Designing a Non-inferiority Study in Kidney Transplantation: A Case Study

Steffen Witte (1), Heinz Schmidli (1), Anthony O‟Hagan (2), Amy Racine (1) (1) Novartis Pharma AG, Basel, Switzerland (2) University of Sheffield, United Kingdom

Abstract

In organ transplantation, placebo controlled clinical trials are not possible for ethical

reasons, and hence non-inferiority trials are used to evaluate new drugs. Patients with a

transplanted kidney typically receive three to four immunosuppressant drugs to prevent

organ rejection. In the described case of a non-inferiority trial for one of these

immunosuppressants the dose is changed and another is replaced by an investigational

drug. This test regimen is compared with the active control regimen. Justification for the

non-inferiority margin is challenging as the putative placebo has never been studied in a

clinical trial. We propose the use of a random-effect meta-regression, where each

immunosuppressant component of the regimen enters as a covariate. This allows to

make inference on the difference between the putative placebo and the active control.

Based on this, various methods can then be used to derive the non-inferiority margin. A

hybrid of the 95/95 and the synthesis approach is suggested. Data from 51 trials with a

total of 17002 patients were used in the meta-regression. Our approach was motivated

by a recent large confirmatory trial in kidney transplantation. The results and the

methodological documents of this evaluation were submitted to FDA. FDA accepted our

proposed non-inferiority margin and our rationale.

Keywords : Non-inferiority margin, 95/95 rule, preservation method, synthesis approach,

hybrid approach, meta analysis, constancy.

1 Introduction

To demonstrate the efficacy of a new test treatment, a clinical trial comparing the test

treatment with placebo is often the preferred option. However, in indications such as

organ transplantation, it is not ethical to conduct a placebo-controlled trial and the

development of simple add-on therapies is rare. Hence, non-inferiority studies are used

which compare the test treatment (T) with an active control therapy (C), with the aim to

provide indirect evidence on the superiority over placebo. Non-inferiority trials intend to

show that a test treatment is not much worse than the control therapy which is usually

the standard treatment in the particular indication. „Not much worse‟ is defined by a non-

inferiority margin (δ). This non-inferiority margin is chosen such that sufficient evidence

of superiority over placebo is indirectly provided. The choice of the non-inferiority margin

can be challenging. Some guidance is given in ICH-E10 (ICH-E10 2000), the

corresponding EMA guideline (EMA 2005) and the recently drafted FDA guidance (FDA

2010). In some cases, indirect evidence on superiority over placebo may not be

considered sufficient, and a requirement might be to preserve a fraction (λ) of the effect

of the control treatment in comparison with placebo.

More formally, these concepts can be described by three different hypotheses of

interest. In the kidney transplantation example discussed in this paper, the primary

endpoint is a failure rate, and differences of failure rates are considered. However, the

same framework can also be applied for other primary endpoints, for example if the

primary endpoint is a continuous variable or a log hazard rate in time to events trials.

The hypothesis to test indirectly for efficacy is

(1) H0: (πP − πT) ≤ 0 versus H1: (πP − πT) > 0 or

H0: (πT − πC) ≥ (πP – πC) versus H1: (πT − πC) < (πP – πC),

where πT is the failure rate of the test group (T) and πP is the failure rate of the putative

placebo (P), i.e. the failure rate of the placebo group if it could have been studied. In

other words to prove efficacy (superiority to placebo) we must show that the test group is

closer to the control than the placebo is. The hypothesis to preserve a fraction of the

control effect indirectly is

(2) H0: (πP − πT) ≤ λ(πP − πC) versus H1: (πP − πT) > λ(πP − πC) or

H0: (πT – πC) ≥ (1-λ) (πP − πC) versus H1: (πT – πC) < (1-λ) (πP − πC),

where πC is the failure rate of the control group (C). The parameter λ between 0 and 1

controls the magnitude of the preservation, where λ=0 means no preservation as in(1)

and λ=1 describes a hypothesis to investigate superiority of the test over the control

treatment. This use of the preservation fraction may also be considered when a change

of the effect over time is suspected, i.e. when the constancy assumption is not fulfilled.

However, any preservation factor seems arbitrary. The hypothesis of non-inferiority is

(3) H0: (πT − πC) ≥ δ versus H1: (πT − πC) < δ,

with the non-inferiority margin δ ≥ 0. The margin δ > 0 could be clinically motivated to

show that test treatment is not much worse than the control treatment. If δ = 0 the

hypothesis (3) investigates superiority of the test over the control treatment. However,

hypotheses (1) or (2) may be considered the primary objectives. When for ethical

reasons placebo can no longer be used in the current study and hence the failure rate

πP cannot be estimated from the two-arm non-inferiority study with test and control

treatment only, the non-inferiority margin δ will be used to reflect hypotheses (1) and (2).

