We derive new estimators of an optimal joint testing and treatment regime under the no direct effect (NDE) assumption that a given laboratory, diagnostic, or screening test has no effect on a patient's clinical outcomes except through the effect of the test results on the choice of treatment. We model the optimal joint strategy using an optimal regime structural nested mean model (opt-SNMM). The proposed estimators are more efficient than previous estimators of the parameters of an opt-SNMM because they efficiently leverage the `no direct effect (NDE) of testing' assumption. Our methods will be of importance to decision scientists who either perform cost-benefit analyses or are tasked with the estimation of the `value of information' supplied by an expensive diagnostic test (such as an MRI to screen for lung cancer).
The methods for parameter estimation under assumption of agreement between observation and model are reviewed. The distribution parameters are obtained for one set of experimental data by using different estimation methods under assumption of Gauss-Laplace theoretical distribution. The results are presented and discussed.
The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the populat…
The assumption that the sampling distribution of the crude odds ratio (ORcrude) is a log-normal distribution with parameters mu and sigma leads to the incorrect conclusion that the expectation of the log of ORcrude is equal to the parameter mu. In fact, exp(mu) is the median of the lognormal distribution, not the mean. If a different parameter is obtained as the expected value of the lognormal distribution, then this quantity can be used to obtain a new estimate of the true odds ratio (ORtrue). Here, simulations are conducted based on a simple randomized clinical trial study design. The simula…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow the design of more accurate estimation procedures, such as Maximum Likelihood. Our aim is to construct a procedure that makes no explicit assumptions, but still providing an accurate estimate of the density. We introduce the self-consistent estimate: the power spectrum of a candidate density is given, and an estimation procedure is constructed on the assump…
The utility of capture-recapture methods is offset by strong underlying assumptions. In this paper we discuss a failure in the perfect linkage assumption in a special case of capture-recapture known as the dual system estimation. We propose a naive linkage error corrected dual system estimator. The advantage of the proposed approach compared with the existing linkage error corrected methods is that it permits an easy way to obtain the corresponding variance estimator.
Background: Instrumental variables (IVs) can be used to provide evidence as to whether a treatment X has a causal effect on an outcome Y. Even if the instrument Z satisfies the three core IV assumptions of relevance, independence and the exclusion restriction, further assumptions are required to identify the average causal effect (ACE) of X on Y. Sufficient assumptions for this include: homogeneity in the causal effect of X on Y; homogeneity in the association of Z with X; and no effect modification (NEM). Methods: We describe the NO Simultaneous Heterogeneity (NOSH) assumption, which requires…
The quantification of modern slavery has received increased attention recently as organizations have come together to produce global estimates, where multiple systems estimation (MSE) is often used to this end. Echoing a long-standing controversy, disagreements have re-surfaced regarding the underlying MSE assumptions, the robustness of MSE methodology, and the accuracy of MSE estimates in this application. Our goal is to help address and move past these controversies. To do so, we review MSE, its assumptions, and commonly used models for modern slavery applications. We introduce all of the pu…
Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are usually merged into the estimation. In this paper a novel boosting-based method is introduced to the nonparametric estimation in univariate cases. We deduce the boosting algorithm by the second-order approximation of nonparametric log-likelihood. Gaussian kernel and smooth spline are chosen as weak learners in boosting to satisfy the smoothing assumptions. Si…
When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using any instrumental variable. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators …
This paper explores bias in the estimation of sampling variance in Respondent Driven Sampling (RDS). Prior methodological work on RDS has focused on its problematic assumptions and the biases and inefficiencies of its estimators of the population mean. Nonetheless, researchers have given only slight attention to the topic of estimating sampling variance in RDS, despite the importance of variance estimation for the construction of confidence intervals and hypothesis tests. In this paper, we show that the estimators of RDS sampling variance rely on a critical assumption that the network is First…
State space models (SSMs) are now ubiquitous in many fields and increasingly complicated with observed and unobserved variables often interacting in non-linear fashions. The crucial task of validating model assumptions thus becomes difficult, particularly since some assumptions are formulated about unobserved states and thus cannot be checked with data. Motivated by the complex SSMs used for the assessment of fish stocks, we introduce a robust estimation method for SSMs. We prove the Fisher consistency of our estimator and propose an implementation based on automatic differentiation and the La…
