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. 2018 May 20;37(11):1767-1787.
doi: 10.1002/sim.7623. Epub 2018 Mar 6.

Some methods for heterogeneous treatment effect estimation in high dimensions

Scott Powers  1 , Junyang Qian  1 , Kenneth Jung  2 , Alejandro Schuler  2 , Nigam H Shah  2 , Trevor Hastie  1 , Robert Tibshirani  1
Affiliations

Some methods for heterogeneous treatment effect estimation in high dimensions

Scott Powers et al. Stat Med. .

Abstract

When devising a course of treatment for a patient, doctors often have little quantitative evidence on which to base their decisions, beyond their medical education and published clinical trials. Stanford Health Care alone has millions of electronic medical records that are only just recently being leveraged to inform better treatment recommendations. These data present a unique challenge because they are high dimensional and observational. Our goal is to make personalized treatment recommendations based on the outcomes for past patients similar to a new patient. We propose and analyze 3 methods for estimating heterogeneous treatment effects using observational data. Our methods perform well in simulations using a wide variety of treatment effect functions, and we present results of applying the 2 most promising methods to data from The SPRINT Data Analysis Challenge, from a large randomized trial of a treatment for high blood pressure.

Keywords: causal inference; machine learning; personalized medicine.

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Figures

FIGURE 1
FIGURE 1
The variance of 2 average treatment effect estimators for n = 10, 30, 100, and 300, as the ratio of the absolute main effect |μ1 + μ0|/2 to the noise level σ increases from 0 to 0.5
FIGURE 2
FIGURE 2
A comparison of raw and pollinated transformed outcome forests. Each method is applied to a randomized simulation and a nonrandomized simulation, and we visually compare the estimated treatment effect with the true treatment effect. We see that in each case, the pollination improves the estimates. For each method, we report the mean square error (MSE) for the treatment effect estimates, along with standard errors
FIGURE 3
FIGURE 3
Results across 8 simulated randomized experiments. For details of the generating distributions, see Table 1. The 7 estimators being evaluated are as follows: NULL = the null prediction, TO = transformed outcome forest, DB = different-basis forest, CF = causal forest, PTO0 = pollinated transformed outcome forest (using propensity = 1/2), CB0 = causal boosting, and BCM0 = causal MARS. The ranges of the y axis are chosen to start from 0 and be at least as great as the response standard deviation in each scenario while showing at least 95% of the data
FIGURE 4
FIGURE 4
Results across 8 simulated observational studies, in which treatment is more likely to be assigned to those with a greater mean effect. The 7 estimators being evaluated are as follows: NULL = the null prediction, CF = causal forest, PTO = pollinated transformed outcome forest, CB1 = causal boosting (propensity adjusted), CB0 = causal boosting, BCM1 = causal MARS (propensity adjusted), BCM0 = causal MARS. CB0 and CM0 are in gray because they would not be used in this setting. They are provided for reference to assess the effect of the propensity adjustment. The ranges of the y axis are chosen to start from 0 and be at least as great as the response standard deviation in each scenario while showing at least 95% of the data
FIGURE 5
FIGURE 5
Illustration of the bias of causal forest and causal multivariate adaptive regression splines (MARS). Patient features were simulated once, and then treatment assignment and response were simulated 50 times. Causal forest and causal MARS were applied to each of the 50 simulations, and the average estimate for each patient is plotted
FIGURE 6
FIGURE 6
Personalized treatment effect estimates from causal boosting and (bagged) causal multivariate adaptive regression splines (MARS). Each circle represents a patient, who gets a personalized estimate from each method. The dashed line represents the diagonal, along which the 2 estimates are the same
FIGURE 7
FIGURE 7
Decision trees summarizing with broad strokes the inferences of causal boosting and (bagged) causal multivariate adaptive regression splines (MARS). The variables are as follows: trr = triglycerides (mg/dL) from blood draw; age = age (y) at beginning of trial; glur = glucose (mg/dL) from blood draw; screat = creatinine (mg/dL) from blood draw; umalcr = albumin/creatinine ratio from urine sample; dbp = diastolic blood pressure (mm Hg); egfr = estimated glomerular filtration rate (mL/min/1.73m2). If the inequality at a split is true for a patient, then that patient is on the left side of the split. The number in each terminal node is the estimated increase in risk due to treatment for a patient in that terminal node
FIGURE 8
FIGURE 8
Training set personalized treatment effects, estimated via causal boosting and (bagged) causal multivariate adaptive regression splines (MARS), versus the estimated glomerular filtration rate. Patients are stratified according to the estimated glomerular filtration rate on the x axis, and each point gives the average personalized treatment effect among patients in that stratum. Error bars correspond to 1 standard error for the mean personalized treatment effect. The vertical dashed line represents a medical cutoff, below which patients are considered to suffer from chronic kidney disease. ATE, average treatment effect
FIGURE 9
FIGURE 9
Validation set personalized treatment effects, estimated via causal boosting and (bagged) causal multivariate adaptive regression splines (MARS), versus the estimated glomerular filtration rate. Patients are stratified according to the estimated glomerular filtration rate on the x axis, and each point gives the average personalized treatment effect among patients in that stratum. Error bars correspond to 1 standard error for the mean personalized treatment effect. The vertical dashed line represents a medical cutoff, below which patients are considered to suffer from chronic kidney disease. ATE, average treatment effect
FIGURE 10
FIGURE 10
Histogram of propensity scores for real observational data application. The propensity score is the estimated probability that the patient would receive an A/B treatment (instead of a C/D treatment) based on the patient's covariates. Patients were binned into propensity score strata with cutoffs at 0.5, 0.6, 0.7, and 0.8
FIGURE 11
FIGURE 11
Densities of causal multivariate adaptive regression splines (MARS) treatment effect estimates in training and validation sets. The results on both data subsets agree that almost all personalized treatment effects are practically 0
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References

    1. Shah NH. Performing an informatics consult. Big Data in Biomedicine Conference-Stanford Medicine. 2016 http://bigdata.stanford.edu/pastevents/2016-presentations.html. Accessed May 1, 2017.
    1. Splawa-Neyman J, Dabrowska DM, Speed TP. On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Stat Sci. 1990;5(4):465–472.
    1. Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol. 1974;66(5):688–701.
    1. Gail M, Simon R. Testing for qualitative interactions between treatment effects and patient subsets. Biom. 1985;41(2):361–372. - PubMed
    1. Bonetti M, Gelber RD. Patterns of treatment effects in subsets of patients in clinical trials. Biostat. 2004;5(3):465–481. - PubMed

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