Optimizing treatment allocation in randomized clinical trials by leveraging baseline covariates

We consider the problem of optimizing treatment allocation for statistical efficiency in randomized clinical trials. Optimal allocation has been studied previously for simple treatment effect estimators such as the sample mean difference, which are not fully efficient in the presence of baseline covariates. More efficient estimators can be obtained by incorporating covariate information, and modern machine learning methods make it increasingly feasible to approach full efficiency. Accordingly, we derive the optimal allocation ratio by maximizing the design efficiency of a randomized trial, assuming that an efficient estimator will be used for analysis. We then expand the scope of optimization by considering covariate-dependent randomization (CDR), which has some flavor of an observational study but provides the same level of scientific rigor as a standard randomized trial. We describe treatment effect estimators that are consistent, asymptotically normal, and (nearly) efficient under CDR, and derive the optimal propensity score by maximizing the design efficiency of a CDR trial (under the assumption that an efficient estimator will be used for analysis). Our optimality results translate into optimal designs that improve upon standard practice. Real-world examples and simulation results demonstrate that the proposed designs can produce substantial efficiency improvements in realistic settings.

Evaluating the heterogeneous effect of a modifiable risk factor on suicide: The case of vitamin D deficiency

OBJECTIVES

To illustrate the use of machine learning methods to search for heterogeneous effects of a target modifiable risk factor on suicide in observational studies. The illustration focuses on secondary analysis of a matched case-control study of vitamin D deficiency predicting subsequent suicide.

METHODS

We describe a variety of machine learning methods to search for prescriptive predictors; that is, predictors of significant variation in the association between a target risk factor and subsequent suicide. In each case, the purpose is to evaluate the potential value of selective intervention on the target risk factor to prevent the outcome based on the provisional assumption that the target risk factor is causal. The approaches illustrated include risk modeling based on the super learner ensemble machine learning method, Least Absolute Shrinkage and Selection Operator (Lasso) penalized regression, and the causal forest algorithm.

RESULTS

The logic of estimating heterogeneous intervention effects is exposited along with the illustration of some widely used methods for implementing this logic.

CONCLUSIONS

In addition to describing best practices in using the machine learning methods considered here, we close with a discussion of broader design and analysis issues in planning an observational study to investigate heterogeneous effects of a modifiable risk factor.

Multi-resolution super learner for voxel-wise classification of prostate cancer using multi-parametric MRI

Multi-parametric MRI (mpMRI) is a critical tool in prostate cancer (PCa) diagnosis and management. To further advance the use of mpMRI in patient care, computer aided diagnostic methods are under continuous development for supporting/supplanting standard radiological interpretation. While voxel-wise PCa classification models are the gold standard, few if any approaches have incorporated the inherent structure of the mpMRI data, such as spatial heterogeneity and between-voxel correlation, into PCa classification. We propose a machine learning-based method to fill in this gap. Our method uses an ensemble learning approach to capture regional heterogeneity in the data, where classifiers are developed at multiple resolutions and combined using the super learner algorithm, and further account for between-voxel correlation through a Gaussian kernel smoother. It allows any type of classifier to be the base learner and can be extended to further classify PCa sub-categories. We introduce the algorithms for binary PCa classification, as well as for classifying the ordinal clinical significance of PCa for which a weighted likelihood approach is implemented to improve the detection of less prevalent cancer categories. The proposed method has shown important advantages over conventional modeling and machine learning approaches in simulations and application to our motivating patient data.

Sensitivity analysis of unmeasured confounding in causal inference based on exponential tilting and super learner

Causal inference under the potential outcome framework relies on the strongly ignorable treatment assumption. This assumption is usually questionable in observational studies, and the unmeasured confounding is one of the fundamental challenges in causal inference. To this end, we propose a new sensitivity analysis method to evaluate the impact of the unmeasured confounder by leveraging ideas of doubly robust estimators, the exponential tilt method, and the super learner algorithm. Compared to other existing methods of sensitivity analysis that parameterize the unmeasured confounder as a latent variable in the working models, the exponential tilting method does not impose any restrictions on the structure or models of the unmeasured confounders. In addition, in order to reduce the modeling bias of traditional parametric methods, we propose incorporating the super learner machine learning algorithm to perform nonparametric model estimation and the corresponding sensitivity analysis. Furthermore, most existing sensitivity analysis methods require multivariate sensitivity parameters, which make its choice difficult and subjective in practice. In comparison, the new method has a univariate sensitivity parameter with a nice and simple interpretation of log-odds ratios for binary outcomes, which makes its choice and the application of the new sensitivity analysis method very easy for practitioners.

