We propose a class of two-sample statistics for testing the equality of proportions and the equality of survival functions. We build our proposal on a weighted combination of a score test for the difference in proportions and a Weighted Kaplan-Meier statistic-based test for the difference of survival functions. The proposed statistics are fully non-parametric and do not rely on the proportional hazards assumption for the survival outcome. We present the asymptotic distribution of these statistics, propose a variance estimator and show their asymptotic properties under fixed and local alternatives. We discuss different choices of weights including those that control the relative relevance of each outcome and emphasize the type of difference to be detected in the survival outcome. We evaluate the performance of these statistics with a simulation study, and illustrate their use with a randomized phase III cancer vaccine trial. We have implemented the proposed statistics in the R package SurvBin, available on GitHub (https://github.com/MartaBofillRoig/SurvBin).
Covariate adjustment is an important tool in the analysis of randomized clinical trials and observational studies. It can be used to increase efficiency and thus power, and to reduce possible bias. While most statistical tests in randomized clinical trials are nonparametric in nature, approaches for covariate adjustment typically rely on specific regression models, such as the linear model for a continuous outcome, the logistic regression model for a dichotomous outcome and the Cox model for survival time. Several recent efforts have focused on model-free covariate adjustment. This paper makes…
Instrumental variable (IV) methods allow us the opportunity to address unmeasured confounding in causal inference. However, most IV methods are only applicable to discrete or continuous outcomes with very few IV methods for censored survival outcomes. In this work we propose nonparametric estimators for the local average treatment effect on survival probabilities under both nonignorable and ignorable censoring. We provide an efficient influence function-based estimator and a simple estimation procedure when the IV is either binary or continuous. The proposed estimators possess double-robustnes…
We propose efficient nonparametric statistics to compare medical imaging modalities in multi-reader multi-test data and to compare markers in longitudinal ROC data. The proposed methods are based on the weighted area under the ROC curve which includes the area under the curve and the partial area under the curve as special cases. The methods maximize the local power for detecting the difference between imaging modalities. The asymptotic results of the proposed methods are developed under a complex correlation structure. Our simulation studies show that the proposed statistics result in much be…
This paper develops a nonparametric model that represents how sequences of outcomes and treatment choices influence one another in a dynamic manner. In this setting, we are interested in identifying the average outcome for individuals in each period, had a particular treatment sequence been assigned. The identification of this quantity allows us to identify the average treatment effects (ATE's) and the ATE's on transitions, as well as the optimal treatment regimes, namely, the regimes that maximize the (weighted) sum of the average potential outcomes, possibly less the cost of the treatments. …
We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors. The outcomes are not well-characterized by simple parametric models, so we use a nonparametric approach with a binomial likelihood wherein the latent probabilities are drawn from a mixture with an arbitrary number of components, analogous to a Dirichlet Process (DP). We use a fl…
Researchers are often interested in predicting outcomes, conducting clustering analysis to detect distinct subgroups of their data, or computing causal treatment effects. Pathological data distributions that exhibit skewness and zero-inflation complicate these tasks - requiring highly flexible, data-adaptive modeling. In this paper, we present a fully nonparametric Bayesian generative model for continuous, zero-inflated outcomes that simultaneously predicts structural zeros, captures skewness, and clusters patients with similar joint data distributions. The flexibility of our approach yields p…
In international football (soccer), two-legged knockout ties, with each team playing at home in one leg and the final outcome decided on aggregate, are common. Many players, managers and followers seem to believe in the `second-leg home advantage', i.e. that it is beneficial to play at home on the second leg. A more complex effect than the usual and well-established home advantage, it is harder to identify, and previous statistical studies did not prove conclusive about its actuality. Yet, given the amount of money handled in international football competitions nowadays, the question of existe…
This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulatio…
Missing exposure information is a very common feature of many observational studies. Here we study identifiability and efficient estimation of causal effects on vector outcomes, in such cases where treatment is unconfounded but partially missing. We consider a missing at random setting where missingness in treatment can depend not only on complex covariates, but also on post-treatment outcomes. We give a new identifying expression for average treatment effects in this setting, along with the efficient influence function for this parameter in a nonparametric model, which yields a nonparametric …
When studying treatment effects in multilevel studies, investigators commonly use (semi-)parametric estimators, which make strong parametric assumptions about the outcome, the treatment, and/or the correlation structure between study units in a cluster. We propose a novel estimator of treatment effects that does not make such assumptions. Specifically, the new estimator is shown to be doubly robust, asymptotically Normal, and often more efficient than existing estimators, all without having to make any parametric modeling assumptions about the outcome, the treatment, and the correlation struct…
Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstra…
In many scientific studies, it is of interest to determine whether an exposure has a causal effect on an outcome. In observational studies, this is a challenging task due to the presence of confounding variables that affect both the exposure and the outcome. Many methods have been developed to test for the presence of a causal effect when all such confounding variables are observed and when the exposure of interest is discrete. In this article, we propose a class of nonparametric tests of the null hypothesis that there is no average causal effect of an arbitrary univariate exposure on an outco…
In randomized clinical trials with survival outcome, there has been an increasing interest in subgroup identification based on baseline genomic, proteomic markers or clinical characteristics. Some of the existing methods identify subgroups that benefit substantially from the experimental treatment by directly modeling outcomes or treatment effect. When the goal is to find an optimal treatment for a given patient rather than finding the right patient for a given treatment, methods under the individualized treatment regime framework estimate an individualized treatment rule that would lead to th…
This article aims to consider a new univariate nonparametric cumulative sum (CUSUM) control chart for small shift of location based on both change-point model and Mann-Whitney statistic. Some comparisons on the performances of the proposed chart with other charts as well as the properties of the test statistic are presented. Simulations indicate that the proposed chart is sensitive in detection of the small mean shifts of the process by a high intensive accumulation of sample information when the underlying variable is completely distribution-free.
