Short and long term prognosis of disability in Multiple Sclerosis Some Tools, Models and Validation...

Short and long term prognosis of disability in Multiple Sclerosis

Some Tools, Models and Validation

A. Neuhaus, M. Daumer

Outline

Background about MS

Online Analytical Processing Tool “Risk Profile” Segmented Regression and Correction for Error

Validation Strategy & examples

Multiple Sclerosis (MS)

common neurological degenerative disease

2.5 million people affected worldwide

drugs have shown efficacy on short-term outcomes

agents are by no means ‘cure’ – many patients have disease activity

long term determination of efficacy is necessary

Background

Multiple Sclerosis (MS)

Multiple Sclerosis

Disease courses

Disability

Relapse

MRI

Cause

CNS

Background

Disease courses

Disability

Relapse

MRI

Cause

CNSSpecific cause is unknown

female : male = 2 : 1 more common in Caucasians

autoimmune process

environmental factors

genetic predisposition

MRI

http://medstat.med.utah.edu

BackgroundMultiple Sclerosis (MS)

Relapse

Causeunknown

Disability

Disease courses

MRI

CNS

http://www.msdecisions.org.uk

Multiple Sclerosis (MS)Background

Disease courses

Disability

Relapse

MRI

Causeunknown

CNS

Lesion Volume

Number of enhancing lesions


Disease courses

Disability

Relapse

MRI

Causeunknown

CNSSudden failures in functional systems

Recovery after a few days or weeks

vision problems

problems with walking

tremor

difficulties with speech

fatigue

bladder and bowel problems


Disease courses

Disability

Relapse

MRI

Causeunknown

CNS

sudden failures


Disease courses

Disability

Relapse

MRI

Causeunknown

CNS

sudden failures

EDSS

time

dis

ab

ilit

y Relapsing Remitting

time

dis

ab

ilit

y Secondary Progressive

timed

isa

bil

ity Primary Progressive

time

dis

ab

ilit

y Clinically Isolated Syndrome


Outline

Background

OnLine Analytical Processing Tool Segmented Regression and Correction for Error

Improvement of Outcome Measures

Validation Strategies

Make the database of the SLCMSR (20.000 patients, 45 data sets)available to health care professionals via the internet

Identification of database subgroups based on clinical parameters

Statistical analyses of subgroups

Illustration of future disease course of subgroups

AimOLAP

Tool

OnLine Analytical Processing Tool (OLAP-Tool)

accessible via the internet

no need for data transfer

no need for local software installation

server based on Java and R

Individual Risk Profile (IRP)

1059 MS patients from placebo arms of controlled clinical trials

definition of patient profile

display the course of database patients with same characteristics

OLAP

Hurdles

Patient profile can be defined by combining

Course EDSS Age atMS onset

DiseaseDuration

Number ofRelapses

4 20 420 10

64.000combinations

1.059 patients

?

OLAP

Hurdles

if a few or no matching patients are found …

weight characteristics according to their importance

determine weights by means of:

number of relapses in the first year

increase of disability

Poisson Regression Linear Regression

OLAP

Selection of most similar patientsOLAP

OutcomesOLAP

OLAPNext steps

Evaluate performance of expert opinion vs. tool/model (“Validation”)

Include patient history & treatment data

Develop and validate models for predicting treatment (non-)responders

OLAP tool for evidence based decision support when to switch treatment

(“Disease Management”)

Prospective evaluation in a clinical trial if promising

Similar to path taken for CTG monitoring

Outline

Background




secondary progressive phase

time

dis

ab

ilit

y relapsing remitting phase

What are the factors affecting the start of the progressive phase?

What are the factors predicting subsequent disability best?

Problem Models

Joint work with J. Noseworthy, Mayo clinic, Rochester, USA, L. Kappos, Basel, CH, T. Augustin & H. Küchenhoff, LMU, Munich, Germany

Restrictions to data

Patients in the first phase of the disease (RRMS)

disability level < 6.5

inclusion in a controlled clinical trial

at least 4 observations in longitudinal data

complete data in covariates

355 RRMS patients from placebo arms of 16 clinical trials

Models

Data

Mean S.D. Range

Female to male ratio 2.7

Age of onset (years) 28.3 7.0 13 – 48

Disease duration before entry (years) 7.0 6.1 0.7 – 34.8

Observation period (months) 26.6 12.7 2.8 – 59.3

EDSS score at entry 2.7 1.4 0 – 6

Relapse rate 2 years prior study 1.5 0.7 0 – 4

Models

Methods

Two – Step – Analysis

EDSS

Time to progressive phase

Segmented Regression Model

Predictive factors

Survival Analysis(with error correction)

