28 Mai 2019

1. TraumaMatrix • SéMINAIRe – Inférence causale 28 Mai 2019

2. Causal inference on observational data Estimate the effect of tranexamic acid treatment on TBI Imke Mayer & Teresa Alves de Sousa Statistics and applied maths Context / Objectives Approach Outputs • Estimate the effect of tranexamic acid (TA) on the in-ICU mortality among patients with traumatic brain injury (TBI), based on the observational database TraumaBase • Goal 1: estimate average treatment effect as difference in percentage points between mortality rates in treatment and control groups • Challenge: Real world data is incomplete and missing values occur almost everywhere • Goal 2: Estimate heterogeneous treatment effects → decision support • Translate causal a priori into a causal graph (confounding, potential mediators, biases) • Develop treatment effect estimator that handles incomplete confounders and leverages informative missingness: based on random forests: handles missing values and mixed data • From average treatment effect to heterogeneous treatment effect: cluster the observations based on similarities or classify the observations them by lesion type and/or severity • Double robust estimation augments propensity score approach: • Use more information related to traumatic brain injury • Robust to model misspecification • No evidence for rejecting null hypothesis of no effect of TA on in-ICU mortality among TBI patients • Heterogeneity: Differentiate w.r.t. pre-treatment characteristics or severity and/or type of lesion

3. Identify the problem and relevant variables • Causal graph

4. Causal inference on observational data Estimate the effect of tranexamic acid treatment on TBI Context / Objectives Approach Outputs • Estimate the effect of tranexamic acid (TA) on the in-ICU mortality among patients with traumatic brain injury (TBI), based on the observational database TraumaBase • Goal 1: estimate average treatment effect as difference in percentage points between mortality rates in treatment and control groups • Challenge: Real world data is incomplete and missing values occur almost everywhere • Goal 2: Estimate heterogeneous treatment effects → decision support • Translate causal a priori into a causal graph (confounding, potential mediators, biases) • Develop treatment effect estimator that handles incomplete confounders and leverages informative missingness: based on random forests: handles missing values and mixed data • From average treatment effect to heterogeneous treatment effect: cluster the observations based on similarities or classify the observations them by lesion type and/or severity • Double robust estimation augments propensity score approach: • Use more information related to traumatic brain injury • Robust to model misspecification • No evidence for rejecting null hypothesis of no effect of TA on in-ICU mortality among TBI patients • Heterogeneity: Differentiate w.r.t. pre-treatment characteristics or severity and/or type of lesion

5. Handle missing values • Percentage of missing values in the selected variables

6. Missing values in the relevant variables

7. Causal inference Estimate the effect of a treatment/intervention on a target variable • Complete case analysis: eliminate all incomplete observations • In our study, we have 7487 observations and 40 variables, not a single observation is complete for these 40 variables! • Often the complete case approach leads to biased estimates when the data is not missing completely at random Imputation: complete the observations with plausible values • Attention to correctly estimate the level of uncertainty due to the missing values, use multiple imputation • Can only be used with uninformative missing values, i.e. the fact that a variable is missing does not tell us anything about the missing value (counter-example: rich people tend to keep silent about their revenue) Likelihood-based approaches • Expectation Maximization (Wei Jiang’s and Manuel Pichon’s seminar on hemorrhagic shock prediction) Tree-based estimation exploiting missingness information directly in the models • Random trees and a special encoding of missingness (Missing Incorporated in Attributes, MIA) • Flexible method: can be used on quantitative and categorical data • Generic method: Does not require model specifications such as “logistic propensity model” or “linear target model” • Handling missing values

8. Causal inference Estimate the effect of a treatment/intervention on a target variable • Missing values can bias the ATE estimation considerably! • Yet, in practice, missing values rarely addressed more closely (before or during the analyses) • Even on small synthetic examples, missing values can screw up the estimations • Very careful handling of missing values in causal inference is required • Need to adjust/extend the main working hypothesis (unconfoundedness) to missing values • Heads up!