The margin δ corresponds to (1-λ) (πP − πC), i.e. a margin δ which is purely based on a

clinical justification must not be larger than the control effect (πP − πC).

This paper will describe how the non-inferiority margin δ can be justified using an

example from the transplantation area where treatment regimens consist of several

immunosuppressant drugs, and where the putative placebo has never been studied in a

clinical trial. We introduce the case study in Section 2, and discuss various methods for

deriving the non-inferiority margin in Section 3. In Section 4, the meta-analysis is

described, starting with selection of the historical clinical trials, and providing details of

the random-effect meta-regression using frequentist and Bayesian methods. In Section

5, results from the meta-analysis are used to justify the non-inferiority margin using the

various methods introduced in Section 3. The analysis of the actual non-inferiority study

is not subject of this article. The paper closes with a discussion in Section 6.

2 Clinical Background

Over the past decades, kidney transplantation has become a common medical

procedure with favorable impact on the life of patients with end stage renal failure. To

maximize efficacy (prevent allograft rejection and graft loss) and minimize adverse

effects, current immunosuppressant regimens combine immunosuppressant drugs. Care

is taken to achieve synergy and/or additive effects by co-administration of agents with

different mechanism of action while avoiding overlapping toxicities. Currently, most

widely used regimens combine corticosteroids (CS) with an anti-IL2 induction such as

basiliximab or daclizumab, a calcineurin inhibitor (CNI) such as cyclosporine A (CsA) or

tacrolimus (Tac), and either with lymphocyte proliferation inhibitor such as

mycophenolate mofetil or mycophenolic acid (MPA) or with an inhibitor or mammalian

target of rapamycin (mTOR) such as sirolimus and everolimus or with an inhibitor of

purine synthesis such as azathioprine (AZA). Typically used regimens are for example

(anti-IL2+CS+Tac+MPA) or (anti-IL2+CS+CsA+MPA) (Kälble et al. 2009, KDIGO 2009,

Webster et al. 2005).

Everolimus (EVR, Certican®, Zortress®) is an mTOR inhibitor which is approved in

more than 80 countries and received FDA approval in April 2010 to prevent organ

rejection in adult kidney transplant recipients.

In the pivotal Phase III study (CRAD001A2309, NCT00251004, Tedesco et al. 2010)

everolimus was tested in two doses. Only one of the doses is considered for simplicity.

The following regimens are compared.

T = (anti-IL2+CS+CsA(r)+EVR)

C = (anti-IL2+CS+CsA(s)+MPA)

(s) indicates the standard dose, (r) indicates the reduced dose of CsA. The primary

efficacy endpoint is a binary endpoint consisting of biopsy proven acute rejection

(BPAR), graft loss, or death within 12 months. The purpose of the trial is to show that the

new regimen is non-inferior to the control group. This non-inferiority margin δ should be

chosen to fulfill two requirements, namely, it should be small enough to indirectly

conclude superiority over putative placebo (1) as well as clinical non-inferiority (3). Here

putative placebo (P) consists of the components (anti-IL2+CS+CsA(r)). The clinical

justification of the margin is based on medical rather than statistical considerations; the

clinical justification is not subject of this article. To justify the margin for the indirect

comparison with putative placebo the „control effect‟ is needed, i.e. the effect of the

control group versus the putative placebo, which was not studied before:

control effect = P – C = (anti-IL2+CS+CsA(r)) - (anti-IL2+CS+CsA(s)+MPA)

For the convenience of notation P=P, and likewise with C and T.

3 Derivation of a non-inferiority margin

Several approaches are described in the literature to derive a non-inferiority margin.

Here we describe three approaches. The 95/95 approach and the synthesis approach

have been previously discussed in literature. In addition, we discuss a new approach

which is a hybrid of previous approaches.

3.1 95/95 approach

The so called 95/95 approach or indirect confidence interval comparison method

calculates in the first step the lower bound of a two-sided 95% confidence interval of the

control effect from historical information and uses this margin as the predefined non-

inferiority margin (Wang & Hung & Tsong 2002, Wiens 2002, Rothmann et al. 2003).

(4)

PCPC SEz 2/1)1( ,

where

PC and SEPC are estimates of the treatment difference between P and C and its

standard error derived from historical information, z denotes the inverse of the

cumulative standard normal distribution. In a second step the two-sided 95% confidence

interval of the effect test over control in the new trial is calculated and the margin

compared with the predefined margin to conclude non-inferiority to C and superiority

over P. The non-inferiority margin defined with this approach is independent of the new

study and hence can be used for designing the new study. This approach can also be

used to test if T preserves a certain effect of C. However, this approach is known to be

conservative in many circumstances and possibly requires a high number of patients for

the new study.