Linear regression models are useful statistical tools to analyze data sets in several different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors with zero mean and constant variance. However, for some data sets error terms may not satisfy these or some of these assumptions. If error terms are correlated, such as the regression models with autoregressive (AR(p)) error terms, the Conditional Maximum Likelihood (CML) under normality assumption or the Least Square (LS) methods…
Instrumental variables (IVs) are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard IV model, however, the average treatment effect (ATE) is only partially identifiable. To address this, we propose novel assumptions that allow for identification of the ATE. Our identification assumptions are clearly separated from model assumptions needed for estimation, so that researchers are not required to commit to a specific observed data model in establishing identification. We then construct multiple estimators that are consistent under three differe…
In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate sh…
Randomized experiments on social networks pose statistical challenges, due to the possibility of interference between units. We propose new methods for estimating attributable treatment effects in such settings. The methods do not require partial interference, but instead require an identifying assumption that is similar to requiring nonnegative treatment effects. Network or spatial information can be used to customize the test statistic; in principle, this can increase power without making assumptions on the data generating process.
The estimation of the potential impact fraction (including the population attributable fraction) with continuous exposure data frequently relies on strong distributional assumptions. However, these assumptions are often violated if the underlying exposure distribution is unknown or if the same distribution is assumed across time or space. Nonparametric methods to estimate the potential impact fraction are available for cohort data, but no alternatives exist for cross-sectional data. In this article, we discuss the impact of distributional assumptions in the estimation of the population impact …
The use of causal mediation analysis to evaluate the pathways by which an exposure affects an outcome is widespread in the social and biomedical sciences. Recent advances in this area have established formal conditions for identification and estimation of natural direct and indirect effects. However, these conditions typically involve stringent no unmeasured confounding assumptions and that the mediator has been measured without error. These assumptions may fail to hold in practice where mediation methods are often applied. The goal of this paper is two-fold. First, we show that the natural in…
Suppose one wishes to estimate the effect of a binary treatment on a binary endpoint conditional on a post-randomization quantity in a counterfactual world in which all subjects received treatment. It is generally difficult to identify this parameter without strong, untestable assumptions. It has been shown that identifiability assumptions become much weaker under a crossover design in which subjects not receiving treatment are later given treatment. Under the assumption that the post-treatment biomarker observed in these crossover subjects is the same as would have been observed had they rece…
The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment. An additional assumption that is often made for the IV method is deterministic monotonicity, which is an assumption that for each subject, the level of the treatment that a subject would t…
Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We show that one can evade the curse of dimensionality by assuming a simplified vine copula model for the dependence between variables. We formulate a general nonparametric estimator for such a model and show under high-level assumptions that the speed of convergence is independent of dimension. We further discuss a particular implementation for which we validate the high-level assumptions and es…
Consistent Empirical Bayes estimation of the mean of a mixing distribution without identifiability assumption. With applications to treatment of non-response
Recent years have seen a swell in methods that focus on estimating "individual treatment effects". These methods are often focused on the estimation of heterogeneous treatment effects under ignorability assumptions. This paper hopes to draw attention to the fact that there is nothing necessarily "individual" about such effects under ignorability assumptions and isolating individual effects may require additional assumptions. Such individual effects, more often than not, are more precisely described as "conditional average treatment effects" and confusion between the two has the potential to hi…
Identifying causal treatment (or exposure) effects in observational studies requires the data to satisfy the unconfoundedness assumption which is not testable using the observed data. With sensitivity analysis, one can determine how the conclusions might change if assumptions are violated to a certain degree. In this paper, we propose a new technique for sensitivity analysis applicable to clusters observational data with a normally distributed or binary outcome. The proposed methods aim to assess the robustness of estimated treatment effects in a single study as well as in multiple studies, i.…
