In biomarker studies it is popular to perform an unsupervised clustering of high-dimensional variables like genome wide screens of SNPs, gene expressions, and protein data and regress for example treatment response, patient recorded outcome measures, time to disease progression, or overall survival on these potentially mislabelled clusters. It is well-known from the statistical literature that errors in continuous and categorical covariates can lead to loss of important information about effects on outcome (Carroll et al., 2006). However, to our surprise this is often ignored when regressing outcome on classes identified by unsupervised learning, which might lead to important clinical effect measures being overlooked (Alizadeh et al., 2000; Veer et al., 2002; Guinney et al., 2015; Zhan et al., 2006; Broyl et al., 2010). We suggest to cast the problem as a covariate misclassification problem. This leaves us with a concourse of possible modelling and analysis options, see for example the book by Carroll et al. (2006) or the recent review by Brakenhoff et al. (2018).
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose an efficient neural network design for estimating measurement error models, in which we use a fully connected feed-forward neural network (FNN) to approximate the regression function $f(x)$, a normalizing flow to approximate the prior distribution of $X$, and an inference network to approximate the posterior distribution of $X$. Our method utilizes recent advances in variational inference for deep neural networks, such as the importance weight autoencoder, doubly reparametrized gradient estimator, and non-linear independent components estimation. We conduct an extensive numerical study to compare the neural network approach with classical nonparametric methods and observe that the neural network approach is more flexible in accommodating different classes of regression functions and performs superior or comparable to the best available method in nearly all settings.
Measurement error in observational datasets can lead to systematic bias in inferences based on these datasets. As studies based on observational data are increasingly used to inform decisions with real-world impact, it is critical that we develop a robust set of techniques for analyzing and adjusting for these biases. In this paper we present a method for estimating the distribution of an outcome given a binary exposure that is subject to underreporting. Our method is based on a missing data view of the measurement error problem, where the true exposure is treated as a latent variable that is marginalized out of a joint model. We prove three different conditions under which the outcome distribution can still be identified from data containing only error-prone observations of the exposure. We demonstrate this method on synthetic data and analyze its sensitivity to near violations of the identifiability conditions. Finally, we use this method to estimate the effects of maternal smoking and opioid use during pregnancy on childhood obesity, two import problems from public health. Using the proposed method, we estimate these effects using only subject-reported drug use data and substantially refine the range of estimates generated by a sensitivity analysis-based approach. Further, the estimates produced by our method are consistent with existing literature on both the effects of maternal smoking and the rate at which subjects underreport smoking.
In epidemiology, identifying the effect of exposure variables in relation to a time-to-event outcome is a classical research area of practical importance. Incorporating propensity score in the Cox regression model, as a measure to control for confounding, has certain advantages when outcome is rare. However, in situations involving exposure measured with moderate to substantial error, identifying the exposure effect using propensity score in Cox models remains a challenging yet unresolved problem. In this paper, we propose an estimating equation method to correct for the exposure misclassification-caused bias in the estimation of exposure-outcome associations. We also discuss the asymptotic properties and derive the asymptotic variances of the proposed estimators. We conduct a simulation study to evaluate the performance of the proposed estimators in various settings. As an illustration, we apply our method to correct for the misclassification-caused bias in estimating the association of PM2.5 level with lung cancer mortality using a nationwide prospective cohort, the Nurses' Health Study (NHS). The proposed methodology can be applied using our user-friendly R function published online.
Causal inference requires theory and prior knowledge to structure analyses, and is not usually thought of as an arena for the application of prediction modelling. However, contemporary causal inference methods, premised on counterfactual or potential outcomes approaches, often include processing steps before the final estimation step. The purposes of this paper are: (i) to overview the recent emergence of prediction underpinning steps in contemporary causal inference methods as a useful perspective on contemporary causal inference methods, and (ii) explore the role of machine learning (as one approach to'best prediction') in causal inference. Causal inference methods covered include propensity scores, inverse probability of treatment weights (IPTWs), G computation and targeted maximum likelihood estimation (TMLE). Machine learning has been used more for propensity scores and TMLE, and there is potential for increased use in G computation and estimation of IPTWs.