3.2 Synthesis approach

The synthesis approach (Fisher 1998, Hasselblad & Kong 2001, Snapinn & Jiang

2008a, Snapinn & Jiang 2008b) is also called the virtual comparison method (VC

method, Wang & Hung & Tsong 2002), comparing the test treatment with the putative

placebo in a meta-analysis framework. The comparison is performed using a contrast

within the meta-analysis. Therefore it is not necessary to predefine the non-inferiority

margin. This method can also be used to test if T preserves a certain effect of C without

defining a non-inferiority margin explicitly.

The synthesis approach can be seen as a method which implicitly defines a non-

inferiority margin which however is not fixed at the design stage and depends on the

outcome of the new trial. Therefore it may be more difficult for the sponsor to plan the

sample size. The implicit non-inferiority margin of the synthesis approach can be derived

as follows

(5) PCPCTCPCTCPC SEzSESESESE 2/1

222 //)1(ˆ)1( or

TCTCPCPC SESESEz

222

2/1 )1(ˆ)1( ,

This formula is the modified formula from (Hauck & Anderson 1999). The same can be

found in (Wang & Hung 2003), (Rothmann et al. 2003) and (Witte 2005) with a different

notation. Formula (5) contains information from the new trial „T versus C‟, the standard

error of the treatment difference between T and C, SETC which is unknown prior to the

completion of the study, hence this non-inferiority margin is a function of the future study

results and can therefore not be specified beforehand.

3.3 Hybrid approach

In the synthesis approach, as SETC decreases e.g. when the size of the new trial

increases, the non-inferiority margin defined by (5) converges to its lower limit,

(6)

PCPCPCPC SEzSEz 2/12/1 )1(1)1(

which is the same as that of the 95/95 approach. Hence the 95/95 rule can be

considered as conservative.

One possible approach to define a fixed margin is to choose a lower limit for SETC from a

range of possible outcomes of the new study. For example, in designing a trial with

normally distributed outcome with known variance, one needs to prespecify the

maximum number of patients anticipated to be allocated in each treatment arm at end of

the study to derive the minimum value of SETC and the corresponding non-inferiority

margin (5). This non-inferiority margin is more conservative than that of a “standard”

synthesis approach while the “actual” standard error will be higher than that derived from

the maximum possible number of patients. For illustration, we consider a new study

which is planned to include 250 patients in the T and in C arm, and the estimated

treatment difference and standard error between P and C are 1 and 0.4, respectively

(the known variance is 1). A maximum sample size of 300 patients per arm may be used

to calculate a fixed non-inferiority margin. Figure 1 illustrates the probability of a type I

error under the null hypothesis that there is no difference between T and P as a function

of sample size (n) per arm of the new study with T versus C for the hybrid approach

(solid line), the synthesis method (dotted line), and the 95/95 rule (dashed line), the

horizontal reference is 0.025, the type I error requirement, the vertical line is 300, the

maximum sample size of the hybrid approach for deriving the non-inferiority margin. The

probability of type I error of the hybrid approach increases with n and is 0.025 at 300

(=n). The probability of type I error of the 95/95 rule approaches 0.025 as the sample

size per arm (n) increases beyond 100000. Figure 2 shows the non-inferiority margin

using the synthesis method as a function of (n). The horizontal reference is 300 with a

non-inferiority margin for the new study of 0.36 using the hybrid approach. For

comparison purposes the results of 95/95 methods is also shown (non-inferiority margin

= 0.22). This demonstrates that the proposed hybrid methods maintains the type I error

as long as the new study is not larger than the maximal expectation while being less

conservative than the 95/95 rules.

[Figure 1 about here]

[Figure 2 about here]

When the variance of the new study is unknown, the lower limit of the variance for the

historical study can be used to derive the non-inferiority margin.

For a trial with success or failure rates as the outcome, SETC depends on the success or

failure rates of T and C in addition to the sample sizes of the two treatment arms. One

therefore needs to consider not only using the maximum sample sizes at end of the

study but also the range of possible risk rates of T and C. These ranges could be

derived from historical data for the C and a most extreme effect of T.

4 Meta-analysis

4.1 Literature search

MEDLINE (http://www.ncbi.nlm.nih.gov/pubmed) was used to find relevant studies.

Clinical trials were searched by the query: (renal OR kidney) AND Randomized

Controlled Trial[PTYP] AND humans[MeSH] AND (rejection OR rejections). The search

was performed on the 18th of May 2009. To find additional relevant studies, trials cited

in meta-analysis publications on kidney transplantation were checked and medical

experts were consulted.

Only randomized controlled multicenter de-novo kidney transplantation trials were

included. Studies with special patient populations or with withdrawal therapy were

excluded. Also excluded were studies when comparisons were not relevant for the

current purpose e.g. if different methods of biopsies were evaluated. Only studies were

included with treatments consisting of combinations of the following drugs/drug classes:

CS (corticosteroids), CNI (cyclosporine or tacrolimus), anti-IL2 (basiliximab or

daclizumab), MPA (enteric-coated mycophenolate sodium or mycophenolate mofetil),

mTOR (everolimus or sirolimus), AZA (azathioprine) and FTY720.

The primary endpoint in the planned non-inferiority trial is the binary composite endpoint

(efficacy failure rate) defined as treated biopsy-proven acute rejection (BPAR) of grade

IA or higher, graft loss, death, or lost to follow-up at month 12. This endpoint was not

always available from the publications: some studies reported only the 6 or 12 month

BPAR endpoint, or only the 6 month composite endpoint. However, since BPAR is the

dominating component of the composite endpoint, and the vast majority of efficacy

failures occur before the end of month 6, studies with these endpoints were included as

well. Covariates were added to the statistical model to overcome the issue with different

endpoints.

4.2 Statistical models

A mixed effect logistic regression model was used to estimate the contribution of each of

the immunosuppressive drugs to the event rate, assuming additive drug effects in a

combination therapy on the log-odds scale. More precisely, let Yij denote the number of

events in study i and treatment arm j. It was assumed that

Yij ~ Binomial( Nij , πij )

where Nij is the number of patients and πij is the event rate in study i and treatment arm

j. The log-odds of the event rate was related to the effects of the study based on a linear

model with random study effect:

logit( πij ) = μ + δi + xij β ,

with parameters μ (intercept) and β (a vector of the effects of the immunosuppressant

drugs and of covariates), and random study effect δi ~ N(0, σ2). The vector xij contains

information on the presence or absence of each of the immunosuppressive drugs

(presence/absence of: CsA standard, CsA reduced, Tac standard, Tac reduced, CS,

anti-IL2, MPA, mTOR, AZA or FTY720), and on covariate values. Two dichotomous

covariates were included (available outcome composite endpoint or BPAR, available

outcome at 6 months or 12 months). The model was fitted by the maximum-likelihood

method (PROC NLMIXED in SAS 8.2). The goodness of fit of the model was checked by

graphically comparing predicted versus observed event rates.

The model allowed to derive a point estimate with standard error for the control effect,

i.e. the difference between the putative placebo (anti-IL2+CS+CsA(r)) and the control

arm (anti-IL2+CS+CsA(s)+MPA).

In the model building stage, interactions between the covariates were considered.

To assure that the normal approximation in the above approach is adequate, the final

model was also analyzed using a Bayesian approach. A Bayesian analysis with non-

informative priors (WinBUGS 1.4.3, Lunn et al., 2000) was done. Defining μ = logit(μ0),

the prior for μ0 (probability scale) was chosen as a uniform distribution. The prior on the

fixed effects log-odds βk for each covariate was chosen to correspond to a mean of 0

and a 95% CI [-4.7, 4.7] in log-odds scale or in probability scale of [0.009, 0.99]. This

was implemented by setting βk given k to a normal distribution with mean 0 and

standard deviation k, where k is from a half-normal distribution obtained by truncating

the normal distribution with mean 0 and variance 10 at zero. Half-normal distributions as

priors for standard deviations are discussed in (Spiegelhalter et al., 2004, section 5.7.3).

The standard deviation σ of the random study effect was also given the same half-

normal prior distribution.

4.3 Results

Of the 1155 potentially relevant publications found, 51 publications were finally selected.

These 51 trials contained information of 17002 patients. The extracted results are shown

in Table 1.

[Table 1 about here]

The data was fitted by the mixed effect logistic regression model. As illustrated in

Figure 3 the main assumption of the statistical model (additivity in the log-odds scale)

seems to hold. The grey bullets are the fits for the control arm (anti-

IL2+CS+CsA(s)+MPA). The estimates and standard errors for control effect are shown

in Table 2. The main analysis results in a control effect of 24.6% with a 95% confidence

interval (18.9% to 30.2%). The sensitivity analysis with a restricted set of 14 studies

excluding studies with mTOR inhibitors, FTY720, AZA, Tac but including studies with or

without anti-IL2, CS, CsA, MPA supports the main results. Other sensitivity analyses

showed even larger estimates (data not shown). As expected the Bayesian approach led

to higher standard errors but supports in general the main results.

[Figure 3 about here]

[Table 2 about here]

The plots of the estimates of the random study effect against time (Figure 4) suggest no

systematic changes over time. Similarly, the plots of estimated efficacy failure rates of

the control group against time (Figure 5) are consistent with the assumption of

constancy.

[Figure 4 about here]

[Figure 5 about here]

5 Derivation of the non-inferiority margin

Given an estimate of the control effect of 24.6% and its standard error of 2.8% from the

meta-analysis of all 51 studies, different approaches were used to derive a non-

inferiority margin.

The 95/95 confidence interval approach can be applied as follows. The lower bound of

the confidence interval justifies a non-inferiority margin of 18.9% (or 18.7% based on the

result from the sensitivity analysis). This approach is known to be conservative for

maintaining cross-study type I error rate, even in case of slight deviations from the

constancy assumption.

For comparison the hybrid non-inferiority margin was applied. An upper bound of the

sample size of 300 patients per arm was chosen. From historical information the failure

rates of the control group will be around 20%. Table 3 shows the non-inferiority margin

under a range of control failure rates between 10 to 30% and under the assumption that

the T failure rate is 5% lower. In addition, the non-inferiority margins were also

calculated assuming a control effect of 30.66% and standard error 5.5%, based on the

result from the sensitivity analysis in Table 3.

[Table 3 about here]

The non-inferiority margins were between 22 to 25% as compared to 18.9% from the

95/95 rule. In addition, if one wishes to preserve 50% of the control effect, this will lead

to a margin between 11 to 13.5%. A margin of 10% appears to be adequate not only for

defending superiority to the putative placebo but also for defending a preservation of

50% of the control effect based on the hybrid approach. Based on the 95/95 rule the

10% margin translates into a preservation of 47%. The 10% margin was chosen in our

case study.

6 Discussion

The meta-analysis of 51 clinical trials in combination with the 95/95 rule was the

rationale to justify the 10% non-inferiority margin which was submitted to and accepted

by FDA. It played a key role in the positive feedback from the FDA. Internally, we worked

closely with the clinical team for the study selection, for the understanding of the

limitations of our assumptions, the extrapolation to the event rate of the putative

placebo, the impact of the recommended margin on the size of our study, and on the

probability of study success.

Our documentation to justify the margin was quite extensive. Our impression was that

the line of thought was very important, for internal as well as external readers. Therefore

we suggest to cover as part of the non-inferiority justification (a) what needs to be

shown, (b) what is the best way to answer those questions, (c) what are the limitations in

the given setting, (d) what is the best feasible approach to evaluate and answer those

questions as well as possible under the limitations, and (e) what is the result and

implication of the evaluations.

In our case study the key limitation was that there is no study investigating the putative

placebo group. Therefore no direct evidence (putative placebo versus control) could be

used to estimate the control effect. As a consequence we could not use effects (such as

ratios or differences) from randomized trials but estimated the individual contribution of a

treatment component to the success of a regimen. The proposed methodology gives us

the necessary flexibility to estimate the control effect.

Crucial assumptions are the additivity on the log-odds scale of each component within a

regimen and constancy in time. The additivity assumption was checked by goodness of

fit and a study level random effect was introduced to account for the between study

variation. The constancy assumption was evaluated by examining the possible time

trend in the study level random effects and in control log odds. As the applied

immunosuppressive therapies changed over time, e.g. reduced CsA therapy after 2005

and newly approved regimens were introduced, it was challenging to examine a

potential time trend in control effects. The proposed method, in spite of its limitations and

assumptions appeared to be adequate for our purpose.

7 References

International Conference on Harmonisation. Guidance on choice of control group and

related design and conduct issues in clinical trials (ICH E-10). International

Conference on Harmonization, July 2000.

Committee for Medicinal Products for Human Use (CHMP). Guideline on the choice

of the non-inferiority margin. EMEA/CPMP/EWP/2158/99, July 27, 2005.

Guidance for Industry: Non-inferiority clinical trials (Draft, 2010) FDA/CDER/CBER

Immunosuppression after kidney transplantation. In: Kälble T, Alcaraz A, Budde K,

Humke U, Karam G, Lucan M, Nicita G, Süsal C. Guidelines on renal transplantation.

Arnhem, The Netherlands: European Association of Urology (EAU); 2009; pp. 55-65.

KDIGO Clinical Practice Guidelines for the Care of Kidney Transplant Recipients.

American Journal of Transplantation 2009; 9 (Suppl 3): S10–S13

Webster A, Taylor RS, Chapman JR, Craig JC. Tacrolimus versus cyclosporin as

primary immunosuppression for kidney transplant recipients. Cochrane Database of

Systematic Reviews 2005, Issue 4. Art. No.: CD003961.

Tedesco SH Jr, Cibrik D, Johnston T, Lackova E, Mange K, Panis C, Walker R,

Wang Z, Zibari G, Kim YS. Everolimus Plus Reduced-Exposure CsA versus

Mycophenolic Acid Plus Standard-Exposure CsA in Renal-Transplant Recipients, Am

J Transplant. 2010; 10:1401-13.