We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive assumption of independence. We illustrate that this distribution tends to be skewed and multi-modal, and that an independence assumption can lead to substantial bias in the estimation of the policy loss. Further, we extend our framework to regression models by combining marginal generalized linear models with a copula. We show that this approach leads to a flexibl…
Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. It is a semiparametric forward regression model based exhaustive sufficient dimension reduction estimation method that is shown to be consistent under mild assumptions. It is shown to outperform central subspace mean average variance estimation (c…
We study nonparametric estimation for the partially conditional average treatment effect, defined as the treatment effect function over an interested subset of confounders. We propose a hybrid kernel weighting estimator where the weights aim to control the balancing error of any function of the confounders from a reproducing kernel Hilbert space after kernel smoothing over the subset of interested variables. In addition, we present an augmented version of our estimator which can incorporate estimations of outcome mean functions. Based on the representer theorem, gradient-based algorithms can b…
This paper provides a set of methods for quantifying the robustness of treatment effects estimated using the unconfoundedness assumption (also known as selection on observables or conditional independence). Specifically, we estimate and do inference on bounds on various treatment effect parameters, like the average treatment effect (ATE) and the average effect of treatment on the treated (ATT), under nonparametric relaxations of the unconfoundedness assumption indexed by a scalar sensitivity parameter c. These relaxations allow for limited selection on unobservables, depending on the value of …
Multiple comparison procedures that control a family-wise error rate or false discovery rate provide an achieved error rate as the adjusted p-value for each hypothesis tested. However, since such p-values are not probabilities that the null hypotheses are true, empirical Bayes methods have been devised to estimate such posterior probabilities, called local false discovery rates (LFDRs) to emphasize the frequency interpretation of their priors. The main approaches to LFDR estimation, relying either on numerical algorithms to maximize likelihood or on the selection of smoothing parameters for no…
The Matusita overlapping coefficient is defined as agreement or similarity between two or more distributions. The parametric normal distribution is one of the most important statistical distributions. Under the assumption that the data at hand follow two independent normal distributions, this paper suggests a new technique to estimate the Matusita coefficient. In contrast to the studies in the literature, the suggested technique requires no assumptions on the location and scale parameters of the normal distributions. The finite properties of the resulting estimators are investigated and compar…
Inverse probability of treatment weighting (IPTW), which has been used to estimate sample average treatment effects (SATE) using observational data, tenuously relies on the positivity assumption and the correct specification of the treatment assignment model, both of which are problematic assumptions in many observational studies. Various methods have been proposed to overcome these challenges, including truncation, covariate-balancing propensity scores, and stable balancing weights. Motivated by an observational study in spine surgery, in which positivity is violated and the true treatment as…
Longitudinal cohorts to determine the incidence of HIV infection are logistically challenging, so researchers have sought alternative strategies. Recency test methods use biomarker profiles of HIV-infected subjects in a cross-sectional sample to infer whether they are "recently" infected and to estimate incidence in the population. Two main estimators have been used in practice: one that assumes a recency test is perfectly specific, and another that allows for false-recent results. To date, these commonly used estimators have not been rigorously studied with respect to their assumptions and st…
The causal effect of an intervention (treatment/exposure) on an outcome can be estimated by: i) specifying knowledge about the data-generating process; ii) assessing under what assumptions a target quantity, such as for example a causal odds ratio, can be identified given the specified knowledge (and given the measured data); and then, iii) using appropriate statistical estimation techniques to estimate the desired parameter of interest. As regression is the cornerstone of statistical analysis, it seems obvious to ask: is it appropriate to use estimated regression parameters for causal effect …
In this study, we develop a novel estimation method for quantile treatment effects (QTE) under rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and proposes a parametric estimation based on the minimum distance method. However, when the dimensionality of the covariates is large, the minimum distance estimation using this process is computationally demanding. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance methods. We then…
We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution …
The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The implementation is performed through recent outcomes in high-dimensional MCMC algorithms, and the performance of our method is assessed on simulated data.
The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data is drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly …
