Decision Trees: an application to LTC Insurance Thibault ANTOINE - - PowerPoint PPT Presentation

Decision Trees: an application to LTC Insurance

Thibault ANTOINE Head of Critical Illness R&D Centre Guillaume BIESSY P.h.D. candidate – LTC & Disability R&D Centre

SCOR Global Life

1

Introduction

2

Decision Trees

3

Portfolio study : Example 1

4

Portfolio study : Example 2

Contents April 2016

3

Introduction

Some examples of machine learning methods:

• Support Vector Machines
• Boosting
• Decision trees
• Random forests
• Neural networks
• . . .

Those methods rely on letting the algorithm learn the structure of data instead of forcing a model. Each method has its own advantages and drawbacks

4

Introduction

Figure 1 : Overview of strengths and weaknesses for several methods. Source : Conference on Actuarial & Data Science, SCOR, November 2015.

Algorithms High number of variables Dealing with missing Data Threshold effects No distribution hypothesis No Global hierarchy between variables Predictive power Interpretation

• f the results

Association Rules Sparse Regressions SVM Decision Trees Random Forests Neural Networks & Deep Learning K-nearest neighbors

Very good Good Average Poor

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Introduction

Popular belief : machine learning is a set of obscure methods which give a slight gain of accuracy but

• nly in the case where a tremendous amount of data is available.

When to use machine learning ?

• A lot of individuals, but also. . .
• A lot of covariates
• Heterogeneous covariates
• Limited knowledge about the data

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Introduction

 Good news : in LTC we have several covariates and limited knowledge about their effect as LTC is a complex risk. This is favorable to the use of machine learning.  Bad news 1 : the amount of data is limited.  Bad news 2 : in LTC we work with survival data which are censored. Machine learning methods cannot be applied directly.

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Introduction

Why using machine learning methods in LTC Insurance ?

• Get an idea of the relative importance of covariates in a dataset.
• Bring added value to portfolio studies
• Increase our knowledge about the risk and covariates effects
• Quickly compare several portfolios

Concrete examples :

• Life expectancy based on underlying pathology : classification of pathologies, better knowledge
• f the risk both qualitatively and quantitatively.
• Probability of becoming disabled given the characteristics of the insured life (age at subscribing,

gender, amount of premium, level of underwriting, substandard risk) : impact of underwriting, adverse selection effects, segmentation

SCOR Global Life

1

Introduction

2

Decision Trees

3

Portfolio study : Example 1

4

Portfolio study : Example 2

Contents April 2016

9

Decision Trees

Why decision trees ?

• Transparency on choices made by the algorithm at each step
• Intuitive interpretation of the results

Figure 2 : Example of a decision tree. The variable of interest is the life expectancy in the disabled state.

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Decision Trees

Two families of decision trees :

• Classification tree : the variable to be explained takes a handful of values. Example : incidence
• f dependency on a given interval.
• Regression tree : the variable to be explained is continuous. Example : life expectancy in

dependency. To obtain a decision tree, there are two main steps :

• Build the tree
• Prune the tree

Classification and regression trees use different methods for both steps.

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Decision Trees – Build the Tree

For this step, a criterion to create new branches is required.

• For the classification tree, an impurity function needs to be defined. Popular functions include

entropy and the twoing function. Other can be defined, they just need to respect a few criteria (symmetry, unique maximum and minimum) A new branch is created if it reduces the global impurity of the tree, i.e. if the impurity of both leaves is lower than the impurity of the initial leaf.

• For the regression tree, the criterion used is the minimization of a quadratic error among each

group.

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Decision Trees – Pruning

 At this step, we want to reduce the tree to avoid any overfitting effect. There are several ways to do this :

• Split the data in a learning sample and a test sample (size is usually 2 thirds / 1 third)
• n-fold validation : the dataset is divided in n samples of roughly equal size. Every set except
• ne is used as learning sample and the remaining set as a test sample. We repeat by selecting

each sample and take the mean error.  The choice of the final tree aim at minimizing either :

• The global mean error
• The global mean error + the standard deviation if this global mean error, computed for the tree

which minimizes the global mean error. This approach introduces an extra safety margin and results in even smaller trees where each leaf is significant.

SCOR Global Life

1

Introduction

2

Decision Trees

3

Portfolio study : Example 1

4

Portfolio study : Example 2

Contents April 2016

14

Portfolio study : Example 1 – Portfolio of annuitants

Available covariates :

• Time survived in LTC (variable of interest, can be censored)
• Age at onset of dependency
• Gender

Characteristics of portfolio

• Total exposure : 49,170 person years
• Non censored trajectories : 70.6 %

DISCLAIMER:  For confidentiality purpose the scale of the figures has been changed  The figures have been obtained on a subset of our portfolios  The definitions used are not “standard”

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Portfolio study : Example 1 – Data representation

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Portfolio study : Example 1 – Tree

Time spent in LTC Nb of insured in the cluster Nb of Deaths

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Portfolio study : Example 1 – Full Tree

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Portfolio study : Example 1 – Pruned Tree

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Portfolio study : Example 1 – Over pruned Tree

SCOR Global Life

1

Introduction

2

Decision Trees

3

Portfolio study : Example 1

4

Portfolio study : Example 2

Contents April 2016

21

Portfolio study : Example 2 – Portfolio of annuitants

Available covariates :

• Time survived in the disabled state (variable of interest)
• Age at onset of dependency
• Gender
• Pathology (11 categories)
• Amount of annuity bought
• Residence (home / institution)
• Level of premium for substandard risk
• Level of medical underwriting (void or basic)

Characteristics of the portfolio

• Total exposure : 9,175 person years
• Non censored trajectories : 61.8 %

DISCLAIMER:  For confidentiality purpose the scale of the figures has been changed  The figures have been obtained on a subset of our portfolios  The definitions used are not “standard”

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Portfolio study : Example 2– Data representation

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Portfolio study : Example 2– Full Tree on pathologies

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Portfolio study : Example 2– Pruned on pathologies

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Portfolio study : Example 2– Full Tree All variables

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Portfolio study : Example 2– Pruned Tree All variables

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Conclusion

 At least, decision trees are an interesting tool for the actuary.  Results are easy to share, especially with non-actuaries.  Application to those methods extends to other risk, among them disability. Disability offers a better context to apply those methods : more data, more covariates, limited benefit period

Thank you for your attention !