Wang SJ, Hung HMJ, Tsong Y. Utility and pitfalls of some statistical methods in

active controlled clinical trials. Control Clin Trials 2002; 23:15-28.

Wiens BL. Choosing an equivalence limit for noninferiority or equivalence studies.

Control Clin Trials 2002; 23:2-14.

Rothmann M et al. Design and analysis of non-inferiority mortality trials. Stat Med

2003; 22:239-264.

Fisher LD. Active control trials: What about a placebo? A method illustrated with

clopidogrel, aspirin and placebo (abstract). J Am Coll Cardiol 1998; 31:49A.

Hasselblad V, Kong DF. Statistical methods for comparison to placebo in active-

control trials. Drug Inf J 2001; 35:435-449.

Snapinn S, Jiang Q. Controlling the type 1 error rate in non-inferiority trials. Stat Med

2008; 27:371-381.

Snapinn S, Jiang Q. Preservation of effect and the regulatory approval of new

treatments on the basis of non-inferiority trials. Stat Med 2008; 27:382-391.

Hauck WW and Anderson S. Some issues in the design and analysis of equivalence

trials. Drug Inf J 1999; 33:109-118.

Wang SJ and Hung HMJ. Assessing treatment efficacy in noninferiority trials. Control

Clin Trials 2003; 24:147-155.

Witte, S. Meta-analytische Methoden für Äquivalenzfragestellungen. Dissertation.

Forschungsberichte der Abteilung Medizinische Biometrie, Universität Heidelberg

2005.

Lunn, D.J., Thomas, A., Best, N., and Spiegelhalter, D. (2000) WinBUGS -- a

Bayesian modelling framework: concepts, structure, and extensibility. Statistics and

Computing 2000; 10:325-337.

Spiegelhalter, D. J., Abrams, K. R. and Myles, J. P. Bayesian Approaches to Clinical

Trials and Health Care Evaluation. Wiley, New York, 2004.

