Cpmp ewp 1776 99 ptc on missing data
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CPMP/EWP/1776/99: PtC on Missing Data. Evolución de los sujetos. Datos faltantes (missing data) (1). ¿Qué son los datos faltantes? ¡¡¡¡¡ Casillas vacías en los CRDs!!! Viola el principio de la estricto principio de la ITT La posibles causas son, por ejemplo : Pérdida de seguimiento

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Cpmp ewp 1776 99 ptc on missing data

CPMP/EWP/1776/99: PtC on Missing Data

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Evoluci n de los sujetos

Evolución de los sujetos

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Datos faltantes missing data 1

Datos faltantes (missing data)(1)

  • ¿Qué son los datos faltantes? ¡¡¡¡¡ Casillas vacías en los CRDs!!!

  • Viola el principio de la estricto principio de la ITT

  • La posibles causas son, por ejemplo :

    • Pérdida de seguimiento

    • Fracaso o éxito terapéutico

    • Acontecimiento adverso

    • Traslado del sujeto

  • No todas las razones de abandono están relacionadas con el tratamiento

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Datos faltantes missing data 2

Datos faltantes (missing data) (2)

  • Afectando a :

    • Solo un dato

    • Varios datos en una visita

    • Toda una visita

    • Varias visitas

    • Toda una variable

    • Todas las visitas tras la inclusión

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Datos faltantes missing data 3

Datos faltantes (missing data) (3)

  • Por qué son un problema? Potencial fuente de sesgos en el análisis

    • Tanto mayor cuanto mayor la proporción de datos afectados

    • Tanto más sesgo cuanto menos aleatorios

    • Tanta más interferencia cuanto más relacionados con el tratamiento

    • Impide la ITT

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Ejemplos

EJEMPLOS

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Ejemplo descripci n de poblaciones 1

Ejemplo: Descripción de poblaciones (1)

Distribución de pacientes :

Patients withdrawing before treatment

Patients without Baseline VA

  • No Major Protocol Violation

    • E.g., Cataract

    • E.g., Only a Baseline VA

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Ejemplo 2 incorrecto uso de poblaciones 1

Ejemplo 2: Incorrecto uso de poblaciones (1)

Diseño

  • Cirugía vs Tratamiento Médico en estenosis carotidea bilateral (Sackket et al., 1985)

  • Variable principal: Número de pacientes que presenten TIA, ACV o muerte

  • Distribución de los pacientes:

    • Pacientes randomizados:167

    • Tratamiento quirúrgico: 94

    • Tratamiento médico: 73

  • Pacientes que no completaron el estudio debido a ACV en las fases iniciales de hospitalización:

    • Tratamiento quirúrgico: 15 pacientes

    • Tratamiento médico: 01 pacientes

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Ejemplo 2 incorrecto uso de poblaciones 2

Ejemplo 2: Incorrecto uso de poblaciones (2)

Primer análisis que se realiza :

  • Población Por Protocolo (PP):

    Pacientes que hayan completado el estudio

  • Análisis

    • Tratamiento quirúrgico:43 / (94 - 15) = 43 / 79 = 54%

    • Tratamiento médico:53 / (73 - 1) = 53 / 72 = 74%

    • Reducción del riesgo:27%, p = 0.02

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Ejemplo 2 incorrecto uso de poblaciones 3

Ejemplo 2: Incorrecto uso de poblaciones (3)

El análisis definitivo queda de la siguiente forma :

  • Población Intención de Tratar (ITT):

    Todos los pacientes randomizados

  • Análisis

    • Tratamiento quirúrgico:58 / 94 = 62%

    • Tratamiento médico:54 / 73 = 74%

    • Reducción del riesgo:18%, p = 0.09(PP: 27%, p = 0.02)

Conclusiones:

 La población correcta de análisis es la ITT

 El tratamiento quirúrgico no ha demostrado

ser significativamente superior al tratamiento médico

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Relaci n de los valores faltantes con 1 tratamiento 2 resultado

Relación de los valores faltantes con1) Tratamiento2) Resultado

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Cpmp ewp 1776 99 ptc on missing data

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Tipos de missing

Tipos de Missing

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Cpmp ewp 1776 99 ptc on missing data

MCAR

  • Missing completely at random

  • La probabilidad de obtener un missing es completamente independiente de:

    • Valores observados:

      • Variables basales, otras mediciones de la misma variable...

