Hot Topics in Clinical Trials

Graybill Conference VII Biopharmaceutical Statistics June 11, 2008

Scott Evans, Lingling Li, LJ Wei, Marvin Zelen Program for Quantitative Sciences in Medicine Department of Biostatistics Harvard University Meta Analysis Introduction What is Meta Analysis

LJ Wei z What is meant by the word “Meta-analysis” Harvard University ¾ Meta is Greek for “later in time” ¾ Meta is now used to denote something that goes to a higher level or is more comprehensive. ¾ How is an analysis made more comprehensive? z In empirical research, there are often multiple studies addressing the same research question ¾ A standard analysis attempts to reach a conclusion based on a single study without reference to any other studies. ¾ A meta-analysis attempts to reach a conclusion based on a set of studies that address the same hypothesis.

Introduction Introduction History of Meta Analysis Why Meta Analysis z In 1805, Legendre developed least squares to combine data on the orbits z There are several reasons for conducting a meta-analysis of of comets from different observatories. the results of previous studies: z In 1930’s, statisticians working in agricultural research developed methods ¾ The increasingly large # of research studies for combining the results of studies. Most notable are Fisher and ¾ 40,000 journals for the sciences Cochrane. ¾ 1 article every 30 seconds 5000 4000 z In 1960’s, Cohen popularized the notion of effect size for use in sample 3000 size determination in the social and behavioral sciences 2000 1000 ¾ Effect size measures the differences between null hypothesis and the truth 0 ¾ Effect size + sample size determines the power. 1986 1991 1996 2001 z In 1976, Grass published an article “Primary, secondary and meta-analysis ¾ Unsystematic expert reviews of an area of research are often biased or of research”. This is when the term “meta-analysis” was first used. years behind the current research. ¾ Systematic and quantitative reviews are needed to summarize findings in a timely manner without bias. Formulating Hypothesis and Principles of Meta-analysis Effect Measures

z Meta-analysis is typically a two stage process z Before conducting a meta analysis, it is important to decide 1) Summary statistic calculated from each study. the hypothesis or aim of the analysis. When formulating a ¾ For controlled trials, these values describe the treatment effects hypothesis for meta-analysis, it is important to determine observed in each trial. 2) Pooled effect is calculated by combining treatment effect ¾ the precise question the meta-analysis aims to address estimates from individual studies. ¾ whether the meta analysis is exploratory or hypothesis testing ¾ Typically a weighted average of individual effects ¾ Hypothesis testing: is the intent of the study to provide a definitive test (usually a test of average effect = 0)

z The combination of treatment effect estimates across ¾ Exploratory: are there variations in the treatment or characteristics of the studies may assume studies that lead to better outcomes? ™ Fixed effects: treatment effects the same across studies. ¾ One also needs to select an appropriate effect measure ™ Random effects: treatment effects ~ a distribution across studies.

Type of Data and Effect Measures Type of Data and Effect Measures z Dichotomous or binary outcome z Ordinal outcome ¾ Takes values y < y < … < y ¾ when events of interest are rare 1 2 K ¾ Example: “mild”, “moderate” and “severe”. ¾ 1 – p1 # 1 and 1 – p0 # 1 Î RR # OR ¾ When the number of categories is large, such data are often ¾ essential to assess the absolute risk in addition to relative risk analyzed as continuous data.

¾ RR and OR = f if there are no events in the control group ¾ One may transform ordinal data into binary data by combining adjacent categories.

¾ RR and OR not defined if both groups have zero events ¾ Proportional odds ratio under a proportional odds model ¾ Standard procedures either exclude studies with 0/0 events or add 0.5 to empty cells. logit P(Y d yk | Trt) D k  ȕ˜Trt

¾ E, the log-odds ratio, summarizes the treatment effect Statistical Methods for Combining Fixed Effects Results Across Studies Vote Count z What is the true effect? Depends on the underlying ¾ Consider # of studies in favor of the conclusion (say, assumption about the study specific effect reach the 0.05 level of significance ) and examine if they are the majority ¾ Fixed Effects Assumption ¾ Assumes that all studies have the same true effect ¾ This approach has been used a lot due to its simplicity, ¾ Variability only within each study but has several drawbacks ¾ Precision depends mainly on study size ¾ Significance depends on study sample size and effect size. ¾ Random Effects Assumption ¾ Even if the null hypothesis is wrong and studies are not small, the percentage of trials reaching significance could still be less than 50% ¾ Studies allowed to have different underlying or true effects Î low power of detecting a treatment effect ¾ Allows variation between studies as well as within studies ¾ Vote counts do not provide an estimate of effect size. z Basic assumption: study results are independent.

Fixed Effects Fixed Effects Pooling Using Effect Sizes Pooling Using Effect Sizes

¾ Binary Outcomes

¾ Since Glass’s work in 1976, combining effect sizes has ¾ When the event rates are low or trial sizes are small, the standard become the main form of meta-analysis. error estimates used in the inverse variance method may be poor. ¾ Cochrane-Mantel-Hansel uses a different weighting scheme that ¾ Suppose the estimated effect sizes are depends upon the effect measure (eg RR, OR, RD). { ˆ , i 1,..., S} Ei ¾ Cochrane-Mantel-Hansel pooled OR: ¾ To ascertain the true underlying effect, a common S S m (n  m ) OR MH wˆ MH OR wˆ MH wˆ MH 0i 1i 1i ¦ i i ¦ i i approach is to consider a weighted average of the effect i 1 i 1 n1i  n0i estimates from individual studies: E S S ith Study Event No Event Total ˆ ˆ m (n  m ) wi Ei wi OR 1i 0i 0i ¦ ¦ Intervention m1i n1i -m1i n1i i i 1 i 1 m0i (n1i  m1i ) Control m0i n0i -m0i n0i Between Study Heterogeneity Between Study Heterogeneity

z Testing for heterogeneity z The key assumption of fixed effects meta analysis S Q wˆ (ȕˆ ȕˆ )2 ~ F 2 under H methods is that all primary studies are estimating ¾ Cochran’s Q-test: ¦ i pooled i S 1 0 i 1 the same underlying true effect ¾ Provides a measure of between study variation. z The underlying effects across studies may be ¾ Other descriptive measures of heterogeneity ¾ H statistic:H Q /(S 1) has mean 1 under H . heterogeneous 0 ˆ ¾ Hoggins and Thompson (2002) suggested: H > 1.5 Îcaution regarding z Each study effect sizeEi is estimating an individual heterogeneity; H < 1.2 Î little heterogeneity population effect Ei. ¾ I2 statistic = (H2 –1)/H2 E z ˆ ¾ % of total variability in effect size due to between study variation As study sample size Ni Æ f, i o Ei ¾ I2 ~ 0 Î little heterogeneity; I2 ~ 1 Î high heterogeneity z Some of the Ei may be the same, but not all of them. ¾ termed the “inconsistency” of the trials included in meta-analysis and has become a preferred measure of heterogeneity.