9. Causal inference on observational data Estimate the effect of tranexamic acid treatment on TBI Context / Objectives Approach Outputs • Estimate the effect of tranexamic acid (TA) on the in-ICU mortality among patients with traumatic brain injury (TBI), based on the observational database TraumaBase • Goal 1: estimate average treatment effect as difference in percentage points between mortality rates in treatment and control groups • Challenge: Real world data is incomplete and missing values occur almost everywhere • Goal 2: Estimate heterogeneous treatment effects → decision support • Translate causal a priori into a causal graph (confounding, potential mediators, biases) • Develop treatment effect estimator that handles incomplete confounders and leverages informative missingness: based on random forests: handles missing values and mixed data • From average treatment effect to heterogeneous treatment effect: cluster the observations based on similarities or classify the observations them by lesion type and/or severity • Double robust estimation augments propensity score approach: • Use more information related to traumatic brain injury • Robust to model misspecification • No evidence for rejecting null hypothesis of no effect of TA on in-ICU mortality among TBI patients • Heterogeneity: Differentiate w.r.t. pre-treatment characteristics or severity and/or type of lesion

10. Causal inference Estimate the effect of a treatment/intervention on a target variable • Estimate the Average Treatment Effect (ATE) on • Experimental data • Treatment and control groups are identical w.r.t. pre-treatment features • Take difference of means of the target variable in both groups: average(Ytreated) – average(Ycontrol) • Observational data • Treatment bias/Confounding: treatment is given conditionally on pre-treatment features • Emulate an experiment by adjusting for confounding Precursor study: Help designing experiments (formulate question, inclusion criteria, etc.)

11. Causal inference Estimate the effect of a treatment/intervention on a target variable • For an individual i, we are interested in the individual treatment effect. • Target variable Yi. • Two worlds that cannot coexist – only one can be observed: • is the value of the target if the individual gets the treatment . • is the value of the target if the individual does not get the treatment. • Individual treatment effect, , is never observed! • But we can estimate and by taking averages over the individuals. • And then estimate the Average Treatment Effect (ATE). • Average Treatment Effect

12. Causal inference Estimate the effect of a treatment/intervention on a target variable • Unconfoundedness: we observe enough information to capture the confounding, i.e. we can adjust the bias due to non-random treatment assignment. • Propensity score: probability of receiving treatment (T), given the pre-treatment variables (X) • Inverse propensity score weights (IPW) estimator: reweight observations by the inverse of their probability of being assigned to their group • Adjusts for treatment bias • Makes the two groups comparable/similar on the pre-treatment variables • In our study, X contains information that allow to evaluate the risk of hemorrhagic shock (red nodes on the causal graph) • Propensity scores and inverse-propensity-weighted estimation

13. Causal inference Estimate the effect of a treatment/intervention on a target variable • Propensity score: probability of receiving treatment (T), given the pre-treatment variables (X) • Estimate the propensity score? • Assume a model and then fit the model on the data, e.g. logistic regression • Propensity scores and inverse-propensity-weighted estimation Treated (T=1) e(X) ê(X) Control (T=0)

14. Causal inference Estimate the effect of a treatment/intervention on a target variable • Estimate the propensity score? • Assume a model and then fit the model on the data • But, what if the model is not good, i.e. the relationship between T and X is different than assumed? • Then and are bad estimations! • Wrong model/a priori on the relationship between T and X → biased ATE estimation • Propensity scores and inverse-propensity-weighted estimation Treated (T=1) e(X) ê(X) Control (T=0) X

15. Causal inference Estimate the effect of a treatment/intervention on a target variable • Solution to model mis-specification: construct double robust estimators by using more (a priori) information for the target variable Y. • Model the target Y as a function of confounders X (and other covariates Z). • e.g. linear model: • Theory tells us: if either the propensity scores or the target Y are correctly modelled then we can estimate the ATE without bias and with smaller variance than IPW estimate. • In our study, Z contains predictors of the severity of the TBI (blue nodes in the causal graph) • Double robust estimation

16. Causal inference Estimate the effect of a treatment/intervention on a target variable Double robust estimation For estimation of propensity scores ê(X) For estimation of target Y

17. Causal inference Estimate the effect of a treatment/intervention on a target variable • Theory tells us: if either the propensity scores or the target Y are correctly modelled then we can estimate the ATE without bias and with smaller variance than IPW estimate. • Double robust approach allows flexible learning of propensity model and target model using powerful (blackbox) methods (deep networks, random forests, etc.) • WITHOUT HARMING THE INTERPRETABILITY OF THE ESTIMATOR: • Double robust estimation

18. Causal inference on observational data Estimate the effect of tranexamic acid treatment on TBI Context / Objectives Approach Outputs • Estimate the effect of tranexamic acid (TA) on the in-ICU mortality among patients with traumatic brain injury (TBI), based on the observational database TraumaBase • Goal 1: estimate average treatment effect as difference in percentage points between mortality rates in treatment and control groups • Challenge: Real world data is incomplete and missing values occur almost everywhere • Goal 2: Estimate heterogeneous treatment effects → decision support • Translate causal a priori into a causal graph (confounding, potential mediators, biases) • Develop treatment effect estimator that handles incomplete confounders and leverages informative missingness: based on random forests: handles missing values and mixed data • From average treatment effect to heterogeneous treatment effect: cluster the observations based on similarities or classify the observations them by lesion type and/or severity • Double robust estimation augments propensity score approach: • Use more information related to traumatic brain injury • Robust to model misspecification • No evidence for rejecting null hypothesis of no effect of TA on in-ICU mortality among TBI patients • Heterogeneity: Differentiate w.r.t. pre-treatment characteristics or severity and/or type of lesion

