Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations

Nonparametric kernel estimation of the probability of cure in a mixture cure model when the cure status is partially observed

Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care.

An alternative robust estimator of average treatment effect in causal inference

The problem of estimating the average treatment effects is important when evaluating the effectiveness of medical treatments or social intervention policies. Most of the existing methods for estimating the average treatment effect rely on some parametric assumptions about the propensity score model or the outcome regression model one way or the other. In reality, both models are prone to misspecification, which can have undue influence on the estimated average treatment effect. We propose an alternative robust approach to estimating the average treatment effect based on observational data in the challenging situation when neither a plausible parametric outcome model nor a reliable parametric propensity score model is available. Our estimator can be considered as a robust extension of the popular class of propensity score weighted estimators. This approach has the advantage of being robust, flexible, data adaptive, and it can handle many covariates simultaneously. Adopting a dimension reduction approach, we estimate the propensity score weights semiparametrically by using a non-parametric link function to relate the treatment assignment indicator to a low-dimensional structure of the covariates which are formed typically by several linear combinations of the covariates. We develop a class of consistent estimators for the average treatment effect and study their theoretical properties. We demonstrate the robust performance of the estimators on simulated data and a real data example of investigating the effect of maternal smoking on babies' birth weight.

Nonparametric methods for doubly robust estimation of continuous treatment effects

Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve, and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via simulation and in a study of the effect of nurse staffing on hospital readmissions penalties.

Enhanced precision in the analysis of randomized trials with ordinal outcomes

We present a general method for estimating the effect of a treatment on an ordinal outcome in randomized trials. The method is robust in that it does not rely on the proportional odds assumption. Our estimator leverages information in prognostic baseline variables, and has all of the following properties: (i) it is consistent; (ii) it is locally efficient; (iii) it is guaranteed to have equal or better asymptotic precision than both the inverse probability-weighted and the unadjusted estimators. To the best of our knowledge, this is the first estimator of the causal relation between a treatment and an ordinal outcome to satisfy these properties. We demonstrate the estimator in simulations based on resampling from a completed randomized clinical trial of a new treatment for stroke; we show potential gains of up to 39% in relative efficiency compared to the unadjusted estimator. The proposed estimator could be a useful tool for analyzing randomized trials with ordinal outcomes, since existing methods either rely on model assumptions that are untenable in many practical applications, or lack the efficiency properties of the proposed estimator. We provide R code implementing the estimator.