Meta Regression Meta Regression Special Cases z The pooled effect size estimates the average effect across all z The DerSimonian and Laird (1986) Model: studies Yˆ ˆ z In the presence of heterogeneity i Į  ȕi ] i ¾ the validity of such an average measure? ¾ not a single population effect size that applies to all studies z The Begg and Pilote (1991) Model: ¾ random effects pooling addresses heterogeneity to some extent ˆ ˆ z Meta regression Yi XiĮ  ȕi ] i ¾ provide an alternative approach that allows exploration of why studies have varied effect sizes. ¾ This model allows the inclusion of single treatment historical controls as well as comparative trials in a treatment effect assessment. ¾ one uses characteristics of the studies to explain the excess variation in effect sizes ¾ Thompson and Higgins (2002) reviewed several meta-regression methods Example Effect of Rosiglitazone on MI or CVD Deaths

z Nissen and Wolski (2007) performed a meta analysis to examine whether Rosiglitazone (Avandia, GSK), a drug for treating type 2 diabetes mellitus, significantly increases the risk of MI or CVD related death. Exact Procedure for z Avandia was introduced in 1999 and is widely used as monotherapy or in fixed-dose combinations with either Avandamet or Avandaryl. Combining 2x2 Tables for The original approval of Avandia was based on the ability of the Rare Events drug to reduce blood glucose and glycated hemoglobin levels. z Initial studies were not adequately powered to determine the effects of this agent on microvascular or macrovascular complications of diabetes, including cardiovascular morbidity and mortality.

Exact Meta-Analysis Procedure Combining Exact Intervals

z Questions:

z Could we combine information across studies without z excluding studies with 0 events or z artificial imputation?

z Could we make exact inference without relying on possibly inaccurate large sample approximations when z the total number of studies is small, or z the sample sizes of individual studies are small, or z when the event rates are low.

• Event Rates from 0% to 2.70% for MI • Event Rates from 0% to 1.75% for CVD Death Exact Meta-Analysis Procedure Exact Meta-Analysis Procedure Combining Exact Intervals Combining Exact Intervals

z Thus, we proposeK to include ' in the 100(1 – D)% level z For a given confidence levelK, Iˆ (K) Study 1 1 confidence interval (a, f) if z one may obtain S study specific one-sided S K-level confidence intervals for the risk Iˆ ( ) Study i K i K t(', ) w {y (', ) K} t c difference. ¦ i i i 1 z each interval is constructed based on the z where wi is a study specific positive weight (e.g. sample size) Iˆ (K) Study S data only from its corresponding study. S K z c is chosen such that P(T(K) < c) dD, S T ( ) w (B K) z For any given value of ', we examine whether ' is the true z ¦ i i is the null counterpart of t(',K) i 1 value. If ' = ' , then by the definition of K-level confidence 0 z {Bi, i = 1, …, S} are n independent Bernoulli random variable intervals with “success” probability of K. z any given such interval should contain ' with probability K z We repeat this process will all other possible values for z on average ' should belong to at least 100K% of the above S ' independent intervals. and obtain the final interval.

Example Exact Meta-Analysis Procedure Effect of Rosiglitazone on MI or CVD Deaths Combining Exact Intervals z Similarly, we obtain combined (1 – D)% one sided interval z For RR or OR effect measures

(–f, b) based on the corresponding one-sided study specific z unless prior information about the underlying event rates is intervals. available, it is not clear how to utilize studies with zero events without continuity correction. z Thus, (a, b) would be a (1 – 2D)% two-sided interval for the risk difference. z RD may be used as an alternative effect measure z appealing interpretation ˆ z exact inference may be used z A point estimator for '0 may be obtained as ' , the mid-point of the intersection of all two-sided intervals for ' across all 0 z We examine the effect of Rosiglitazone on MI or CVD possible values of D deaths based on ' = RD (Rosiglitazone – Control). z 'ˆ is the value of ' with the least evidence of being rejected as the truth. n 1 1 2 ( ȕ ˆ 1  ȕ Random EffectsMetaAnalysis 1 StudyData 1 ) ~ CVD Death N ( E 0

,

1 V ˆ 1 2 ) P-value =0.83 95%CI: (-0.13, 0.23)% ' ˆ Exact Inference

n 1 2 2 ( 0 ȕ ˆ . 2 063 StudyData 2  ȕ 2 ) Super Population E % ~ 2 N ( 0

, V ˆ ȕ 2 2 ) ~ ...... F( n S ˜ 1 2 - ) 1 ( ȕ ˆ S - 1 Study S-1Data  ȕ E S Asymptotic Inference - 1 S-1 ) P-value = 0.05 95% CI: (0.00, 0.31)% ' ~ ˆ N

( 0 0

,

. V 11 ˆ S 2 - 1 % ) n StudyData S S 1 2 E ( ȕ S ˆ S  ȕ S ) ~ N ( 0

, V ˆ S 2 ) z z

the RandomEffectsDistribution E Suppose weareinterested inestimating themedian of of procedures forthequantiles Wang etal(2008)proposed intervalestimation the number ofstudies tobelarge. z Non-parametric Inferencefor i Random EffectsMetaAnalysis

denoted by by inverting asigntest: If ¾ The null distribution of T( E i Non-parametric Estimation oftheMedian Non-parametric known, exact confidence intervalfor known, exact confidence in MetaAnalysis P 0 . T

( P )

¦ P i S 0 1 ) +S/2 is aBinomial(S,0.5). { I

( E i

E P i ) without requiring  0 . 5 P } 0 can beobtained Random Effects Meta Analysis Random Effects Meta Analysis Non-parametric Estimation of the Median Non-parametric Estimation of the 100pth Percentile P Eˆ th ¾ Alternatively, one may replace I ( i P ) with a measure ¾ For the 100p percentile, the test statistic is S P E P E of likelihood for the event i ˆ ˆ ˆ Tp ( ) ¦[){(  i ) /V i} 0.5] ¾ Example: the observed coverage level of the interval (-f,P) i 1 P for Ei which is E ¾ Unconditionally T ˆ ( ) is asymptotically Binomial(S,p) ˆ ˆ p P ){(  i ) /V i} P P ¾ The test statistic based on the coverage level is Pˆ S P ¾ The null distribution of T p ( P E ) can be approximated by ˆ Eˆ V T( ) [){(  i ) /Vˆi} 0.5] S ¦ * i 1 ˆ ˆ T p ( ) ¦| ){(  i ) / i} 0.5 | (2H i 1) ¾ Studies with data that are more informative for the event E i P i 1 would yield coverage level closer to either 0 or 1 and thus carry more weight in the test statistic. ¾ {Hi, i=1,…,S} ~ Bernoulli(p) independent of data

Example Effect of ESA on the Risk Mortality

95% Confidence Intervals for the Hazard Ratio

Median 25th Percentile 75th Percentile DL (1.01, 1.20) ~ T (˜) with I(˜) (0.90, 1.26) (0.49, 0.93) (1.25, 1.72) Tˆ(˜) with )(˜) (0.94, 1.21) (0.70, 0.99) (1.18, 1.48) Practical Questions Data Monitoring in Clinical Trials Using Prediction • Should the trial be stopped? – For efficacy? – For futility? Scott Evans Harvard University • Are there non-efficacious arms that should be dropped? Graybill Conference – E.g., if there are several arms (e.g., doses) June 11, 2008

Motivation Limitations of Many Traditional Methods

• Answering these questions has: • Do not provide – Estimates of effect or associated precision (only – Ethical attractiveness test statistics, p-values, and decision rules) • Fewer patients generally exposed to inefficacious and potentially harmful therapies • Cannot evaluate “clinical relevance” – Information regarding the reasons for: – Economical advantages • High p-values (or test statistics): • Smaller expected sample sizes and shorter expected duration – Negligible effect vs. insufficient data than designs without interim analyses • Low p-values (or test statistics): – Saving time, money, and other resources – Large effect vs. lots of data Repeated Confidence Intervals Limitations of Repeated CIs

• Simultaneous coverage of all sequential CIs • At the interim, we wish to weigh the options of stopping vs. continuing

• Provides estimates of effects sizes • But we do not know the ramifications of continuing

• Methods do not answer “What will happen if the trial • Allows for flexibility in decision making continues?” – Can terminate trial based on current CI, but overall – What effect size estimates and associated precision will be confidence level is guaranteed regardless of way that observed if the trial continues? the decision to stop is made • Thus how do we weigh the options?

Interim Analysis Results: NARC 009 NARC 009 95% CI for 95% CI for 95% PI for 95% PI for Required Treatment N Mean Change Diff1 Diff2 Diff3 Diff4

• Randomized, double-blind, placebo-controlled, Placebo 31 (-0.35, -0.11) multicenter, dose-ranging study of prosaptide (PRO) for

the treatment of HIV-associated neuropathic pain 2 mg 34 (-0.21, -0.04) (-0.04, 0.25) (-0.01, 0.21) (-0.16, 0.06) -0.54

• Subjects randomized to 2, 4, 8, 16 mg/d PRO or placebo 4 mg 34 (-0.38, -0.12) (-0.19, 0.16) (-0.14, 0.10) (-0.23, 0.01) -0.45 administered via subcutaneous injection 8 mg 32 (-0.18, -0.02) (-0.01, 0.28) (0.03, 0.23) (-0.15, 0.05) -0.56

• Primary endpoint: 16 mg 36 (-0.34, -0.09) (-0.16, 0.19) (-0.11, 0.14) (-0.21, 0.04) -0.54 – 6 week change from baseline in weekly average of random daily

Gracely pain scale prompts using an electronic diary 1: 95% CI for the difference in mean changes vs. placebo 2: 95% PI for the difference in mean changes vs. placebo assuming full enrollment, assuming current trend

3: 95% PI for the difference in mean changes vs. placebo assuming full enrollment, assuming per protocol, ˩placebo = - 0.17 and ˩drug = -0.34 4: Difference in mean changes needed in the remaining patients for the CI for the difference in mean changes to exclude zero (in favor of active treatment) at the end of the trial PIPs: Schema for Construction DMC Predicted Intervals Adjusted PI Observed dataset at interim point • Intuitive + Assumption of HR Calculate the • Practical “final” result – Provides information on effect size and associated precision (clinical relevance) – Invariant to study design (superiority vs. noninferiority) – Allows flexibility in decision process Simulate future A simulated complete outcome dataset at the end – Can use for binary, continuous, or time-to-event of the trial endpoints • 1 and 2 sample problems

PIPs: Schema for Construction Predicted Interval Plot DMC Adjusted PI 18M after the 2nd interim analysis (4Y from the Observed dataset start) Assumed HR = 0.975. at interim point

+ Assumption of HR Calculate the Current Interval “final” result [0.88, 1.08] Length:0.20

Simulate future A simulated complete

dataset at the end 5 25507595

outcome Estimateof Distribution Point Percentile of the trial In favor of Comb In favor of Mono therapy Simulate many times 0.9 1.0 1.1

and get many adjusted PIs Hazard Ratio CONSORT Diagram

Sensitivity Analyses N=XX Screened N=XX Screening Failure Reason 1 XX Reason 2 XX

N=XX Randomized • Perform sensitivity analyses to evaluate the N=XX Received No Medication Reason 1 XX effect of the uncertainty of the model Reason 2 XX assumption by creating PIPs for various assumed models N=XX Treatment A N=XX Treatment B

– E.g., observed trend is true, HA is true, H0 is

true, optimistic/pessimistic case scenarios, etc. N=XX Completed N=XX On Study N=XX Completed N=XX On Study N=XX Withdrawn N=XX Withdrawn Study Study

N=XX Off Treatment N=XX Off Treatment N=XX On Treatment Reason 1 XX N=XX On Treatment Reason 1 XX Reason 2 XX Reason 2 XX

Mean Difference and 95% CI in Response Rates AE Summary

ITT Fatigue Per Protocol Hypertension

Headache Males Dry Mouth Females Paraesthesia

White Anemia Non-white Depression

-10% 0 10% 0510 15 20 25 30 00.5124816 Placebo Percent Relative Risk Difference in Response Rates Treatment If you were a DMC member, what is Should we re-think event-driven trials? your recommendation?

• Time-to-event endpoints Continue? Stop? – Power determined by number of events (numerator) due to estimation of relative risk Case #1 Case #2 At interim analysis At interim analysis • Absolute risk Relative Risk Absolute Risk Diff. – Powering on absolute risk may be more efficient [-0.04%, 0.12%] because it uses denominator data [0.3, 158] – Presentation of absolute risk may be more interpretable than relative risk HINT: Very wide HINT: Very tight. – Can still calculate relative risk The difference is at most 0.12% RANDOMIZATION Basic Ideas and Insights

Marvin Zelen Harvard University

Graybill Conference Ft.Collins, Colorado

June 11, 2008

Randomization Disadvantages of Randomization Each patient has the same opportunity, ƒ Patient or physician may not care to as any other patient, of receiving any of participate in experiment involving a the treatments under study. chance mechanism to decide treatment. Allocation of treatments to patients is generally carried out using a chance mechanism so that neither the patient ƒ May interfere with physician-patient nor the physician know in advance relationship which therapy will be assigned. Randomized clinical trials are regarded as the best way to carry out clinical trials. 3. Conditioning on Sample Size

Two Methods of Randomization Cluster Sampling

Up to now we have considered randomization in which an individual experimental unit (patients) are randomized to treatments.

In some situations it is more feasible to randomize treatments to groups of experimental units ; i.g. groups may be patients in a hospital , families , geographic regions. Cluster randomization or cluster sampling is used to describe this kind of random assignment.

We will show that cluster and individual randomization are equivalent if the outcomes have low probabilities of ocurring. Hence Z=(S pS ) / pqS Is asymptotic a Idealized Clinical Trial Process N(0,1)

Where p = na/ N , q = 1 –p, S = 6 Yi

Population with Disease

Random Sample of Patients

A Conclusion : Cluster Sampling from a Poisson Randomization B distribution is equivalent to individual randomization.

Random Sample of Patients ??? Investigations of Local Inference : ƒ Nearly all clinical trials do not have a random Power sample of patients . ƒ Outcome variables : continuous, binomial, survival

ƒ Randomized multi center trials (two treatments) ƒ Only a local inference can be made unless additional assumptions are assumed. ƒ Methodology conditions on the number of patients randomized within a center (conditions on ancillary statistic)

ƒ The randomization process can serve as the ƒ Study design is permuted blocks of size four : Sample size for each treatment is equalized for every basis for making a local inference. fourth patient entered on trial.

ƒ Group sequential and fixed sample size. ƒ In most situations power will be increased as the inference is more narrow. Thank you for coming ! 6bgViHgVaT (qH`cYR 2

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Noninferiority Trials • Noninferiority Trials – Design Issues •Fixed Margin Scott Evans • Combination Approach • Precision-Based Approach Harvard University • Synthesis Method – Analyses and Reporting • Interim Analyses • CONSORT Graybill Conference • ITT vs. PP • Missing Data June 11, 2008 • Switching between Noninferiority and Superiority

Background on Scientific Designs Single Arm Study to Evaluate an Intervention • Single arm study • Limitations:

– Administer an intervention to a group of – Cannot control for “natural history” patients and see if they improve or are cured • People may have improved anyway

– Placebo-effect (or Hawthorne effect) • Patients/clinicians believe that they are getting better because of treatment; manifesting itself in better outcomes – E.g., pain

– Miss a “good result” when you observe no change but patients would have gotten worse if left untreated. P = efficacy of new1 treatment A p = efficacy of Placebo Controlled Trial control2 group B

C • Randomize to one of two arms Superiority:

– New intervention or placebo D HO: p1-p2 = 0 E HA: p1-p2 z 0 • Blind the intervention to patients and investigators when possible F

• Analysis compares the two arms with respect to response 0 p1-p2

Absence of Evidence is Not Evidence of Absence Noninferiority Trial

• Hypothesis testing is analogous to a court trial: • Randomize to one of two arms – New intervention or active-control

– People are assumed innocent until proven guilty • Blind the intervention to patients and investigators when •H: Innocent 0 possible •HA: Guilty • Analysis compares the two arms with respect to response – If VERDICT = Not Guilty (i.e., do not reject H0), then: • We cannot say that we have proven innocence • Need to show new intervention is “no worse” than the • We say that we failed to find enough evidence to prove guilt active control – There is a subtle but important difference between the two Noninferiority Trial Statistical vs. Clinical Significance

• Decide on a NI margin, M (more later) • Not the same thing!

• Analysis – Get a confidence interval (CI) for the difference between arms (new intervention minus active control with respect to efficacy) and note if lower bound of CI is within the NI region

Example: ACTG 116A Example: FDA SGE Experience

• DDI vs. placebo is not ethical with availability of • A randomized, double-blind, multicenter AZT study comparing the efficacy and safety of Piperacillin/Tazobactam (PT, 4G/500MG) • Endpoint and Imipenem/Cilastatin (IC, – Time to AIDS defining event or death 500MG/500MG) administered intravenously every six hours to treat • Noninferiority nosocomial pneumonia in hospitalized – If upper bound of CI for HR (DDI vs. AZT) < 1.6 patients • DDI (500mg): HR=1.02 90% CI = (0.79, 1.33) • DDI (750mg): HR=1.04 90% CI = (0.80, 1.34) Noninferiority Trial

Example: FDA SGE Experience It is impossible to show that two treatments have identical efficacy. Instead we choose a NI margin, M, and seek to • Lower bound of 95% CI for the difference in prove that ȕTC is less than M. This is done by testing the null response rates (PT-IC) is –0.066 (> –0.20) hypothesis: – Was a margin of 20% too large? H : > M – Noninferiority would be shown for a margin as small as 0 ȕTC 7% against the one-sided alternative • Result H : < M – PT was noninferior to IC 0 ȕTC – Approved by the FDA Note: The traditional roles of the hypotheses are reversed.

T is Often Better than C in Other Ways Assumption: Constancy

• Better safety profile • Historical data: – C showed superiority to P in historical trial ( > 0) • Less expensive ȕCP,H • More convenient to administer • Constancy Assumption – Less invasive – ȕCP,H = ȕCP,NI if placebo was present in the NI trial – Fewer pills • May not be the case in the presence of resistance development or with differing trial conduct (e.g., administration of • Easier to comply treatment, differences in populations or endpoints, etc.) • Shorter treatment duration – Not verifiable in current trial (without placebo) – Implication: to conduct the NI trial in the same manner

as the trial that established ȕCP > 0 Assumption: Assay Sensitivity Choice of Active Control

• Trial is able to detect differences between • Must have clinical efficacy treatments if they exist – Of substantial magnitude – That is precisely estimated – With estimates that are relevant to the setting in which • Need a sensitive enough instrument to measure the NI trial is being conducted • Constancy assumption response and detect differences if they exist – Preferably measured by multiple controlled trials – Otherwise, all interventions will display similar responses due to the insensitivity of the instrument • Regulatory approval does not necessarily imply that an intervention can be used as an active control in an NI study – Superiority to placebo must be reliably established

Choice of the Active Control Biocreep

• Must have assurance that the active control • The tendency for recently demonstrated would be superior to placebo if a placebo noninferior treatments to be active controls in new arm was employed in the trial NI trials even though they are slightly inferior to historically proven active controls vs. placebo (D’Agostino, SIM, 2003)

• If A is noninferior to B and B is noninferior to C, then it does NOT necessarily follow that A is noninferior to C Choice of Active Control Choice of Active Control

• Example: OHARA is developing a treatment trial • Similar issues have arisen with treatments for oral candidiasis (OC) in Africa within the that were once shown to be effective but ACTG system may no longer be effective because of the – Fluconazole is not readily available in Africa (too expensive) development of resistance – Nystatin is used in many places as the standard of care – Example: MRSA – Gentian Violet (GV, an inexpensive topical agent) showed excellent in vitro activity – A NI trial of GV compared to Nystatin was proposed

MRSA DMC Discussion

• Methicillin-resistant Staphylococcus aureus • ID clinicians insist antimicrobials are "highly effective" in treating skin infections, but seem – Bacterial infection that has become resistant to unable to site evidence to back this claim other antibiotics (such as penicillin, amoxicillin, than anecdotal (and then claim it is "unethical" to methicillin) do any other trial design other than NI). – Lives on the skin • Without the data to support one of the drugs as the – Community acquired "control" based upon reliable and reproducible • Spread through contact evidence of the magnitude of the benefit of the control compared to placebo, the results of an NI trial are not meaningful Choosing the Noninferiority Margin (M) Traditional Approach Choosing the Noninferiority Margin (M)

• Subjective but structured Investigators frequently set M equal to half of the estimated – Combination of statistical reasoning and clinical effect of the active control (C) relative to placebo (P) from the judgment (CHMP Guidance) historical evidence. That is, set M ˆ /2 • Concepts E CP, H – “Maximum treatment difference that is clinically irrelevant” – “Largest treatment difference that is acceptable in order This is known as “preserving a fraction of the effect”. Note to gain other advantages of the experimental that the method does not consider the fact that the estimate intervention” from historical data is subject to uncertainty.

• Design parameter is not present in superiority trials

Tamoxifen vs. Placebo: NSABP P1 Trial STAR Trial: Claiming NI Subset of Women t 50 years old Favors Placebo Favors Tamoxifen RR = 2.12 (1.52 - 3.03) • Thus the upper bound of the 95% CI estimate for the relative risk needs to be less

Interpretation: P increases than 1.56 the rate of invasive breast cancer incidence compared to Tam by 112% (CI: 52% to 303%)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Relative Risk for Invasive Br Ca: Placebo / Tamoxifen Failed Noninferiority Trials Tamoxifen vs. Placebo: NSABP P1 Trial Poor Choice of Noninferiority Margin Subset of Women t 50 years old Favors Placebo Favors Tamoxifen In the SPORTIF trials, ximelegatran was compared to RR = 2.12 (1.52 - 3.03) warfarin for stroke prevention in atrial fibrillation patients. The event rates in the warfarin group (control) were 2.3% (Sportif III) and 1.2% (Sportif V). Based on the historical NI margin: Lower bound evidence, the sponsor chose an absolute NI margin of 2%. of the 95% CI estimate Because of the low event rates in the control arm, this for the RR of Tamoxifen vs. placebo resulted in a NI margin that allowed the conclusion of NI even if the trial did not rule out a doubling of the event rate. RR = 1.52 1.28 1.84 The common theme in these trials was that a NI margin based 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 on the effect of the comparator drug was not consistent with Relative Risk for Invasive Br Ca: Placebo / Tamoxifen the community standard for therapeutic equivalence.

Sample Size NI Trials May Not Be Appropriate When:

• Still only get Į=0.025 on the one side • Constancy assumption is in doubt – Using 0.05 lowers the level of evidence for drawing conclusions vs. accepted practice in superiority trials • Assay sensitivity is in doubt • General wisdom (including regulatory agencies) is to use 2-sided 95% CIs to evaluate both superiority and NI • Historical data of active control effect over placebo are thin • Important to power for per protocol analyses too – More on this later • Variability of active control effect is very large Testing for NonInferiority Fixed Margin Method To address O1, noninferiority, we determine a NI margin, M, which, if met will allow us to conclude that T is NI to C. M should be chosen based on clinical considerations, not the • Define NI margin M historical data regarding the effect of C relative to P. – Using data from historical trials • Note: subject to bias and uncertainty Given the margin, M, we test the null hypothesis

H10: ȕTC= M • Use the 2-sided 95% CI to rule out M Against the alternative hypothesis

H : ȕ < M • Too conservative? 1A TC Using standard methods for NI trials.

