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.
We introduce a simple, interpretable strategy for making predictions on test data when the features of the test data are available at the time of model fitting. Our proposal—customized training—clusters the data to find training points close to each test point and then fits an ℓ1-regularized model (lasso) separately in each training cluster. This approach combines the local adaptivity of k-nearest neighbors with the interpretability of the lasso. Although we use the lasso for the model fitting, any supervised learning method can be applied to the customized training sets. We apply the method to a mass-spectrometric imaging data set from an ongoing collaboration in gastric cancer detection which demonstrates the power and interpretability of the technique. Our idea is simple but potentially useful in situations where the data have some underlying structure.
Personal predictive models for disease development play important roles in chronic disease prevention. The performance of these models is evaluated by applying them to the baseline covariates of participants in external cohort studies, with model predictions compared to subjects’ subsequent disease incidence. However the covariate distribution among participants in a validation cohort may differ from that of the population for which the model will be used. Since estimates of predictive model performance depend on the distribution of covariates among the subjects to which it is applied, such differences can cause misleading estimates of model performance in the target population. We propose a method for addressing this problem by weighting the cohort subjects to make their covariate distribution better match that of the target population. Simulations show that the method provides accurate estimates of model performance in the target population, while un-weighted estimates may not. We illustrate the method by applying it to evaluate an ovarian cancer prediction model targeted to US women, using cohort data from participants in the California Teachers Study. The methods can be implemented using open-source code for public use as the R-package RMAP (Risk Model Assessment Package) available at http://stanford.edu/~ggong/rmap/.
We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our method, nuclear penalized multinomial regression (NPMR), to Major League Baseball play-by-play data to predict outcome probabilities based on batter-pitcher matchups. The interpretation of the results meshes well with subject-area expertise and also suggests a novel understanding of what differentiates players.
Background: Rapid growth in the availability of genome-wide transcript abundance levels through gene expression microarrays and RNAseq promises to provide deep biological insights into the complex, genome-wide transcriptional behavior of single-celled organisms. However, this promise has not yet been fully realized.Results: We find that computation of pairwise gene associations (correlation; mutual information) across a set of 2782 total genome-wide expression samples from six diverse bacteria produces unexpectedly large variation in estimates of pairwise gene association—regardless of the metric used, the organism under study, or the number and source of the samples. We pinpoint the cause to sampling bias. In particular, in repositories of expression data (e.g., Gene Expression Omnibus, GEO), many individual genes show small differences in absolute gene expression levels across the set of samples. We demonstrate that these small differences are due mainly to “noise” instead of “signal” attributable to environmental or genetic perturbations. We show that downstream analysis using gene expression levels of genes with small differences yields biased estimates of pairwise association.Conclusions: We propose flagging genes with small differences in absolute, RMA-normalized, expression levels (e.g., standard deviation less than 0.5), as potentially yielding biased pairwise association metrics. This strategy has the potential to substantially improve the confidence in genome-wide conclusions about transcriptional behavior in bacterial organisms. Further work is needed to further refine strategies to identify genes with small difference in expression levels prior to computing gene-gene association metrics.
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