Using electronic health records to identify candidates for human immunodeficiency virus pre-exposure prophylaxis: An application of super learning to risk prediction when the outcome is rare

Human immunodeficiency virus (HIV) pre-exposure prophylaxis (PrEP) protects high risk patients from becoming infected with HIV. Clinicians need help to identify candidates for PrEP based on information routinely collected in electronic health records (EHRs). The greatest statistical challenge in developing a risk prediction model is that acquisition is extremely rare.

METHODS

Data consisted of 180 covariates (demographic, diagnoses, treatments, prescriptions) extracted from records on 399 385 patient (150 cases) seen at Atrius Health (2007-2015), a clinical network in Massachusetts. Super learner is an ensemble machine learning algorithm that uses k-fold cross validation to evaluate and combine predictions from a collection of algorithms. We trained 42 variants of sophisticated algorithms, using different sampling schemes that more evenly balanced the ratio of cases to controls. We compared super learner's cross validated area under the receiver operating curve (cv-AUC) with that of each individual algorithm.

RESULTS

The least absolute shrinkage and selection operator (lasso) using a 1:20 class ratio outperformed the super learner (cv-AUC = 0.86 vs 0.84). A traditional logistic regression model restricted to 23 clinician-selected main terms was slightly inferior (cv-AUC = 0.81).

CONCLUSION

Machine learning was successful at developing a model to predict 1-year risk of acquiring HIV based on a physician-curated set of predictors extracted from EHRs.

Super Learner for Survival Data Prediction

Survival analysis is a widely used method to establish a connection between a time to event outcome and a set of potential covariates. Accurately predicting the time of an event of interest is of primary importance in survival analysis. Many different algorithms have been proposed for survival prediction. However, for a given prediction problem it is rarely, if ever, possible to know in advance which algorithm will perform the best. In this paper we propose two algorithms for constructing super learners in survival data prediction where the individual algorithms are based on proportional hazards. A super learner is a flexible approach to statistical learning that finds the best weighted ensemble of the individual algorithms. Finding the optimal combination of the individual algorithms through minimizing cross-validated risk controls for over-fitting of the final ensemble learner. Candidate algorithms may range from a basic Cox model to tree-based machine learning algorithms, assuming all candidate algorithms are based on the proportional hazards framework. The ensemble weights are estimated by minimizing the cross-validated negative log partial likelihood. We compare the performance of the proposed super learners with existing models through extensive simulation studies. In all simulation scenarios, the proposed super learners are either the best fit or near the best fit. The performances of the newly proposed algorithms are also demonstrated with clinical data examples.

Machine learning to predict venous thrombosis in acutely ill medical patients

BACKGROUND

The identification of acutely ill patients at high risk for venous thromboembolism (VTE) may be determined clinically or by use of integer-based scoring systems. These scores demonstrated modest performance in external data sets.

OBJECTIVES

To evaluate the performance of machine learning models compared to the IMPROVE score.

METHODS

The APEX trial randomized 7513 acutely medically ill patients to extended duration betrixaban vs. enoxaparin. Including 68 variables, a super learner model (ML) was built to predict VTE by combining estimates from 5 families of candidate models. A "reduced" model (rML) was also developed using 16 variables that were thought, a priori, to be associated with VTE. The IMPROVE score was calculated for each patient. Model performance was assessed by discrimination and calibration to predict a composite VTE end point. The frequency of predicted risks of VTE were plotted and divided into tertiles. VTE risks were compared across tertiles.

RESULTS

The ML and rML algorithms outperformed the IMPROVE score in predicting VTE (c-statistic: 0.69, 0.68 and 0.59, respectively). The Hosmer-Lemeshow goodness-of-fit P-value was 0.06 for ML, 0.44 for rML, and <0.001 for the IMPROVE score. The observed event rate in the lowest tertile was 2.5%, 4.8% in tertile 2, and 11.4% in the highest tertile. Patients in the highest tertile of VTE risk had a 5-fold increase in odds of VTE compared to the lowest tertile.

CONCLUSION

The super learner algorithms improved discrimination and calibration compared to the IMPROVE score for predicting VTE in acute medically ill patients.