Testing for Superiority to Placebo Design and Analysis

Since the goal of the NI design is to reject both H01, the Assuming assay constancy, we test the null hypothesis: hypothesis of inferiority, and H02, the hypothesis of no difference relative to placebo, we perform sample size calculations for each test and choose N equal to the larger of the two sample sizes. H20: ȕTP (= ȕTC + ȕCP) = 0 The analyses do not require two unrelated tests. Since the against the alternative HA: ȕTP < 0 with the test statistic results from the historical trials are known at the time the NI trial is conducted, the two hypothesis tests can be reduced to two tests involving the estimated treatment effect of T relative Eˆˆ E TC,, NI CP H to C in the NI trial. The two tests can be expressed as VVˆˆ inequalities involving TC,, NI CP H ˆ ETC, NI

If we assume approximate normality of the estimates, this can If the estimate satisfies the more stringent of the two be done with standard methods. inequalities, we reject both H01 and H02 and achieve both objectives. Designs Based on Precision Inconsistency with Preservation of Effect?

• Based on principles of estimation rather than hypothesis • New intervention could look better than active testing – Do not specify explicit hypotheses control (point estimates) but not meet the • Avoid making the distinction between superiority and NI preservation of effect condition

• Specify the precision with which you want to estimate treatment differences (e.g., the maximum length of a CI for • Two trials with different active controls have the treatment effect difference) different standards for success – Power the study to estimate the effects with this precision – Interpret the CI as usual (ruling out effects in either direction as appropriate) • If new intervention is better than active control, – May wish to pre-specify a NI margin for regulatory purposes should the active control be withdrawn?

Synthesis Method Issues with Synthesis Method

• Combines standard errors from historical • Proper control of conditional type I error is not warranted trials and NI trial • Assumes no bias in historical point estimate – Note: not the standard error from a randomized – Often not the case with publication bias – Problematic when constancy assumption does not hold comparison • Cannot produce a fixed NI margin

• NI is not considered • No consensus on role of across-trial error – M is irrelevant • Too liberal? Interim Result: What Would You Recommend? CONSORT

CLINICALLY INFERIOR CLINICALLY NONINFERIOR

A B

C D Noninferiority: E

HO: p1-p2 > - ' F HA: p1-p2 >= - ' STATISTICALLY INFERIOR STATISTICALLY SUPERIOR

- ' 0 Noninferiority Margin p1-p2

Analyses Interpretation Issues

• 2-sided CIs are generally used • If active control displays different efficacy – Consistent between significance testing and than in prior trials vs. placebo, then the subsequent estimation validity of the pre-defined NI margin may – Consistent with ICH E-9 be suspect and the interpretation of – P-values are not appropriate treatment differences is challenging – Can we model the changes in the effect of C vs. P • May not have appropriate data as we need a • Choice of NI margin plays a direct role and comparison of C vs. P from multiple trials thus must be justified conducted at different times ITT vs. Per Protocol Idea: Analysis of Missing Data

• Sensitivity analyses are important • Consistent with the null hypothesis of the – ITT and Per Protocol should both be conducted NI trial – Need consistency of qualitative result (CPMP, 2000, points to consider) – E.g., continuous endpoint: impute reasonable expected value (i) for the active control and (i- • PP usually results in a larger effect size M) for the new intervention – ITT dilutes effects – E.g., binary data: impute expected proportion (p) for active control and (p-M) for new • PP usually has wider CIs intervention – Fewer patients than ITT • Then analyze using analysis of means

Switching from Superiority to Noninferiority Switching from Superiority to Noninferiority

• Generally not acceptable to go from failing • May be feasible if: – Noninferiority margin was pre-specified (or can be to demonstrate superiority to NI justified, which is difficult to do) – Unless a NI margin was pre-specified • Must be based on external information and not chosen to fit the data – Post-hoc definition of NI margin is difficult to – ITT and PP show similar results justify – The trial was of high quality with few drop-outs and • Choice of NI margin needs to be independent of trial good adherence data – The control group displayed similar efficacy to trials vs. placebo – The trial was sensitive enough to detect effects Benefit:Risk

Benefit:Risk • Fundamental concept in clinical trials – Weighed by regulators in product approval Scott Evans decisions – Evaluated by sponsors to aid in development Harvard University decisions – Assessed by data monitoring committees during Graybill Conference interim analyses to make recommendations June 11, 2008

Benefit:Risk BRAT - PhRMA

• September, 2006 •Goal – Institutes of Medicine recommended that FDA – Develop a structured, transparent benefit:risk develop and continually improve a systematic framework and integrate it into the regulatory approach to benefit:risk review process • Quantitative and qualitative elements • December, 2006 • Pilot studies being planned – European Committee for Proprietary Medicinal Products (CPMP) called for improved methodology leading to a more systematic approach to benefit:risk analysis BRAT - PhRMA Benefit: Risk ? May be acceptable • Separate B:R balance by each indication with a very serious WINNER disease with no known • Consider all data cure Æ

• Incorporate uncertainty ? May not be acceptable with a disease that is BENEFIT • Evaluate temporal effects ? not life-threatening and other effective • Transparency via systematic, consistent, reproducible and safe treatment model LOSER options are available

RISK Æ

Challenges Challenges

• Clarity of objective • Disease-specific context – Toleration of toxicities for some indications but not – Benefit:risk of the population vs. the trial others cohort vs. an individual patient • Patient-specific context – E.g., benefits and risks are different for old vs. young • Generalizing benefit:risk assessment in clinical trials to a population • Population-specific context – Trials may not be representative of real patient – Multinational trials with differing cultures, ethics, and availability of medicines usage MRSA (The “Superbug”) Benefits and Risks Tradeoff