Nonparametric estimation of the conditional expectation $E(Y | U)$ of an outcome $Y$ given a covariate vector $U$ is of primary importance in many statistical applications such as prediction and personalized medicine. In some problems, there is an additional auxiliary variable $Z$ in the training dataset used to construct estimators, but $Z$ is not available for future prediction or selecting patient treatment in personalized medicine. For example, in the training dataset longitudinal outcomes are observed, but only the last outcome $Y$ is concerned in the future prediction or analysis. The lo…
A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity.…
Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally precludes the nonparametric identification of causal effects. Nonparametric bounds can provide a way to narrow the range of possible values for a nonidentifiable causal effect without making additional untestable assumptions. The nonparametric bounds literature has almost exclusively focused on settings with random sampling, and the bounds have often been derive…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach is adequate for univariate classification tasks, it is especially advantageous for filter-type variable selection. It constitutes a robust and nonparametric method which may identify important otherwise neglected variables. It can incorporate the operating conditions of the classification task. Last but not least, the exact finite sample distribution of the…
In this article, we introduce the BNPqte R package which implements the Bayesian nonparametric approach of Xu, Daniels and Winterstein (2018) for estimating quantile treatment effects in observational studies. This approach provides flexible modeling of the distributions of potential outcomes, so it is capable of capturing a variety of underlying relationships among the outcomes, treatments and confounders and estimating multiple quantile treatment effects simultaneously. Specifically, this approach uses a Bayesian additive regression trees (BART) model to estimate the propensity score and a D…
Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also…
There is a long-standing debate in the statistical, epidemiological and econometric fields as to whether nonparametric estimation that uses data-adaptive methods, like machine learning algorithms in model fitting, confer any meaningful advantage over simpler, parametric approaches in real-world, finite sample estimation of causal effects. We address the question: when trying to estimate the effect of a treatment on an outcome, across a universe of reasonable data distributions, how much does the choice of nonparametric vs.~parametric estimation matter? Instead of answering this question with s…
Colocalization is a powerful tool to study the interactions between fluorescently labeled molecules in biological fluorescence microscopy. However, existing techniques for colocalization analysis have not undergone continued development especially in regards to robust statistical support. In this paper, we examine two of the most popular quantification techniques for colocalization and argue that they could be improved upon using ideas from nonparametric statistics and scan statistics. In particular, we propose a new colocalization metric that is robust, easily implementable, and optimal in a …
Hypothesis testing and other statistical inference procedures are most efficient when a reliable low-dimensional parametric family can be specified. We propose a method that learns such a family when one exists but its form is not known a priori, by examining samples from related populations and fitting a low-dimensional exponential family that approximates all the samples as well as possible. We propose a computationally efficient spectral method that allows us to carry out hypothesis tests that are valid whether or not the fit is good, and recover asymptotically optimal power if it is. Our m…
We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a special regressor type restriction and monotonicity in the nonlinear relationship between the observed and unobserved true outcome. Nonparametric identification is then obtained under a normalization of the unknown link function, which is a natural extension of the classical measurement error case. We propose a novel sieve rank estimator for the regression functi…
Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999). We derive an analytic expression for the $n^{-1}$ term, which may be used to calibrate the nominal coverage level to get $O\bigl(n^{-3/2}[\log(n)]^3\bigr)$ coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with as…
We consider the problem of testing for treatment effect heterogeneity in observational studies, and propose a nonparametric test based on multisample U-statistics. To account for potential confounders, we use reweighted data where the weights are determined by estimated propensity scores. The proposed method does not require any parametric assumptions on the outcomes and bypasses the need for modeling the treatment effect for each study subgroup. We establish the asymptotic normality for the test statistic, and demonstrate its superior numerical performance over several competing approaches vi…
The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical genomics data from these studies are often high-dimensional. The high-dimensional linear instrumental-variables regression has been considered in the literature due to its simplicity albeit a true nonlinear relationship may exist. We propose a more data-driven approach by considering the nonparametric additive models between the instruments and the treatment…
Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation methods exist, little is known about its distribution when the noise is not weakly stationary. In this paper we develop a nonparametric method to estimate the distribution of an SNR statistic when the noise belongs to a fairly general class of stochastic processes that encompasses both short and long-range dependence, as well as nonlinearities. The method is b…
Inference procedures in sequential trial emulation with survival outcomes: comparing confidence intervals based on the sandwich variance estimator, bootstrap and jackknife
A case-control family study is a study where individuals with a disease of interest (case probands) and individuals without the disease (control probands) are randomly sampled from a well-defined population. Possibly right-censored age at onset and disease status are observed for both probands and their relatives. Correlation among the outcomes within a family is induced by factors such as inherited genetic susceptibility, shared environment, and common behavior patterns. For this setting, we present a nonparametric estimator of the marginal survival function, based on local linear estimation …
In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are shown. Numerical evidence is also provided using various real life data sets to assess the performance of the model. Our proposed nonparametric ensemble classifier doesn't suffer from the `curse of dimensionality' and can be used in a wide variety of feature selection cum classification problems. Performance of the proposed model is quite better when compare…
