (e.g. 20% worse than the control is ok)

• Background rate = 10%

• Drug would be equivalent if incidence <12%

• Power = 90%, significance level = 5%

• 5134 subjects per group!

Requested sample size for a comparative trial

Fracture rate Differences in efficacy from control drug (%)

in treated power=80% power=90%

patients (%) 10 30 10 30

1.2 235000 18080 313700 23944

2.5 100300 8438 139200 11200

5.0 50800 4092 67700 5414

7.5 36700 2658 45000 3516

10.0 24900 1902 33200 2514

15.0 14700 1200 19600 1586Sample size was base on 5% significant level

(Kanis JA et al, 2002)

Probability (%) of the relative efficacy between two drugs

Alendronate Etidronate Risedronate Ibandronate

Etidronate vs. equivalent 23

better 41

acceptable 53

Risedronate vs. equivalent 24 21

better 27 31

acceptable 40 43

Ibandronate vs. equivalent 20 18 20

better 43 44 56

acceptable 53 53 66

Zoledronic acid equivalent 8 8 4 10

vs. better 93 91 97 86

acceptable 96 94 98 90

Comparison efficacy of vertebral fracture reduction among drug treatments

Probability (%) of the relative efficacy between two drugs

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Stront. ranelate (7) vs. p1 20 19 22 16 4 17

p2 35 37 50 35 4 31

p3 46 47 60 43 7 40

Raloxifene (8) vs. p1 25 22 27 18 3 19 20

p2 34 37 51 35 2 30 43

p3 47 48 65 44 4 40 53

Calcitonin (9) vs. p1 15 14 19 13 2 12 15 17

p2 18 20 29 21 1 17 26 24

p3 26 28 39 28 2 24 34 34

Fluoride (10) vs. p1 20 18 23 16 2 16 18 22 20

p2 26 29 40 28 2 23 35 35 54

p3 37 39 53 37 3 32 44 47 64

PTH vs. p1 10 10 7 11 16 12 9 8 5 7

p2 88 86 93 81 36 81 86 90 94 92

p3 92 91 96 86 45 87 91 94 96 95