• Methicillin-resistant Staphylococcus aureus • FDA Advisory Committee (CDRH) – Bacterial infection that has become resistant to – “Substantial Equivalence” antibiotics (such as penicillin, amoxicillin, • Distinct from traditional concept of noninferiority methicillin) • Simultaneous evaluation of benefit and risk – NeuroStar™ for the treatment of Major – Lives on the skin Depressive Disorder – Community acquired • Repetitive transcranial magnetic stimulation (rTMS) • Spread through contact • Vs. Electroconvulsive Therapy (ECT) – Causes a seizure via electronic stimulation

Substantial Equivalence Censoring

• From my packet sent by the FDA: • Important safety data is often censored by the end of the study or by treatment discontinuation “the experimental device does not need to be as effective as the predicate device, if the clinical • Important efficacy data is often censored by SAEs data demonstrated that any reduction in effectiveness was off-set by an improvement in patient safety/risk” • Safety data often gathered after approval, but not always the case for efficacy data • What metric/weights? Asymmetry of Attention to ITT Principle Benefits and Risks • Passive collection of some safety data • Important with respect to safety data – Report only if abnormal • Need to follow patients that withdraw from – Cannot distinguish between normal (indicating treatment no safety issue) vs. missing data – Otherwise adverse outcomes may not be obtained as they can occur after withdrawal from exposure – Potential for informative censoring if subjects that withdraw are dissimilar to subjects that complete the study

Importance of Follow-up

• Carefully consider the length of T in design to W Proposed Methods evaluate safety

• Count events in interval of TS + TW to avoid informative censoring and avoid bias – More diligent follow-up needed on patients that discontinue the treatment early • Else can bias Kaplan-Meier estimates of cumulative incidence

• Lagakos, NEJM, 2006. Combined Marginal Analyses Benefit:Risk Ratio

• Current Practice • Advantages – Separate and marginal analyses of efficacy and safety – Easy to understand and communicate • Then informal (usually non-quantitative) aggregation of the two marginal analyses are conducted as an assessment of benefit:risk • Disadvantages – Does not account for the relative timing of these events • Meta-analyses of several trials – Does not account for the censoring by competing events – E.g., Integrated Summary of Efficacy and Safety (ISES) – Can be challenging to identify a threshold at which benefits and risks are neutralized

NNTB and NNTR Ratio based on NNT •Let ʌA and ʌB (> ʌA) be the incidence rates of a beneficial outcome in treatment groups A (control) • R = NNTB/NNTR and B (experimental) respectively, then – If the events of benefit and harm are of equal importance, then considering benefits and risks: • R=1, suggests that A and B are similar NNTB = 1/(ʌB – ʌA) • R>1, suggests that B is better than A since B provides benefits at a faster rate than providing • E.g., if ʌB – ʌA = 0.5 then NNTB=2 harms (relative to A) – Implying that on average if 4 patients are treated (2 on • R<1, suggests that B is worse than A since B each arm), then we expect one more beneficial outcome provides benefits at a slower rate than providing on treatment B than treatment A harms (relative to A) NNT and the Ratio based on NNT NNT Extensions

• Statistical inference based on NNT or R is • NNT for time-to-event data challenging – Altman et.al., BMJ, 1999. – Hutton, JRSS, 2000. – Lesaffre et.al., CCT, 1999. – Walter, SIM, 2001. • “Unqualified success” and “unmitigated – Walter & Irwig, SIM, 2001. – Grieve, PS, 2003. failure” – Thabane, Biostatistics, 2003. – Mancini and Schulzer, Circulation, 1999. – Duncan & Olkin, SIM, 2005. – Alemayehu et.al., JBS, 2006.

ECOG 1684: Q-TWiST Q-TWiST

• Quality-adjusted Time Without Symptoms or Overall Survival Toxicity (Gelber, et.al., Biometrics, 1989) Percent – Proposed to evaluate adjuvant therapies for breast 100 cancer 80 • Has been used in other disease settings – HIV, melanoma, rectal cancer, lymphoma, prostate cancer, 60 childhood AML 40 – Evaluates benefit:risk “trade-offs” in clinical trials 20 Interferon Alfa-2b Observation P = 0.06 0 0 1224364860728496 Months from Randomization ECOG 1684 Q-TWiST ECOG 1684: Q-TWiST

Toxicity summary Step 1: Define clinical health states • Grade 3 or worse toxicity occurred in 78% • Toxicity of patients – Time with grade 3 or worse treatment-related – Dosing delays or reductions occurred in 62% of toxicity patients during the IV phase and for 51% • The entire treatment duration was assigned to Tox if during the SQ phase any grade 3 or worse toxicity was experienced – Included constitutional, myelosuppression, • Relapse hepatotoxicity and neurological – All time following disease relapse •TWiST – All remaining survival time

ECOG 1684: Q-TWiST ECOG 1684: Q-TWiST Step 2: Partitioning overall survival Step 2: Partitioning overall survival Interferon Alfa-2b Observation Percent Percent 100 100

80 80

60 60

OS Rel 40 40 OS RFS 20 20 Tox TWiST

0 0 0 1224364860728496 0 1224364860728496 Months from Randomization Months from Randomization ECOG 1684: Q-TWiST Step 3: Compare treatments using weighted components Threshold Utility Plot

Treatment • Fundamental outcome of a Q-TWiST analysis Group – Compares treatments across combinations of weights Outcome Obs IFN Difference (95% C.I.)

Tox 0.0 5.8 5.8 (5.0 to 6.7) • Vertical axis TWiST 30.0 33.1 3.1 (-4.8 to 11.0) – Weight for time with toxic effects Rel 12.4 10.4 -2.0 (-6.2 to 2.3) Q-TWiST* 34.9 42.5 7.6 (0.0 to 15.1) u =.9, u =.4 Tox Rel • Horizontal axis OS 42.4 49.3 7.0 (-0.6 to 14.5) RFS 30.0 38.9 8.9 (0.8 to 17.0) – Weight for time after relapse Patients 137 143 • Plots contours of similar treatment effects *Q-TWiST = uTox x Tox + TWiST + uRel x Rel

Weight Coefficients ECOG 1684: Q-TWiST Q-TWiST Gain Analysis for fixed weights • 95 patients with melanoma provided their 10 patient-specific weights for the clinical health 8 states 6 4 Months • Applied to threshold analysis Gained 2 for 0 • 16% had preferences in the region of IFND-2b -2 -4 significant Q-TWiST gain with interferon -6 -8 • 84% had preferences in the region of non- -10 significant Q-TWiST gain 0 1224364860728496