    • Valores no observados o missing

      • Ejemplo: Cambio de ubicación geográfica

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    Cpmp ewp 1776 99 ptc on missing data

    MAR

    • Missing at random

  • La probabilidad de obtener un missing depende:

    • Sí: Valores observados:

    • No: Valores no observados o missing

      • Ejemplo: Sujetos con peor puntuación basal abandonan el estudio independientemente del resultado

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    Non ignorable

    Non-Ignorable

    • La probabilidad de obtener un missing depende:

      • Valores no observados o missing

        • Ejemplo: malas o excelentes respuestas cursan con una mayor tasa de abandonos

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    Manejo de los valores faltantes

    Manejo de los valores faltantes

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    General strategies

    General Strategies

    • Complete-case analysis

    • “Weigthing methods”

    • Imputation methods

    • Analysing data as incomplete

    • Other methods

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    Complete case analysis

    Complete-case analysis

    • Analyse only subjects with complete data

    • Problems:

      • Loss of power

      • Bias

        • Only if MCAR may be assumed

        • Against the ITT principle

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    Weigthing methods

    “Weigthing methods”

    (Sometimes considered as a form of imputation)

    • To constuct weigths for incomplete cases:

      • Each patient belongs to a subgroup in which all subjects have the same characteristics

      • A proportion within each subgroup are destined to complete the study

        • Heyting el al.

        • Robins et al.

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    Datos faltantes m todos de tratamiento 2

    Randomización

    Inicio del tratamiento

    Datos faltantes : métodos de tratamiento (2)

    Sujetos con valores missing en la variable de eficacia

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    Datos faltantes m todos de tratamiento 3

    Randomización

    Inicio del tratamiento

    Datos faltantes : métodos de tratamiento (3)

    Se aplica el método LOCF (Last Observation Carried Forward)

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    Datos faltantes m todos de tratamiento 4

    Randomización

    Inicio del tratamiento

    Datos faltantes : métodos de tratamiento (4)

    Se aplica el método BOCF (Basal Observation Carried Forward)

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    Cpmp ewp 1776 99 ptc on missing data

    Ejemplo: LOCF & Extrapolación lineal

    Adas-Cog

    36

    32

    28

    24-

    20

    16

    12

    8

    4

    REGRESIÓN LINEAL

    LOCF =

    Sesgo de la información

    0 2 4 6 8 10 12 14 16 18

    Time month

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    Cpmp ewp 1776 99 ptc on missing data

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    Imputation methods

    Imputation methods

    • LOCF and variants

      • Bias:

        • depending on the amount and timing of drop-outs:

        • Ej: The conditions under study has a worsening course

          • Conservative:

            • Drop-outs beacuse of lack of efficacy in the control group

          • Anticonservative:

            • Drop-outs beacuse of intolerance in the test group

      • Otros: interpolación, extrapolación

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    Cpmp ewp 1776 99 ptc on missing data

    Adas-Cog

    36

    32

    28

    24-

    20

    16

    12

    8

    4

    0 2 4 6 8 10 12 14 16 18

    Time month

    Ejemplo: falta el resultado de Adas-cog en alguno de los tiempos

    Imputación por regresión

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    Imputation methods1

    Imputation methods

    • Worst case analysis:

      • Impute:

        • The worst response to the test

        • The best response to the control

          • Ultraconservative. Increases the variability.

          • Robustness of results:

            • Second approach: “Sensitivity analysis”

            • Lower bound of efficacy

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    Group means

    Group Means

    • Continuous variable:

      • group mean derived from a grouping variable

    • Categorical – ordinal variable:

      • Mode

      • If no unique mode:

        • Nominal: a value will be randomly selected

        • Ordinal: the ‘middle’ category or a value is randomly chosen from the middle two (even case)

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    Predicted mean

    Predicted Mean

    • Continuous or ordinal variables:

      • Least-squares multiple regression algorithm to impute the most likely value

  • Binary or categorical variable:

    • a discriminant method is applied to impute the most likely value.

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    Imputation class methods

    Imputation Class methods

    • Imputed values from responders that are similar with respect to a set of auxiliary variables.

      • Clinical experience

      • Statistical methods: Hot-Decking

        • Respondents and non-respondents are sorted into a number of imputation subsets according to a user-specified set of covariates.

        • An imputation sub-set comprises cases with the same values as those of the user-specified covariates.

        • Missing values are then replaced with values taken from matching respondents.