Using Administrative Data to Predict Suicide After Psychiatric Hospitalization in the Veterans Health Administration System

There is a very high suicide rate in the year after psychiatric hospital discharge. Intensive postdischarge case management programs can address this problem but are not cost-effective for all patients. This issue can be addressed by developing a risk model to predict which inpatients might need such a program. We developed such a model for the 391,018 short-term psychiatric hospital admissions of US veterans in Veterans Health Administration (VHA) hospitals 2010-2013. Records were linked with the National Death Index to determine suicide within 12 months of hospital discharge (n=771). The Super Learner ensemble machine learning method was used to predict these suicides for time horizon between 1 week and 12 months after discharge in a 70% training sample. Accuracy was validated in the remaining 30% holdout sample. Predictors included VHA administrative variables and small area geocode data linked to patient home addresses. The models had AUC=.79-.82 for time horizons between 1 week and 6 months and AUC=.74 for 12 months. An analysis of operating characteristics showed that 22.4%-32.2% of patients who died by suicide would have been reached if intensive case management was provided to the 5% of patients with highest predicted suicide risk. Positive predictive value (PPV) at this higher threshold ranged from 1.2% over 12 months to 3.8% per case manager year over 1 week. Focusing on the low end of the risk spectrum, the 40% of patients classified as having lowest risk account for 0%-9.7% of suicides across time horizons. Variable importance analysis shows that 51.1% of model performance is due to psychopathological risk factors accounted, 26.2% to social determinants of health, 14.8% to prior history of suicidal behaviors, and 6.6% to physical disorders. The paper closes with a discussion of next steps in refining the model and prospects for developing a parallel precision treatment model.

Machine learning methods for leveraging baseline covariate information to improve the efficiency of clinical trials

Clinical trials are widely considered the gold standard for treatment evaluation, and they can be highly expensive in terms of time and money. The efficiency of clinical trials can be improved by incorporating information from baseline covariates that are related to clinical outcomes. This can be done by modifying an unadjusted treatment effect estimator with an augmentation term that involves a function of covariates. The optimal augmentation is well characterized in theory but must be estimated in practice. In this article, we investigate the use of machine learning methods to estimate the optimal augmentation. We consider and compare an indirect approach based on an estimated regression function and a direct approach that aims directly to minimize the asymptotic variance of the treatment effect estimator. Theoretical considerations and simulation results indicate that the direct approach is generally preferable over the indirect approach. The direct approach can be implemented using any existing prediction algorithm that can minimize a weighted sum of squared prediction errors. Many such prediction algorithms are available, and the super learning principle can be used to combine multiple algorithms into a super learner under the direct approach. The resulting direct super learner has a desirable oracle property, is easy to implement, and performs well in realistic settings. The proposed methodology is illustrated with real data from a stroke trial.

Estimating the Population Average Treatment Effect in Observational Studies with Choice-Based Sampling

We consider causal inference in observational studies with choice-based sampling, in which subject enrollment is stratified on treatment choice. Choice-based sampling has been considered mainly in the econometrics literature, but it can be useful for biomedical studies as well, especially when one of the treatments being compared is uncommon. We propose new methods for estimating the population average treatment effect under choice-based sampling, including doubly robust methods motivated by semiparametric theory. A doubly robust, locally efficient estimator may be obtained by replacing nuisance functions in the efficient influence function with estimates based on parametric models. The use of machine learning methods to estimate nuisance functions leads to estimators that are consistent and asymptotically efficient under broader conditions. The methods are compared in simulation experiments and illustrated in the context of a large observational study in obstetrics. We also make suggestions on how to choose the target proportion of treated subjects and the sample size in designing a choice-based observational study.

Estimating inverse probability weights using super learner when weight-model specification is unknown in a marginal structural Cox model context

Correct specification of the inverse probability weighting (IPW) model is necessary for consistent inference from a marginal structural Cox model (MSCM). In practical applications, researchers are typically unaware of the true specification of the weight model. Nonetheless, IPWs are commonly estimated using parametric models, such as the main-effects logistic regression model. In practice, assumptions underlying such models may not hold and data-adaptive statistical learning methods may provide an alternative. Many candidate statistical learning approaches are available in the literature. However, the optimal approach for a given dataset is impossible to predict. Super learner (SL) has been proposed as a tool for selecting an optimal learner from a set of candidates using cross-validation. In this study, we evaluate the usefulness of a SL in estimating IPW in four different MSCM simulation scenarios, in which we varied the specification of the true weight model specification (linear and/or additive). Our simulations show that, in the presence of weight model misspecification, with a rich and diverse set of candidate algorithms, SL can generally offer a better alternative to the commonly used statistical learning approaches in terms of MSE as well as the coverage probabilities of the estimated effect in an MSCM. The findings from the simulation studies guided the application of the MSCM in a multiple sclerosis cohort from British Columbia, Canada (1995-2008), to estimate the impact of beta-interferon treatment in delaying disability progression. Copyright © 2017 John Wiley & Sons, Ltd.