Table 1: Extracted data for Meta analysis

No First Author Year Endpoint Treatment combination n N %

13 Chan 2008 M6 composite CS+B+Tac(r)+EVR 7 49 14.3%

CS+B+Tac(s)+EVR 7 43 16.3%

23 Vincenti 2008 M12 composite B+CsA(s)+MPS 40 112 35.7%

CS+B+CsA(s)+MPS 21 109 19.3%

1121 Andres 2008 M6 composite CS+B+Tac(r)+MPS 22 151 14.6%

CS+B+Tac(s)+MPS 16 141 11.3%

27 Ekberg 2007 M12 BPAR CS+CsA(s)+MMF 101 390 25.8%*

CS+D+CsA(r)+MMF 96 399 24.0%*

CS+D+MMF+S 148 399 37.2%*

CS+D+Tac(r)+MMF 49 401 12.3%*

34 Tedesco-Silva 2007 M12 composite CS+CsA(s)+FTY 26 90 28.9%

CS+CsA(s)+FTY 21 87 24.1%

CS+CsA(s)+MMF 37 94 39.4%

56 Pescovitz 2007 M6 BPAR CS+D+CsA(s)+MMF 2 15 13.3%

CS+D+MMF+S 11 30 36.7%

68 Cibrik 2007 M12 composite CS+B+CsA(s)+MPS 13 75 17.3%

CS+B+CsA(s)+MPS 16 66 24.2%

74 Vincenti 2007 M6 composite CS+B+CsA(s)+MMF 43 336 12.8%

CS+B+Tac(s)+MMF 34 346 9.8%

81 Silva 2007 M12 composite CS+B+CsA(s)+MMF 36 212 17.0%

CS+B+Tac(s)+MMF 30 214 14.0%

CS+B+Tac(s)+MMF 32 212 15.1%

No First Author Year Endpoint Treatment combination n N %

83 Tedesco-Silva 2007 M12 composite CS+CsA(r)+EVR 31 112 27.7%

CS+CsA(r)+EVR 32 125 25.6%

1125 Tedesco-Silva 2007 M12 composite CS+B+CsA(r)+EVR 27 139 19.4%

CS+B+CsA(r)+EVR 19 117 16.2%

72 Budde 2007 M12 composite CS+B+CsA(r)+MMF 8 44 18.2%

CS+B+CsA(s)+MMF 9 45 20.0%

82 Tedesco-Silva 2006 M12 composite CS+CsA(r)+FTY 100 231 43.3%

CS+CsA(s)+FTY 69 224 30.8%

CS+CsA(s)+MMF 70 229 30.6%

95 Salvadori 2006 M12 composite CS+CsA(r)+FTY 106 224 47.3%

CS+CsA(s)+FTY 71 219 32.4%

CS+CsA(s)+MMF 68 225 30.2%

107 Scholten 2006 M6 BPAR CS+B+CsA(s)+MMF 10 63 15.9%

CS+B+Tac(s)+MMF 4 63 6.3%

119 Mulgaonkar 2006 M12 composite CS+CsA(r)+FTY 35 74 47.3%

CS+CsA(r)+FTY 17 72 23.6%

CS+CsA(s)+FTY 17 76 22.4%

CS+CsA(s)+MMF 15 39 38.5%

127 Kamar 2005 M12 composite CS+B+CsA(s)+MMF 23 97 23.7%

CS+B+CsA(s)+MMF 29 100 29.0%

142 Vítko 2005 M6 BPAR B+Tac(s) 40 153 26.1%

CS+Tac(s)+MMF 12 147 8.2%

Tac(s)+MMF 46 151 30.5%

167 Hamdy 2005 M12 BPAR CS+B+MMF+S 9 67 13.4%

No First Author Year Endpoint Treatment combination n N %

CS+B+Tac(r)+S 12 65 18.5%

179 Mendez 2005 M6 BPAR CS+Tac(s)+MMF 20 176 11.4%

CS+Tac(s)+S 24 185 13.0%

182 Lorber 2005 M12 composite CS+CsA(r)+EVR 51 194 26.3%

CS+CsA(r)+EVR 48 193 24.9%

CS+CsA(r)+MMF 54 196 27.6%

235 Parrott 2005 M12 BPAR B+CsA(s) 15 52 28.8%

CsA(s) 24 56 42.9%

246 Vítko 2004 M12 composite CS+CsA(s)+EVR 60 198 30.3%

CS+CsA(s)+EVR 58 194 29.9%

CS+CsA(s)+MMF 61 196 31.1%

308 Salvadori 2004 M12 composite CS+CsA(s)+MMF 59 210 28.1%

CS+CsA(s)+MPS 61 213 28.6%

312 Pescovitz 2003 M12 BPAR CS+CsA(s)+MMF 4 25 16.0%

CS+D+CsA(s)+MMF 7 50 14.0%

354 Charpentier 2003 M12 BPAR CS+AZA+CsA(r) 16 42 38.1%

CS+AZA+S 17 41 41.5%

371 Lawen 2003 M12 BPAR CS+B+CsA(s)+MMF 12 59 20.3%

CS+CsA(s)+MMF 18 64 28.1%

385 Sadek 2002 M12 composite CS+AZA+CsA(s) 73 157 46.5%

CS+CsA(s)+MMF 52 162 32.1%

395 Campos 2002 M12 BPAR CS+AZA+CsA(s) 31 80 38.8%

CS+AZA+Tac(s) 29 84 34.5%

396 Montagnino 2002 M12 BPAR CS+AZA+CsA(s) 116 271 42.8%

No First Author Year Endpoint Treatment combination n N %

CS+AZA+Tac(s) 61 286 21.3%

424 Chang 2002 M12 BPAR CS+AZA+Tac(s) 38 121 31.4%

CS+Tac(s) 40 124 32.3%

436 Ponticelli 2001 M12 BPAR CS+AZA+B+CsA(s) 32 168 19.0%

CS+AZA+CsA(s) 52 172 30.2%

452 Squifflet 2001 M6 BPAR CS+Tac(s) 29 82 35.4%

CS+Tac(s)+MMF 4 71 5.6%

CS+Tac(s)+MMF 12 79 15.2%

461 Kahan 2001 M6 composite CS+CsA(s)+EVR 10 35 28.6%

CS+CsA(s)+EVR 8 34 23.5%

CS+CsA(s)+EVR 14 34 41.2%

475 Busque 2001 M6 BPAR CS+AZA+Tac(s) 8 23 34.8%

CS+CsA(s)+MMF 2 21 9.5%

CS+Tac(s)+MMF 2 23 8.7%

481 Calconi 2001 M12 BPAR CS+AZA+Tac(s) 72 239 30.1%

CS+Tac(s) 71 236 30.1%

488 MacDonald 2001 M12 composite CS+CsA(s) 65 130 50.0%*

CS+CsA(s)+S 68 219 31.0%*

CS+CsA(s)+S 75 227 33.0%*

