ترغب بنشر مسار تعليمي؟ اضغط هنا

A coherent likelihood parametrization for doubly robust estimation of a causal effect with missing confounders

96   0   0.0 ( 0 )
 نشر من قبل Isabel Fulcher
 تاريخ النشر 2020
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

Missing data and confounding are two problems researchers face in observational studies for comparative effectiveness. Williamson et al. (2012) recently proposed a unified approach to handle both issues concurrently using a multiply-robust (MR) methodology under the assumption that confounders are missing at random. Their approach considers a union of models in which any submodel has a parametric component while the remaining models are unrestricted. We show that while their estimating function is MR in theory, the possibility for multiply robust inference is complicated by the fact that parametric models for different components of the union model are not variation independent and therefore the MR property is unlikely to hold in practice. To address this, we propose an alternative transparent parametrization of the likelihood function, which makes explicit the model dependencies between various nuisance functions needed to evaluate the MR efficient score. The proposed method is genuinely doubly-robust (DR) in that it is consistent and asymptotic normal if one of two sets of modeling assumptions holds. We evaluate the performance and doubly robust property of the DR method via a simulation study.



قيم البحث

اقرأ أيضاً

Missing attributes are ubiquitous in causal inference, as they are in most applied statistical work. In this paper, we consider various sets of assumptions under which causal inference is possible despite missing attributes and discuss corresponding approaches to average treatment effect estimation, including generalized propensity score methods and multiple imputation. Across an extensive simulation study, we show that no single method systematically out-performs others. We find, however, that doubly robust modifications of standard methods for average treatment effect estimation with missing data repeatedly perform better than their non-doubly robust baselines; for example, doubly robust generalized propensity score methods beat inverse-weighting with the generalized propensity score. This finding is reinforced in an analysis of an observations study on the effect on mortality of tranexamic acid administration among patients with traumatic brain injury in the context of critical care management. Here, doubly robust estimators recover confidence intervals that are consistent with evidence from randomized trials, whereas non-doubly robust estimators do not.
Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists o f victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First, we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic near-validity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.
We derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs when the number of nodes $n_V$ and the observed times of a graph denoted by $K$ diverge to infinity. Finally, we display the estimation results in a Monte Carlo simulation considering different numbers of latent variables. Besides, we make a comparison between Laplace and variational approximations for inference of our model.
Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model propo sed originally by the sociologist Paul F. Lazarfeld for categorical variables, and we explain its geometric structure. We draw parallels between the statistical and geometric properties of latent class models and we illustrate geometrically the causes of many problems associated with maximum likelihood estimation and related statistical inference. In particular, we focus on issues of non-identifiability and determination of the model dimension, of maximization of the likelihood function and on the effect of symmetric data. We illustrate these phenomena with a variety of synthetic and real-life tables, of different dimension and complexity. Much of the motivation for this work stems from the 100 Swiss Francs problem, which we introduce and describe in detail.
Causal effect sizes may vary among individuals and they can even be of opposite directions. When there exists serious effect heterogeneity, the population average causal effect (ACE) is not very informative. It is well-known that individual causal ef fects (ICEs) cannot be determined in cross-sectional studies, but we will show that ICEs can be retrieved from longitudinal data under certain conditions. We will present a general framework for individual causality where we will view effect heterogeneity as an individual-specific effect modification that can be parameterized with a latent variable, the receptiveness factor. The distribution of the receptiveness factor can be retrieved, and it will enable us to study the contrast of the potential outcomes of an individual under stationarity assumptions. Within the framework, we will study the joint distribution of the individuals potential outcomes conditioned on all individuals factual data and subsequently the distribution of the cross-world causal effect (CWCE). We discuss conditions such that the latter converges to a degenerated distribution, in which case the ICE can be estimated consistently. To demonstrate the use of this general framework, we present examples in which the outcome process can be parameterized as a (generalized) linear mixed model.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا