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Multinomial Logistic regression Model Fit and
Predictive Properties. Breast Tumour Type
predicted from FNA. Stian Lydersen, Ingvild
Bore, Anna Bofin stian.lydersen_at_ntnu.no Presented
at ISCB, Alexandroupolis, 29 July 2 August 2007
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Assessment of model fit and predictive properties

• Measures of performance
• Sensitivities, specificities
• Area under the ROC curves
• Estimated probabilities versus outcomes
• A k-1 dimensional plot
• A multinomial g.o.f. test. (Fagerland, Hosmer,
  Bofin, submitted 2007.)
• Performance in which data set(s)
• In the original data set
• Delete one-at-a time crossvalidation
• Training set and test set
• Bootstrapping. (Steyerberg et al, 2001)

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Dependent variableDiagnostic groups (Breast
tumour types)

• NPBD/PBD - non-proliferative/proliferative
  breast disease
• AIDH/DCIS - atypical intraductal hyperplasia
  /ductal carcinoma in situ
• IDC - invasive ductal carcinoma

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FNA Fine Needle Aspiration
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The smear...
3-15 slides/case
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Predictors Cytological criteria

• Nuclear pleomorphism
• Nuclear size
• Chromatin pattern
• Nucleolus
• Signs of invasion
• Degree of dissociation
• Bipolar naked nuclei
• Myoepithelial cells

• Complex 3-D fragments
• Fragments with cribriform pattern
• Calcium deposits
• Necrosis
• Cytoplasmic vacuoles
• Tubular groups with angular edges
• Cellularity

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Multinomial logistic regression

• Dependent variable 3 diagnostic groups
• Predictors 16 candidates (ordinal or
  dichotomous)
• n133 patients
• Forward LR stepwise variable selection.

Bofin, Lydersen, Hagmar, Diagnostic
Cytopathology, 2004 Bore Statistisk analyse av
celleprøver innen kreftdiagnose. Master thesis,
NTNU, 2007.
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Resulting modelwith P-enter 0.05 and P-remove
0.10.

• g1 lnPNPBD/PBD /PAIDH/DCIS 1.40 1.38pleo
  2.66calcium 2.10naked 1.78comp 0.0048myo
• g2 lnPIDC /PAIDH/DCIS 1.12 1.40pleo
  4.02calcium 0.91naked 2.18comp 1.56myo

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Prediction

• Probability for each of the diagnostic groups
• PNPBD/PBD exp(g1)/1 exp(g1) exp(g2)
• PAIDH/DCIS 1/1 exp(g1) exp(g2)
• PIDC exp(g2)/1 exp(g1) exp(g2)
• Predicted group The one with highest estimated
  probability

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• Diagnostic groups
• NPBD or PBD
• AIDH or DCIS
• IDC

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Area under the receiver operator curve NPBD/PBD
-ROC1- AIDH/DCIS -ROC2- IDC
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Steyerberg et al (Medical Decision Making, 2001)
Prognostic Modeling with Logistic regression
Analysis In Search of a Sensible Strategy in
Small data Sets

• Take B (f.ex 200) bootstrap samples from the
  original sample, identical in size and with
  replacement
• In each sample, fit the model and calculate the
  performance measures (f.ex area under ROC and
  calibration slope)
• Evaluate each of the B models in the original
  sample. The difference between performance
  measure in the bootstrap sample and the original
  sample is an estimate of overoptimism.

Problem Fails to converge in about 50 of our
samples
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Assessment of model fit and predictive properties

• Measures of performance
• Sensitivities, specificities
• Area under the ROC curves
• Estimated probabilities versus outcomes
• A k-1 dimensional plot
• A multinomial g.o.f. test. (Fagerland, Hosmer,
  Bofin, submitted 2007.)
• Performance in which data set(s)
• In the original data set
• Delete one-at-a time crossvalidation
• Training set and test set
• Bootstrapping. (Steyerberg et al, 2001)