          • Options:

            • The first respondent’s value (similar in time)

            • A respondent’s randomly selectedvalue

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    Multiple imputation

    Multiple Imputation

    • Replaces each missing value in the dataset with several imputed values instead of just one. Rubin 1970's

    • Steps:

      • Use complete data to estimate

      • Combine the estimators (i.e. Regresion coefficients) to compute predicted values

      • Randomly simulate a set of residuals to be added to the regression to impute m values

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    Mi assumptions 2

    MI: Assumptions (2)

    • The data model:

      • Probability model on observed data

        • Multivariate normal, loglinear ...

      • Prediction of the missing data

  • The distribution

    • Specification of the distribution for the parameters of the imputation models

      • Use likelihood / bayesian techniques for analysis

        • Noninformative prior distribution

  • The mechanism of nonresponse

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    Multiple imputation1

    Multiple Imputation

    • S-PLUS

    • SOLAS

    • Gary King:

      • Amelia

  • Joe Schafer:

    • web

    • Soft

    • The multiple imputation FAQ page

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    Analysing data as incomplete

    Analysing data as incomplete

    • Time to event variables

    • Mixed models (random-fixed)

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    Other

    Other

    • Gould 1980

      • Converts the variable into an ordinal score.

      • Impute according a pre-defined value (ej. percentile) and the time and cause of drop-out (lack of efficacy, cure, adverse effects...)

  • Miscelanea:

    • Missing data indicators, pairwise deletion...

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    Missing data in clinical trials a regulatory view

    Missing Data in Clinical Trials –A Regulatory View

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    Ich e3 6 9

    ICH-E3,6,9

    • Key points:

      • Potential source of bias

      • Common in Clinical Trials

      • Avoiding MD

      • Importance of the methods of dealing

      • Pre-specification, re-definition

      • Lack of universally accepted method for handling

      • Sensitivity analysis

      • Identification and description of missingness

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    Cpmp ewp 1776 99 ptc on missing data

    Points to Consider on Biostatistical / Methodological issues arising from recent CPMP discussion on licensing applications

    PtC on Missing Data

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    Cpmp ewp 1776 99 ptc on missing data

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    Structure

    Structure

    • Introduction

    • The effect of MD on data analysis

    • Handling of MD

    • General recommendations

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    Cpmp ewp 1776 99 ptc on missing data

    INTRODUCTION

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    Introduction

    Introduction

    • Potential source of bias

    • Many possible sources and different degrees of incompleteness

    • MD violates the ITT principle:

      • Full set analysis requires imputation

    • The strategy employed might in itself provide a source of bias

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    Cpmp ewp 1776 99 ptc on missing data

    The effect of missing values on data analysis and interpretation

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    Effect on data analysis 1

    Effect on data analysis (1)

    • Power:

      • Reduction of cases for analysis:

        • reduction of power

    • Variability:

      • Non-completers (greater likelihood of extreme values):

        • Their loss => underestimate of variability

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    Effect on data analysis 2

    Effect on data analysis (2)

    • Bias:

      • Estimation of treatment effect

      • Comparability of treatment groups

      • Representativeness of the sample

    • The reduction of the statistical power is mainly related to the number of missing values

    • The risk of bias depends upon the relationship between:

      • Missingness

      • Treatment

      • Outcome

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    Effect on data analysis 3

    Effect on data analysis (3)

    • Not expected to lead to bias:

      • if MD are only related to the treatment

        • (an observation is more likely to be missing on one treatment arm than another)

    • but not to the outcome

      • real value of the unobserved measurement (poor outcomes are no more likely to be missing than good outcomes).

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    Effect on data analysis 4

    Effect on data analysis (4)

    • Bias:

      • if MD (unmeasured observations)arerelated to the real value of the outcome

        • (e.g. the unobserved measurements have an higher proportion of poor outcomes)

          • this will lead to bias even if the missing values are not related to treatment (i.e. missing values are equally likely in all treatment arms).

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    Effect on data analysis 5

    Effect on data analysis (5)

    • Bias:

      • If MDif they are related to both the treatment and the unobserved outcome variable

        • (e.g. missing values are more likely in one treatment arm because it is not as effective).

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    Effect on data analysis 6

    Effect on data analysis (6)

    • Pragmatic approach:

      • In most cases it is difficult or impossible to elucidate whether the relationship between missing values and the unobserved outcome variable is completely absent.

      • Thus it is sensible to adopt a conservative approach, considering missing values as a potential source of bias.

