Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model considers measurement error not only in treatment covariates, but also in treatment times, a problem which arises in practice for example when treatment information is based on self-reporting. In a challenging and timely problem of estimating the impact of diet on continuous blood glucose measurements, our model leads to significant improvements in estimation accuracy and prediction.
Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such effects are divided into one of two strands depending on whether they require the conditional independence assumption (i.e., independence of potential outcomes and treatment assignment conditional on a set of observable covariates). When this assumption holds, researchers now have a wide array of estimation techniques from which to choose. However, very little is known about their performance – both in absolute and relative terms – when measurement error is present. In this study, the performance of several estimators that require the conditional independence assumption, as well as some that do not, are evaluated in a Monte Carlo study. In all cases, the data-generating process is such that conditional independence holds with the 'real' data. However, measurement error is then introduced. Specifically, three types of measurement error are considered: (i) errors in treatment assignment, (ii) errors in the outcome, and (iii) errors in the vector of covariates. Recommendations for researchers are provided. A method for inferring causal directions based on errors-in-variables models where both the cause variable and the effect variable are observed with measurement errors is concerned in this paper. The inference technique and estimation algorithms are given. Some experiments are included to illustrate our method. Apparent Diffusion Coefficient (ADC) is a potential quantitative imaging biomarker for tumour cell density and is widely used to detect early treatment changes in cancer therapy. We propose a strategy to improve confidence in the interpretation of measured changes in ADC using a data-driven model that describes sources of measurement error. Observed ADC is then standardised against this estimation of uncertainty for any given measurement. 20 patients were recruited prospectively and equitably across 4 sites, and scanned twice (test-retest) within 7 days. Repeatability measurements of defined regions (ROIs) of tumour and normal tissue were quantified as percentage change in mean ADC (test vs. re-test) and then standardised against an estimation of uncertainty. Multi-site reproducibility, (quantified as width of the 95 confidence bound between the lower confidence interval and higher confidence interval for all repeatability measurements), was compared before and after standardisation to the model. The 95 confidence interval width used to determine a statistically significant change reduced from 21.1 to 2.7 after standardisation. Small tumour volumes and respiratory motion were found to be important contributors to poor reproducibility. A look up chart has been provided for investigators who would like to estimate uncertainty from statistical error on individual ADC measurements. A common strategy for estimating treatment effects in observational studies using individual student-level data is analysis of covariance (ANCOVA) or hierarchical variants of it, in which outcomes (often standardized test scores) are regressed on pretreatment test scores, other student characteristics, and treatment group indicators. Measurement error in the prior test scores, which typically is both large and heteroscedastic, is regularly overlooked in empirical analyses and may erode the ability of regression models to adjust for student factors and may result in biased treatment effect estimates. We develop extensions of method-of-moments, Simulation-Extrapolation, and latent regression approaches to correcting for measurement error using the conditional standard errors of measure of test scores, and demonstrate their effectiveness relative to simpler alternatives using both simulation and a case study of teacher value-added effect estimation using longitudinal data from a large suburban school district.