Survivor-complier effects in the presence of selection on treatment, with application to a study of prompt ICU admission

Pre-treatment selection or censoring (`selection on treatment') can occur when two treatment levels are compared ignoring the third option of neither treatment, in `censoring by death' settings where treatment is only defined for those who survive long enough to receive it, or in general in studies where the treatment is only defined for a subset of the population. Unfortunately, the standard instrumental variable (IV) estimand is not defined in the presence of such selection, so we consider estimating a new survivor-complier causal effect. Although this effect is generally not identified under standard IV assumptions, it is possible to construct sharp bounds. We derive these bounds and give a corresponding data-driven sensitivity analysis, along with nonparametric yet efficient estimation methods. Importantly, our approach allows for high-dimensional confounding adjustment, and valid inference even after employing machine learning. Incorporating covariates can tighten bounds dramatically, especially when they are strong predictors of the selection process. We apply the methods in a UK cohort study of critical care patients to examine the mortality effects of prompt admission to the intensive care unit, using ICU bed availability as an instrument

Understanding Instrumental Variables in Models with Essential Heterogeneity

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters.

Understanding Instrumental Variables in Models with Essential Heterogeneity

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters.

Isolation in the construction of natural experiments

A natural experiment is a type of observational study in which treatment assignment, though not randomized by the investigator, is plausibly close to random. A process that assigns treatments in a highly nonrandom, inequitable manner may, in rare and brief moments, assign aspects of treatments at random or nearly so. Isolating those moments and aspects may extract a natural experiment from a setting in which treatment assignment is otherwise quite biased, far from random. Isolation is a tool that focuses on those rare, brief instances, extracting a small natural experiment from otherwise useless data. We discuss the theory behind isolation and illustrate its use in a reanalysis of a well-known study of the effects of fertility on workforce participation. Whether a woman becomes pregnant at a certain moment in her life and whether she brings that pregnancy to term may reflect her aspirations for family, education and career, the degree of control she exerts over her fertility, and the quality of her relationship with the father; moreover, these aspirations and relationships are unlikely to be recorded with precision in surveys and censuses, and they may confound studies of workforce participation. However, given that a women is pregnant and will bring the pregnancy to term, whether she will have twins or a single child is, to a large extent, simply luck. Given that a woman is pregnant at a certain moment, the differential comparison of two types of pregnancies on workforce participation, twins or a single child, may be close to randomized, not biased by unmeasured aspirations. In this comparison, we find in our case study that mothers of twins had more children but only slightly reduced workforce participation, approximately 5% less time at work for an additional child.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS770 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

College Education and Wages in the U.K.: Estimating Conditional Average Structural Functions in Nonadditive Models with Binary Endogenous Variables

Recent studies debate how the unobserved dependence between the monetary return to college education and selection into college can be characterized. This paper examines this question using British data. We develop a semiparametric local instrumental variables estimator for identified features of a flexible correlated random coefficient model. These identified features are directly related to the marginal and average treatment effect in policy evaluation. Our results indicate that returns to college systematically differ between actual college graduates and actual college non-graduates. They are on average higher for college graduates and positively related to selection into college for 96 percent of the individuals. The dependence between selection into college and returns to college education is strongest for individuals with low math test scores at the age of 7, individuals with less educated mothers, and for working-class individuals.Returns to college education;correlated random coefficient model;local instrumental variables estimation

Finding Young Stellar Populations in Elliptical Galaxies from Independent Components of Optical Spectra

Elliptical galaxies are believed to consist of a single population of old stars formed together at an early epoch in the Universe, yet recent analyses of galaxy spectra seem to indicate the presence of significant younger populations of stars in them. The detailed physical modelling of such populations is computationally expensive, inhibiting the detailed analysis of the several million galaxy spectra becoming available over the next few years. Here we present a data mining application aimed at decomposing the spectra of elliptical galaxies into several coeval stellar populations, without the use of detailed physical models. This is achieved by performing a linear independent basis transformation that essentially decouples the initial problem of joint processing of a set of correlated spectral measurements into that of the independent processing of a small set of prototypical spectra. Two methods are investigated: (1) A fast projection approach is derived by exploiting the correlation structure of neighboring wavelength bins within the spectral data. (2) A factorisation method that takes advantage of the positivity of the spectra is also investigated. The preliminary results show that typical features observed in stellar population spectra of different evolutionary histories can be convincingly disentangled by these methods, despite the absence of input physics. The success of this basis transformation analysis in recovering physically interpretable representations indicates that this technique is a potentially powerful tool for astronomical data mining.Comment: 12 Pages, 7 figures; accepted in SIAM 2005 International Conference on Data Mining, Newport Beach, CA, April 200