Models

Methods / Segmented Regression Model

piecewise linear regression model describes disease process D

Dβ(t) = + β (t-)+

dispersion of estimates

Cov

' p - 3

1(tj - )+

-Itj>

1(tj - )+

-Itj>

j = 1

p

=

'-1

0 10, β > 0, > 0 and (t-)+ = max(0, t-)

Models

Methods / Survival Analysis

Correct determination of time of change is impossible

• , estimated time to progression, is overlaid by an error e

• magnitude of the error will be considered in the survival model

Assumptions:

• true, but unknown, event times t follow a Weibull distribution

• relation between and e: = t · e, t e

log = log t + log e

log = x´β + ( + ), = -1 log e

• exp - ~ (,)

Survival function follows a Burr distribution

S() = [1 + {exp(-x')}-1 -2 2]- 2-2

2 = var (log ) and = 2 -2

Models


Regression parameter are specified using maximum likelihood estimation

The log-likelihood is given by

l() = (1 – S(i))d

d i

logi event

i censored

log S(ci)+...

l() = i = 1

nceni zi - log(i) + log(wi/) + 2i

-2 log(wi)

zi = (log(i) - xi')-1 wi = (1 + -2 i2 exp(zi))-1 where and

Models


Weibull regression Error adjusted regression

Parameter Std.Error p-Value Parameter Std.Error p-Value

Intercept 6.86 0.25 <0.001 7.59 0.22 <0.001

Relapse rate 0.20 0.11 0.08

EDSS -0.10 0.06 0.07 -0.15 0.07 0.02

Log (scale) -0.08 0.07 0.22 0.02 0.09 0.84

Scale 0.92 0.98

The higher the EDSS level, the shorter the time to progression. Higher relapse rate – longer time to progression?Importance of relapse rate instable.

Models

Methods / Survival AnalysisModels

Outline

Background




Need for validation – Model selection

Over-fitting of data

Scenario

Many models checked for describing data set

Model with best fit is used for further analyses

Model fit is tested using standard statistical methodology

Result

Danger of over-fitting since model selection

and model validation is based on same dataset

Danger enhanced if method applied to small subgroups

Validation

Need for validation – Data driven hypothesesValidation

Theory

Neither the model nor the hypothesis to be tested should be data driven

Practice

Data are visualized before models are fit and, frequently, before hypotheses are formulated

Effect

“Promising” hypotheses are being tested

Actual level of tests far exceed nominal levels, leading to a large number of “false positive” results

Our strategy: Splitting of data set

Open part Closed part

„Learning or training sample“

„Confirmation or validation sample“

Confirmation of findings - Final result

Development of tools

Statistical analyses

Significant results

Validation

Free investigation of data set

SLCMSR Database

~ 40 %

~ 10 %

~ 50 %Training sample

Mixing sample

Inclusion/exclusion criteria

Plausibility check

Harmonization/homogenization

Pooling

Split into

training sample (~40%) and validation sample (~50%)

Analysis / modeling

Validation

Validation sample

Validation ProcedureValidation

Validation concept + validation results of „open“ part of SLCMSR database are sent to Validation CommitteeValidation Committee

Validation Committee approvesapproves proposed validation concept or alternately suggests specific modificationsspecific modifications for consideration by the authors of the project

Data trusteeData trustee executes analysis agreed upon by Validation Committee and authors, programming codeprogramming code is provided by project team

Validation Committee and authors agree upon formulation formulation of results summaryof results summary

ExamplesValidation

Relapses and subsequent worsening of disability in RRMS Occurrence of relapses in the first 3 months on study appeared to be the best predictor for a shorter subsequent time to sustained increase of the EDSS. Signif. even after “naïve” Bonferroni adjustment for multiple testing. BUT: Unable to validate this on an independent (validation) part of the SLCMSR dataset: relationship between relapses and subsequent disability either non-existent or very weak

Correlating T2 lesion burden on MRI with the clinical manifestations of multiple sclerosis (Li, Held et al, submitted to Neurology)

Question: How does one validate a plateauing relationship? Visualization, with CI for Spearman‘s correlation coefficient and

significant improvement in model fit with non-linear approach Validation was successful: there is a plateau, lesion load doesn’t increase with disability, no good surrogate marker

ValidationExamples

How to predict on-study relapse rate? (Held et al, Neurology, in press) validation was successful: pre-study relapse rate is the

most important predictor for future relapse rate. MRI information doesn’t add much.

