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Handling of Missing Data.

A regulatory view

Ferran Torres, MD, PhDIDIBAPS. Hospital Clinic BarcelonaAutonomous University of Barcelona (UAB)

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Documentation

• Power Point presentation• Direct links to guidelines• List of selected relevant references

http://ferran.torres.name/edu/eacpt

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Disclaimer• The opinions expressed today are my personal

views and should not be understood or quoted as being made on behalf of any organization.

– Regulatory• Spanish Medicines Agency (AEMPS)• European Medicines Agency (EMA)

– Scientific Advice Working Party (SAWP)– Biostatistics Working Party (BSWP)

– Hospital - Academic - Independent Research• IDIBAPS. Hospital Clinic Barcelona• Autonomous University of Barcelona (UAB)• CAIBER. Spanish Clinical Trials Platform

Best way to deal with Missing Data??

Don’t have any!!!

• Methods for imputation:– Many techniques– No gold standard for every situation

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Regulatory guidance concerning MD

• 1998:: ICHE9. Statistical Principles for Clinical Trials

• 2001:: PtC on Missing Data (rapporteurs: Gonzalo Calvo & Ferran Torres)

• Dec-2007: Recommendation for the Revision of the PtC on MD

• 2009:: Release for consultation

• 2010: Adopted new guideline (rapporteurs: David Wright & Ferran Torres)

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Status in early 2000s

• In general, MD was not seen as a source of bias:– considered mostly as a loss of power issue– little efforts in avoiding MD

• Importance of the methods for dealing with:– Handling of missingness: Mostly LOCF,

Worst Case

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Status in early 2000s

• Very few information on the handling of MD in protocols and SAP (little pre-specification)

• Lack of Sensitivity analysis, or only one, and no justification

• Lack (little) identification and description of missingness in reports

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Key Points

• Avoidance of MD

• Bias: specially when MD was related to the outcome

• Methods:–Warning on the LOCF– Open the door to other methods:

• Multiple imputation, Mixed Models…

• Sensitivity analyses

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Current status in 2008-9Missing data remains a problem in

protocols and final reports:

• Little or no critical discussion on pattern of MD data and withdrawals

• None / only one sensitivity analysis

• Methods:– Inappropriate methods for the handling of MD– LOCF: Still used as a general approach for too

many situations– Methods with very little use in early 2000 are now

common (Mixed Models)

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New Draft PtC1. Executive Summary

2. Introduction

3. The Effect of MD on the Analysis & the Interpretation

4. General Recommendations4.1 Avoidance of Missing Data4.2 Design of the Study. Relevance Of Predefinition4.3 Final Report

5. Handling of Missing Data 5.1 Theoretical Framework5.2 Complete Case Analysis5.3 Methods for Handling Missing Data

6. Sensitivity Analyses

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0 2 4 6 8 10 12 14 16 18 Time (months)

> Worse

< Better

Options after withdrawal

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Options after withdrawal• Ignore that information completely: Available Data

Only approach

• To “force” data retrieval?:– “Pure” estimates valid only when no treatment alternatives

are available– Otherwise the effect will be contaminated by the effect of

other treatments

• Imputation methods

• Analysing data as incomplete – Time to event analysis, direct estimation (likelihood

methods )

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Single imputation methods

• LOCF, BOCF, mean imputation and others

• Many problems described in the previous PtC

• Their potential for bias depends on many factors– including true evolutions after dropout– Time, reason for withdrawal and proportion of

missingness in the treatment arm – they do not necessarily yield a conservative estimation

of the treatment effect

• The imputation may distort the variance and the correlations between variables

• MCAR - missing completely at random– Neither observed or unobserved outcomes are

related to dropout

• MAR - missing at random– Unobserved outcomes are not related to

dropout, they can be predicted from the observed data

• MNAR - missing not at random– Drop-out is related to the missing outcome

Rubin (1976)

Missing Data Mechanisms

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Mixed models & others MAR• MAR assumption

– MD depends on the observed data

– the behaviour of the post drop-out observations can be predicted with the observed data

– It seems reasonable and it is not a strong assumption, at least a priori

– In RCT, the reasons for withdrawal are known

– Other assumptions seem stronger and more arbitrary

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However…

• It is reasonable to consider that the treatment effect will somehow cease/attenuate after withdrawal

• If there is a good response, MAR will not “predict” a bad response

• =>MAR assumption not suitable for early drop-outs because of safety issues

• In this context MAR seems likely to be anti-conservative

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The main analysis: What should reflect ?

A) The “pure” treatment effect:– Estimation using the “on treatment” effect after

withdrawal – Ignore effects (changes) after treatment

discontinuation– Does not mix up efficacy and safety

B) The expected treatment effect in “usual clinical practice” conditions

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MAR

• Estimate the treatment effect that would be seen if patients had continued on the study as planned.

• ...results could be seen as not fully compliant with the ITT principle

Combination of ≠ methods• Imputation Using Drop-out Reason (IUDR)– Penalise treatment related drop-outs (i.e. lack of

efficacy or/and adverse events)

–Worst response // Placebo effect // expected effect (low percentile: P10, Median….)

• Example:• 1) Retrieve data after withdrawal +• 2) IUDR with Multiple Imputation (avoids deflation of

variability) for lack of efficacy/Safety drop-outs +• 3) Perform a Mixed Model for Repeated

Measurements (MMRM) analysis

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Key recommendations (1/4)

• Design– Assume that MD is probably biased – Avoidance of MD– Relevance of predefinition (avoid data-driven

methods)– Detailed description ....– and justification of absence of bias in favour of

experimental treatment

• Final Report– Detailed description of the planned and

amendments of the predefined methods

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Key recommendations (2/4)

Detailed description (numerical & graphical)

• Pattern of MD

• Rate and time of withdrawal– By reason, time/visit and treatment– Some withdrawals will occur between visits: use survival

methods

• Outcome– By reason of withdrawal and also for completers

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Key recommendations (3/4)

Sensitivity Analyses

•a set of analyses showing the influence of different methods of handling missing data on the study results

•Pre-defined and designed to assess the repercussion on the results of the particular assumptions made in the handling of missingness

•Responder analysis

• No universally best method

• Analysis must be tailored to the specific situation at hand

• Better methods than LOCF:• But still useful for sensitivity analyses and as an anchor to compare

with previous trials

• Methods:– MCAR: almost any method is valid but difficult to assume

– MAR: More likely to occur• Likelihood (Mixed Models MMRM, E-M) / weighted-GEE

• Multiple imputation– MNAR: model drop-out as well as response

• Theoretically more useful, in practice highly dependent on drop-out assumptions which are un-checkable

• For sensibility analysis.

Key recommendations (4/4)

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Concluding Remarks• Avoid and foresee MD

• Sensitivity analyses

• Methods for handling:– No gold standard for every situation– In principle, “almost any method may be

valid”:– =>But their appropriateness has to be justified

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http://ferran.torres.name/edu/eacpt