19. Causal inference on the effect of tranexamic acid treatment on TBI • Preliminary results for the ATE ← imputation ← likelihood ← random forest ← imputation ← imputation Double robust Inverse-propensity weighting Difference in % points between mortality rate in treated and in control group

20. R-miss-tastic: more details and examples for analyses with missing values • https://rmisstastic.netlify.com • Theoreticalandpracticaltutorials • Populardatasets • Bibliography • Workflows (in R) Image source: etsy.com

21. References • Hernán, M. A. and Robins, J. M. (2019). CausalInference. Chapman & Hall/CRC. • Imbens, G. W. and Rubin, D. B. (2015). Causalinference in statistics, social, andbiomedicalsciences. Cambridge University Press. • Lederer, D. J., Bell, S. C., Branson, R. D., Chalmers, J. D., Marshall, R., Maslove, D. M., Ost, D. E., Punjabi, N. M., Schatz, M., Smyth, A. R., et al. (2019). Control ofconfoundingandreportingofresults in causalinferencestudies. guidanceforauthorsfromeditorsofrespiratory, sleep, andcritical care journals. Annalsofthe American Thoracic Society, 16(1):22–28. • Textor, J., Hardt, J., and Knüppel, S. (2011). Dagitty: a graphicaltoolforanalyzingcausaldiagrams. Epidemiology, 22(5):745.

22. Causal inference Estimate the effect of a treatment/intervention on a target variable • Unconfoundedness: we observe enough information to capture the confounding, i.e. we can adjust the bias due to non-random treatment assignment. • Propensity score: probability of receiving treatment (T), given the pre-treatment variables (X) • Inverse propensity score weights (IPW) estimator: reweight observations by the inverse of their probability of being assigned to their group • In our study, X contains information that allow to evaluate the risk of hemorrhagic shock (red nodes on the causal graph) • Propensity scores and inverse-propensity-weighted estimation

23. Causal inference Estimate the effect of a treatment/intervention on a target variable • Solution to model mis-specification: construct double robust estimators by using more (a priori) information for the target variable Y. • Model the target Y as a function of confounders X (and other covariates Z). • e.g. linear model: • Theory tells us: if either the propensity scores or the target Y are correctly modelled then we can estimate the ATE without bias. • In our study, Z contains predictors of the severity of the TBI (blue nodes in the causal graph) • Double robust estimation

24. Causal inference on observational data Estimate the effect of tranexamic acid treatment on TBI Context / Objectives Approach Outputs • Estimate the effect of tranexamic acid (TA) on the in-ICU mortality among patients with traumatic brain injury (TBI), based on the observational database TraumaBase • Goal 1: estimate average treatment effect as difference in percentage points between mortality rates in treatment and control groups • Challenge: Real world data is incomplete and missing values occur almost everywhere • Goal 2: Estimate heterogeneous treatment effects → decision support • Translate causal a priori into a causal graph (confounding, potential mediators, biases) • Develop treatment effect estimator that handles incomplete confounders and leverages informative missingness: based on random forests: handles missing values and mixed data • From average treatment effect to heterogeneous treatment effect: cluster the observations based on similarities or classify the observations them by lesion type and/or severity • Double robust estimation augments propensity score approach: • Use more information related to traumatic brain injury • Robust to model misspecification • No evidence for rejecting null hypothesis of no effect of TA on in-ICU mortality among TBI patients • Heterogeneity: Differentiate w.r.t. pre-treatment characteristics or severity or type of lesion

25. Heterogeneity • Method: Use the Hierarchical Clustering technique to identify groups of patients • It performs a classical clustering operation… • 1st step - Grouping patients by their characteristics

26. Heterogeneity • … iteratively, dividing each cluster in two smaller clusters in each iteration: • 1st step - Grouping patients by their characteristics

27. Heterogeneity • Preliminary Results: patients divided in 3 groups, with nearly 0% deaths by TBI in 1st group, 30% in 2nd group and 45% of in 3rd group • 1st step - Grouping patients by their characteristics

28. Heterogeneity • Besides type of TBI, it is the level of lactates, blood pressure, AIS externe and hemorrhagic choc that mostly drive allocation to the 3rd group • 1st step - Grouping patients by their characteristics