Invited Session for IBC 2006, MontrealValidation

Session organizers: M. Daumer, U. Held (SLCMSR)

Discussant: John Petkau (Prof. of Statistics, UBC, Vancouver)

Speakers: Trevor Hastie (Prof. of Statistics, Stanford University)

„Validation in Genomics“

Ulrike Held (SLCMSR)

„Validation Procedure of the SLCMSR: Methodological and Practical Aspects“

Martin Schumacher (Prof. of Biometry, Freiburg University, GER)

„Assessment and Validation of Risk Prediction Models“

Validation

Barkhof F, Held U, Simon JH, Daumer M, Fazekas F, Filippi M, Frank JA, Kappos L, Li D, Menzler S, Miller DH, Petkau J, Wolinsky J. Predicting gadolinium-enhancement status in MS patients eligible for randomized clinical trials. Neurology in press

Compston A, Ebers G, Lassmann H, McDonald I, Matthews B, Wekerle H. Mc Alpines Multiple Sclerosis 3rd Edition, Churchill Livingstone, 1998.

Freedman MS, Patry DG, Grand'Maison F, Myles ML, Paty DW, Selchen DH. Treatment optimization in multiple sclerosis, Can J Neurol Sci 33 (2):157-68, 2004.

Held U, Heigenhauser L, Shang C, Kappos L, Polman C. Predictors of relapse rate in MS clinical trials. Neurology in press

Küchenhoff H. An exact algorithm for estimating breakpoints in segmented generalized linear models, Computational Statistics 12, 235 – 247, 1997.

Kurtzke JF. Rating neurologic impairment in multiple sclerosis: An expanded disability status scale (EDSS), Neurology 33(11):1444-52, Nov. 1983.

Pittock SJ, Mayr WT, McClelland RL, Jorgensen NW, Weigand SD, Noseworthy JH, Weinshenker BG, and Rodriguez M. Change in MS-related disability in a population-based cohort: A 10-year follow-up study. Neurology 62: 51-59, 2004.

Hellriegel B, Daumer M, Neiß A. Analysing the course of multiple sclerosis with segmented regression models, Tech. rep., Ludwig-Maximilians-University Munich, SFB Discussion Paper, 2003.

Skinner CJ, Humphreys K. Weibull Regression for Lifetimes Measured with Error, Lifetime Data Analysis 5, 23-37, 1999.

Neuhaus A. Modelling Time to Progression in Multiple Sclerosis, Diploma Thesis, Ludwig-Maximilians-University Munich, http://www.slcmsr.org, 2004

Schach S, Daumer M, Neiß A. Maintaining high quality of statistical evaluations based on the SLCMSR data base - Validation Policy, http://www.slcmsr.org.

Ioannidis PDA. Why most publishes research findings are false, PLoS Med 2(8): e124, 2005.

Ioannidis PDA. Microarrays and molecular research: noise discovery?, Lancet 365: 454-55, 2005.

Literature

http://www.slcmsr.org/




Outline

Background




Time to progression

Time to sustained worsening/progression

widely used outcome measure in Phase III clinical trials

outcome depends on confirmation period

effective study duration is shortened since last visit(s) can only be used as confirmation

Outcome Measures

Definition of sustained worsening divides cohort in 3 groups

current procedureno worsening

confirmedworsening

non-confirmedworsening

non-confirmedworsening

no worsening

confirmedworsening

What about … ?

confirmedworsening

no worsening

consideration of confirmation period

consideration of visit schedule

Outcome Measures

random matching of ‘non-confirmed worsening’ to one of the other groups

Proportion matched toconfirmed worsening


Cox Model



Logit Model

room forimprovement

Estimation based on standard definition

Estimation without non-confirmed patients

Outcome Measures

Methods / Segmented Regression Model

n = 68 n = 158 n = 129

Prior to first

observation

Estimated start of progressive phase

within observation

period

1.2 y +/- 1.0 y

[0.01 y – 4.6 y]

after last

observation

1.9 y +/- 1.1 y *

[0.2 y – 4.6 y]

* censoring times

Models

Short and long term prognosis of disability in Multiple Sclerosis Some Tools, Models and Validation...

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