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    Cpmp ewp 1776 99 ptc on missing data

    Handling of MD

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    Handling of md 1

    Handling of MD (1)

    • Avoidance of missingness:

      • In the design and conduct of a clinical trial all efforts should be directed towards minimising the amount of missing data likely to occur.

      • Despite these efforts some missing values will generally be expected.

    • The way these missing observations are handled may substantially affect the conclusions of the study.

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    Handling of md 2

    Handling of MD (2)

    • Complete case analysis:

      • Bias, power and variability

      • Not generally appropriate. Exceptions:

        • Exploratory studies, especially in the initial phases of drug development.

        • Secondary supportive analysis in confirmatory trials (robustness)

      • Violates the ITT principle.

      • It cannot be recommended as the primary analysis in a confirmatory trial

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    Handling of md 3

    Handling of MD (3)

    • Imputation of Missing Data:

      • Scope of imputation:

        • Not restricted to main outcomes:

          • (secondary efficacy, safety, baseline covariates...)

      • Methods for imputation:

        • Many techniques

        • No gold standard for every situation

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    Handling of md 4

    Handling of MD (4)

    • Methods for imputation (cont):

      • Not a description of the different methods

      • All methods may be valid:

        • Simple methods to more complex:

          • From LOCF to multiple imputation methods

        • But their appropriateness has to be justified

          • e.g.: LOCF: acceptable if measurements are expected to be relatively constant over time.

            • In Alzheimer’s disease where the patient’s condition is expected to deteriorate over time, the LOCF method is less acceptable

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    Handling of md 5

    Handling of MD (5)

    • Statistical approaches less sensitive to MD:

      • Mixed models

      • Survival models

        • They assume no relationship between treatment and the missing outcome, and generally this cannot be assumed.

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    Cpmp ewp 1776 99 ptc on missing data

    General recommendations

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    General recommendations 1

    General recommendations (1)

    • Avoidance of missing data

      • Try to reduce the number of MD

        • Anticipate sources and try to avoid them in the design

        • Strategies to obtain measurements

        • If large amount of MD is expected:

          • Relevance of blinding (assignment and evaluation)

        • Anticipation of the “acceptable amount of MD”

          • Sample size

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    General recommendations 2

    General recommendations (2)

    • Avoidance of missing data (cont)

      • “Acceptable amount” of MD:

        • Not general rule, depends on

          • Nature of variable

            • Mortality vs sophisticated methods of diagnosis

          • Length of the clinical trial

          • Condition under study

            • Psychiatric disorders: low adherence of patients to study protocol

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    General recommendations 3

    General recommendations (3)

    • Avoidance of missing data (cont)

      • Continue data collection after patient withdrawal

        • ITT based on real data

          • Alternatives

            • Analysis on incomplete data

              or

            • Analysis on imputed data

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    General recommendations 4

    General recommendations (4)

    • Design of the study. Relevance of predefinition

      • Pre-specify in the protocol:

        • Description and justification of the method

        • Anticipation of the expected amount of MD

          • Deviations documented and justified

        • Conservative:

          • To avoid:

            • minimisation of differences in non-inferiority trials, overestimation in superiority trials

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    General recommendations 5

    General recommendations (5)

    • Design of the study. Relevance of predefinition(cont)

      • Update:

        • Unpredictability of some problems

      • Statistical Analysis Plan

      • During the Blind Review

        • Deviation and amendments documented (traceability)

        • Identification of the blinding

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    General recommendations 6

    General recommendations (6)

    • Analysis of missing data

      • Pattern of MD: time and proportion

        • Investigate whether there is any indication of differences between the treatment groups.

      • Elucidate if patients with and without missing values have different characteristics at baseline.

        • This might help to establish:

          • whether the missing values have lead to baseline imbalance, and

          • whether the process generating missing values has differentially influenced the treatment groups.

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    General recommendations 7

    General recommendations (7)

    • Sensitivity analysis

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

  • Some examples:

    • Imputation of Best plausible vs Worst plausible

    • Best possible in control and Worst possible in experimental and inversely

    • Full set analysis vs complete case analysis

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

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    General recommendations 8

    General recommendations (8)

    • Final Report

      • Detailed description of the planned and amendments of the predefined methods

      • Discussion of the MD:

        • Number, Time & Pattern

        • Possible implications in efficacy and safety

      • Imputed values must be listed and identified

      • A sensitivity analysis may give robustness to the conclusions

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