492 Johnson 2000 M12 BPAR CS+AZA+Tac(s) 13 76 17.1%

CS+CsA(s)+MMF 15 75 20.0%

CS+Tac(s)+MMF 11 72 15.3%

510 Kahan 2000 M12 composite CS+AZA+CsA(s) 54 161 33.5%

CS+CsA(s)+S 75 284 26.4%

No First Author Year Endpoint Treatment combination n N %

CS+CsA(s)+S 54 274 19.7%

526 Kreis 2000 M12 BPAR CS+CsA(s)+MMF 7 38 18.4%

CS+MMF+S 11 40 27.5%

539 Kahan 1999 M12 BPAR CS+CsA(r)+S 5 47 10.6%

CS+CsA(s) 8 25 32.0%

CS+CsA(s)+S 16 77 10.6%

585 Shapiro 1999 M12 BPAR CS+Tac(s) 47 106 44.3%

CS+Tac(s)+MMF 27 102 26.5%

596 Kahan 1999 M12 composite CS+B+CsA(s) 71 173 41.0%

CS+CsA(s) 101 173 58.4%

597 Nashan 1999 M6 BPAR CS+CsA(s) 63 133 47.4%

CS+D+CsA(s) 39 140 27.9%

647 Mendez 1998 M6 BPAR CS+AZA+Tac(s) 19 59 32.2%

CS+Tac(s)+MMF 5 58 8.6%

CS+Tac(s)+MMF 18 59 30.5%

652 Amenábar 1998 M12 BPAR CS+AZA+CsA(r) 53 124 42.7%

CS+CsA(s) 51 126 40.5%

662 Vincenti 1998 M6 BPAR CS+AZA+CsA(s) 47 134 35.1%

CS+AZA+D+CsA(s) 28 126 22.2%

636 Nashan 1997 M12 BPAR CS+B+CsA(s) 72 190 37.9%*

CS+CsA(s) 102 186 54.8%*

682 Mayer 1997 M12 BPAR CS+AZA+CsA(s) 66 145 45.7%*

CS+AZA+Tac(s) 78 303 25.9%*

693 Danovitch 1997 M12 BPAR CS+AZA+CsA(s) 67 166 40.4%

No First Author Year Endpoint Treatment combination n N %

CS+CsA(s)+MMF 33 166 19.9%

CS+CsA(s)+MMF 37 167 22.2%

738 Keown 1997 M6 composite CS+AZA+CsA(s) 83 166 50.0%

CS+CsA(s)+MMF 57 164 34.8%

CS+CsA(s)+MMF 66 173 38.2%

M6: Month 6, M12: Month 12, composite consists of BPAR, graft loss, death with or without lost to follow-

up. CS=corticosteroids, AZA=azathioprine, CsA=cyclosporine A, Tac=tacrolimus, EVR=everolimus,

S=sirolimus, B=basiliximab, D=daclizumab, MMF=mycophenolate mofetil, MPS=enteric-coated

mycophenolate sodium, (s)=standard dose, (r)=reduced dose. * Kaplan-Meier estimates were published

and extracted, number of event was derived (n = KM-estimate x N).

Table 2: Difference of event proportions between control group and putative placebo

Analysis estimate standard error 95% C.I.

Maximum Likelihood analysis

All selected studies (51 studies) 0.2458 0.02807 (0.189, 0.302)

Sensitivity analysis (14 studies) 0.3066 0.05549 (0.187, 0.426)

Excluding studies with mTOR inhibitors,

FTY720, AZA, Tac; including studies with or

without anti-IL2, CS, CsA, MPA

Bayesian analysis

All selected studies (51 studies) 0.229 0.030 (0.173, 0.288)

Sensitivity analysis (14 studies) 0.256 0.07 (0.113, 0.390)

Table 3: Non-inferiority margins derived from hybrid approach

Historical information Failure rates to be observed in the control group (πC)

θPS SEPS n λ 0.10 0.15 0.20 0.25 0.30

0.2458 0.02807 300 0.00 0.21857 0.22234 0.22457 0.22604 0.22705

0.2458 0.02807 300 0.25 0.16746 0.17013 0.17165 0.17262 0.17328

0.2458 0.02807 300 0.50 0.11469 0.11616 0.11696 0.11745 0.11778

0.3066 0.05549 300 0.00 0.23199 0.23849 0.24274 0.24572 0.24787

0.3066 0.05549 300 0.25 0.18018 0.18557 0.18896 0.19128 0.19293

0.3066 0.05549 300 0.50 0.12657 0.13030 0.13250 0.13394 0.13494

Note: To derive a conservative NI margin, for this calculation the failure rate in the C group is assumed to

be 5% higher than in the T group, e.g. if the failure rate is 0.2 in the C group the assumed observed rate in

the T group is 0.15.

Figure 1 Probability of type I error as function of number of patients per arm,

Hybrid approach (solid line), 95/95 rule (dotted line), synthesis method (dashed line)

Figure 2 Non-Inferiority margin as a function of number of patients per arm,

Hybrid approach (solid line), 95/95 rule (dotted line), synthesis method (dashed line)

Figure 3: Predicted and observed proportion of events, Control (grey points)

Figure 4: Random study effect as function of year of publication

Figure 5: Estimated event proportion of the control group by year of publication