Kilbridge KL, et al. J Clin Oncol 2001;19:812-23. Months from Randomization Kilbridge KL, et al. J Clin Oncol 2002;20:1311-18. Composite Endpoints Composite Endpoints: Advantages

• Desirable Endpoint Characteristics • More complete characterization of treatment effect – May be interested in a variety of outcomes – Clinically relevant • E.g., Perspective of treating more than a single disease • Addresses the scientific question – Easy to interpret • Reduces bias due to competing risks and informative censoring – Easy to obtain – Quantified/qualified in an unbiased manner • More events could imply more power – Sensitive to changes induced by treatment – If expected effect size is unchanged – Affordably obtained • Avoids multiplicity issue and avoids difficult selection – Results in a reasonable sample size between endpoints (ICH E-9) • Note: continuous responses usually require smaller sample sizes than binary or time-to-event

Composite Endpoints: Disadvantages Composite Endpoints: Considerations

• Competing risk issue • Are the components of similar importance? – If censored patient has a different risk for event than a non-censored patient, then “informative • Do the components occur with similar censoring” • Occurs when an event (e.g., disease progression) is frequency? analyzed while ignoring circumstances (e.g., death) that preclude the occurrence of the event • Is the treatment effect similar across components? Example: Composite Endpoint in HIV Trial Patient Level Measures Time to “treatment failure” – Time from randomization to: • Patients rate their overall experience with respect 1. death due to any cause, or to perceived benefit and risk 2. disease progression - defined as a new or recurrent AIDS-defining opportunistic • Possibly useful for therapies to treat symptoms infection or malignancy occurring after completion of 12 weeks of ARV treatment, or • Problematic when symptoms do not equate with 3. virologic failure defined as two successive risk measurements of plasma HIV-1 RNA – i.e., silent risk of abnormal labs (e.g., LFTs, bilirubin) •1000 copies/mL

Global Benefit:Risk (GBR) Score Benefit-Less-Risk Measure

• Assign non-negative weights • Benefit is discounted for the presence of – Chosen to reflect the relative importance of untoward safety events according to a each category when evaluating treatment prespecified algorithm – Similar discounting approach to Q-TWiST • Then compute summary measures and compare the distributions between treatment • Chuang-Stein, CCT, 1994. groups Benefit-Less-Risk (BLR) Measure Benefit:Risk Index

• Step 2: Suppose benefit is measured on a single • Women’s Health Initiative primary endpoint – 15 year project sponsored by NHLBI – Denote the benefit for subject j as Sj – >161,000 postmenopausal women – Discount Sj by a multiple of Rj using a “conversion – 3 components factor”, f • Randomized clinical trials – Enrolled > 68,000 women – Designed to evaluate effects of hormone replacement BLR = Sj -f Rj therapy (HRT), dietary modification, calcium/vitamin D on clinical endpoints • Use BLR to compare treatments • Observational study • Community prevention trial

Benefit:Risk Index WHI: PREMPRO

• HRT could have preventative effects and • Drug to help women manage symptoms of possible adverse effects (noted by DMC) menopause – Freedman et.al. (CCT, 1996) proposed indices • Product label includes summary of benefits and to combine the estimated treatment effects on risks the five endpoints • Estimate the effect of HRT on each endpoint • Allows individual patients and their physicians to • Combine the effects to form a composite HRT effect make patient-specific decisions based on benefit:risk – Patient-specific weighting and value judgment based on outcomes Within Patient Nonparametric Approach (Personalized Medicine) • Useful when patients can be ranked with respect to each of •Define benefit and risk (i.e., continuous or ordinal measures) • Rank patients with respect to combined benefit and risk – Minimum tolerable benefit when risk = 0 (b1) based on their benefit-specific and risk-specific ranks – Maximum tolerable risk when benefit = 10 (r1) • Compare the combined ranks between groups – Minimum tolerable benefit when risk = r /2 (b ) • Issues 1 2 – Ranking two patients, each higher on one scale (benefit or risk) • Subjective metric or weighting – Handling ties • Fit a smooth “tolerability curve” through – Clinical relevance of effects? these 3 points • Wittkowski, CSS, 2004.

Within Patient Ideas (Personalized Medicine) • Analyses combines benefit and risk data • PK and biomarkers for benefit:risk within patient evaluation? • Allows for flexibility in analyses for – If safety is dependent upon drug concentration varying trade-offs and when predictive biomarkers are available – By selecting different points that will define the tolerability curve – Assessment of treatment differences can be made on a personalized level Absolute Risk

• More easily interpreted and may be more informative than relative risk • More effectively summarizes medical impact • Conveys absolute chance of event • Describe the expected numbers of events (both beneficial and adverse) in a population of patients of a given size – For both the experimental treatment and the control – A comparison can made by defining weights for the events

Interpretation of Graphic Benefit:Risk Reporting

• 100 patients given treatment for disease • Remember CONSORT reporting principles – 86 patients would have been disease free even if they had not received treatment – 9 patients (red faces) are patients that are not cured • Describe how benefit:risk varies across event with treatment subgroups or disease characteristics – 5 patients (yellow faces) show a benefit – Often a single aggregate summary description • They would not have been cured without treatment but are cured when they receive treatment of benefit:risk is not appropriate • NNTB = 20 – E.g., by age, race, etc. • It is not possible to identify which patients will benefit; thus all 100 patients need to be treated in order for 5 to benefit – Can similarly summarize NNTR Concluding Remarks Concluding Remarks

• More formal benefit:risk evaluation is needed to • Prospective planning of the collection and supplement traditional methods of analyses – Estimates should include measures of variability analysis of safety data is important – Analyses should include sensitivity analyses to subjective weighting and other assumptions – Consider analysis by time intervals • Enforce the ITT principle – Follow all randomized subjects until study • Benefit:Risk is an ongoing process completion – Continuous re-assessment is necessary as information accumulates, therapeutic alternatives changes, medical advances evolve, resistance evolves, etc.