Targeted Maximum Likelihood Estimation for Causal Inference in Observational Studies

Estimation of causal effects using observational data continues to grow in popularity in the epidemiologic literature. While many applications of causal effect estimation use propensity score methods or G-computation, targeted maximum likelihood estimation (TMLE) is a well-established alternative method with desirable statistical properties. TMLE is a doubly robust maximum-likelihood-based approach that includes a secondary "targeting" step that optimizes the bias-variance tradeoff for the target parameter. Under standard causal assumptions, estimates can be interpreted as causal effects. Because TMLE has not been as widely implemented in epidemiologic research, we aim to provide an accessible presentation of TMLE for applied researchers. We give step-by-step instructions for using TMLE to estimate the average treatment effect in the context of an observational study. We discuss conceptual similarities and differences between TMLE and 2 common estimation approaches (G-computation and inverse probability weighting) and present findings on their relative performance using simulated data. Our simulation study compares methods under parametric regression misspecification; our results highlight TMLE's property of double robustness. Additionally, we discuss best practices for TMLE implementation, particularly the use of ensembled machine learning algorithms. Our simulation study demonstrates all methods using super learning, highlighting that incorporation of machine learning may outperform parametric regression in observational data settings.

Propensity score and doubly robust methods for estimating the effect of treatment on censored cost

The estimation of treatment effects on medical costs is complicated by the need to account for informative censoring, skewness, and the effects of confounders. Because medical costs are often collected from observational claims data, we investigate propensity score (PS) methods such as covariate adjustment, stratification, and inverse probability weighting taking into account informative censoring of the cost outcome. We compare these more commonly used methods with doubly robust (DR) estimation. We then use a machine learning approach called super learner (SL) to choose among conventional cost models to estimate regression parameters in the DR approach and to choose among various model specifications for PS estimation. Our simulation studies show that when the PS model is correctly specified, weighting and DR perform well. When the PS model is misspecified, the combined approach of DR with SL can still provide unbiased estimates. SL is especially useful when the underlying cost distribution comes from a mixture of different distributions or when the true PS model is unknown. We apply these approaches to a cost analysis of two bladder cancer treatments, cystectomy versus bladder preservation therapy, using SEER-Medicare data. Copyright © 2015 John Wiley & Sons, Ltd.

Super Learner Analysis of Electronic Adherence Data Improves Viral Prediction and May Provide Strategies for Selective HIV RNA Monitoring

OBJECTIVE

Regular HIV RNA testing for all HIV-positive patients on antiretroviral therapy (ART) is expensive and has low yield since most tests are undetectable. Selective testing of those at higher risk of failure may improve efficiency. We investigated whether a novel analysis of adherence data could correctly classify virological failure and potentially inform a selective testing strategy.

DESIGN

Multisite prospective cohort consortium.

METHODS

We evaluated longitudinal data on 1478 adult patients treated with ART and monitored using the Medication Event Monitoring System (MEMS) in 16 US cohorts contributing to the MACH14 consortium. Because the relationship between adherence and virological failure is complex and heterogeneous, we applied a machine-learning algorithm (Super Learner) to build a model for classifying failure and evaluated its performance using cross-validation.

RESULTS

Application of the Super Learner algorithm to MEMS data, combined with data on CD4 T-cell counts and ART regimen, significantly improved classification of virological failure over a single MEMS adherence measure. Area under the receiver operating characteristic curve, evaluated on data not used in model fitting, was 0.78 (95% confidence interval: 0.75 to 0.80) and 0.79 (95% confidence interval: 0.76 to 0.81) for failure defined as single HIV RNA level >1000 copies per milliliter or >400 copies per milliliter, respectively. Our results suggest that 25%-31% of viral load tests could be avoided while maintaining sensitivity for failure detection at or above 95%, for a cost savings of $16-$29 per person-month.

CONCLUSIONS

Our findings provide initial proof of concept for the potential use of electronic medication adherence data to reduce costs through behavior-driven HIV RNA testing.

Finding Quantitative Trait Loci Genes with Collaborative Targeted Maximum Likelihood Learning

Quantitative trait loci mapping is focused on identifying the positions and effect of genes underlying an an observed trait. We present a collaborative targeted maximum likelihood estimator in a semi-parametric model using a newly proposed 2-part super learning algorithm to find quantitative trait loci genes in listeria data. Results are compared to the parametric composite interval mapping approach.