The g-formula can be used to estimate the treatment effect while accounting for confounding bias in observational studies. With regard to time-to-event endpoints, possibly subject to competing risks, the construction of valid pointwise confidence intervals and time-simultaneous confidence bands for the causal risk difference is complicated, however. A convenient solution is to approximate the asymptotic distribution of the corresponding stochastic process by means of resampling approaches. In this paper, we consider three different resampling methods, namely the classical nonparametric bootstrap, the influence function equipped with a resampling approach as well as a martingale-based bootstrap version. We set up a simulation study to compare the accuracy of the different techniques, which reveals that the wild bootstrap should in general be preferred if the sample size is moderate and sufficient data on the event of interest have been accrued. For illustration, the three resampling methods are applied to data on the long-term survival in patients with early-stage Hodgkin's disease.
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This study proposes a novel framework based on the RuleFit method to estimate Heterogeneous Treatment Effect (HTE) in a randomized clinical trial. To achieve this, we adopted S-learner of the metaalgorithm for our proposed framework. The proposed method incorporates a rule term for the main effect and treatment effect, which allows HTE to be interpretable form of rule. By including a main effect term in the proposed model, the selected rule is represented as an HTE that excludes other effects. We confirmed a performance equivalent to that of another ensemble learning methods through numerical simulation and demonstrated the interpretation of the proposed method from a real data application.
Temporally dense single-person "small data" have become widely available thanks to mobile apps and wearable sensors. Many caregivers and self-trackers want to use these data to help a specific person change their behavior to achieve desired health outcomes. Ideally, this involves discerning possible causes from correlations using that person's own observational time series data. In this paper, we estimate within-individual average treatment effects of physical activity on sleep duration, and vice-versa. We introduce the model twin randomization (MoTR; "motor") method for analyzing an individual's intensive longitudinal data. Formally, MoTR is an application of the g-formula (i.e., standardization, back-door adjustment) under serial interference. It estimates stable recurring effects, as is done in n-of-1 trials and single case experimental designs. We compare our approach to standard methods (with possible confounding) to show how to use causal inference to make better personalized recommendations for health behavior change, and analyze 222 days of Fitbit sleep and steps data for one of the authors.
Modelling in biology must adapt to increasingly complex and massive data. The efficiency of the inference algorithms used to estimate model parameters is therefore questioned. Many of these are based on stochastic optimization processes which waste a significant part of the computation time due to their rejection sampling approaches. We introduce the Fixed Landscape Inference MethOd (flimo), a new likelihood-free inference method for continuous state-space stochastic models. It applies deterministic gradient-based optimization algorithms to obtain a point estimate of the parameters, minimizing the difference between the data and some simulations according to some prescribed summary statistics. In this sense, it is analogous to Approximate Bayesian Computation (ABC). Like ABC, it can also provide an approximation of the distribution of the parameters. Three applications are proposed: a usual theoretical example, namely the inference of the parameters of g-and-k distributions; a population genetics problem, not so simple as it seems, namely the inference of a selective value from time series in a Wright-Fisher model; and simulations from a Ricker model, representing chaotic population dynamics. In the two first applications, the results show a drastic reduction of the computational time needed for the inference phase compared to the other methods, despite an equivalent accuracy. Even when likelihood-based methods are applicable, the simplicity and efficiency of flimo make it a compelling alternative. Implementations in Julia and in R are available on //metabarcoding.org/flimo. To run flimo, the user must simply be able to simulate data according to the chosen model.
Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.
Subjects in clinical studies that investigate paired body parts can carry a disease on either both sides (bilateral) or a single side (unilateral) of the organs. Data in such studies may consist of both bilateral and unilateral records. However, the correlation between the paired organs is often ignored, which may lead to biased interpretations. Recent literatures have taken the correlation into account. For example, Ma and Wang (2021) proposed three asymptotic procedures for testing the homogeneity of proportions of multiple groups using combined bilateral and unilateral data and recommended the score test. It is of importance to notice that the asymptotic behavior is not guaranteed if the sample size is small, resulting in uncontrolled type I error rates. In this paper, we extend their work by considering exact approaches and compare these methods with the score test proposed by Ma and Wang (2021) in terms of type I errors and statistical powers. Additionally, two real-world examples are used to illustrate the application of the proposed approaches.
Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e., to quantify how much variation in the response variable can be explained by the covariates, versus how much of the variation is left unexplained. This thesis considers the estimation of these quantities in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no responses $Y$. Our main research question is: how can one use the unlabeled data to better estimate $\tau^2$ and $\sigma^2$? We consider two frameworks: a linear regression model and a linear projection model in which linearity is not assumed. In the first framework, while linear regression is used, no sparsity assumptions on the coefficients are made. In the second framework, the linearity assumption is also relaxed and we aim to estimate the signal and noise levels defined by the linear projection. We first propose a naive estimator which is unbiased and consistent, under some assumptions, in both frameworks. We then show how the naive estimator can be improved by using zero-estimators, where a zero-estimator is a statistic arising from the unlabeled data, whose expected value is zero. In the first framework, we calculate the optimal zero-estimator improvement and discuss ways to approximate the optimal improvement. In the second framework, such optimality does no longer hold and we suggest two zero-estimators that improve the naive estimator although not necessarily optimally. Furthermore, we show that our approach reduces the variance for general initial estimators and we present an algorithm that potentially improves any initial estimator. Lastly, we consider four datasets and study the performance of our suggested methods.
Depression is the most prevalent and serious mental illness, which induces grave financial and societal ramifications. Depression detection is key for early intervention to mitigate those consequences. Such a high-stake decision inherently necessitates interpretability. Although a few depression detection studies attempt to explain the decision based on the importance score or attention weights, these explanations misalign with the clinical depression diagnosis criterion that is based on depressive symptoms. To fill this gap, we follow the computational design science paradigm to develop a novel Multi-Scale Temporal Prototype Network (MSTPNet). MSTPNet innovatively detects and interprets depressive symptoms as well as how long they last. Extensive empirical analyses using a large-scale dataset show that MSTPNet outperforms state-of-the-art depression detection methods with an F1-score of 0.851. This result also reveals new symptoms that are unnoted in the survey approach, such as sharing admiration for a different life. We further conduct a user study to demonstrate its superiority over the benchmarks in interpretability. This study contributes to IS literature with a novel interpretable deep learning model for depression detection in social media. In practice, our proposed method can be implemented in social media platforms to provide personalized online resources for detected depressed patients.
Randomized controlled trials (RCTs) are a cornerstone of comparative effectiveness because they remove the confounding bias present in observational studies. However, RCTs are typically much smaller than observational studies because of financial and ethical considerations. Therefore it is of great interest to be able to incorporate plentiful observational data into the analysis of smaller RCTs. Previous estimators developed for this purpose rely on unrealistic additional assumptions without which the added data can bias the effect estimate. Recent work proposed an alternative method (prognostic adjustment) that imposes no additional assumption and increases efficiency in the analysis of RCTs. The idea is to use the observational data to learn a prognostic model: a regression of the outcome onto the covariates. The predictions from this model, generated from the RCT subjects' baseline variables, are used as a covariate in a linear model. In this work, we extend this framework to work when conducting inference with nonparametric efficient estimators in trial analysis. Using simulations, we find that this approach provides greater power (i.e., smaller standard errors) than without prognostic adjustment, especially when the trial is small. We also find that the method is robust to observed or unobserved shifts between the observational and trial populations and does not introduce bias. Lastly, we showcase this estimator leveraging real-world historical data on a randomized blood transfusion study of trauma patients.
This paper studies inference for the local average treatment effect in randomized controlled trials with imperfect compliance where treatment status is determined according to "matched pairs." By "matched pairs," we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Under weak assumptions governing the quality of the pairings, we first derive the limiting behavior of the usual Wald (i.e., two-stage least squares) estimator of the local average treatment effect. We show further that the conventional heteroskedasticity-robust estimator of its limiting variance is generally conservative in that its limit in probability is (typically strictly) larger than the limiting variance. We therefore provide an alternative estimator of the limiting variance that is consistent for the desired quantity. Finally, we consider the use of additional observed, baseline covariates not used in pairing units to increase the precision with which we can estimate the local average treatment effect. To this end, we derive the limiting behavior of a two-stage least squares estimator of the local average treatment effect which includes both the additional covariates in addition to pair fixed effects, and show that the limiting variance is always less than or equal to that of the Wald estimator. To complete our analysis, we provide a consistent estimator of this limiting variance. A simulation study confirms the practical relevance of our theoretical results. We use our results to revisit a prominent experiment studying the effect of macroinsurance on microenterprise in Egypt.
The aim of this paper is to develop estimation and inference methods for the drift parameters of multivariate L\'evy-driven continuous-time autoregressive processes of order $p\in\mathbb{N}$. Starting from a continuous-time observation of the process, we develop consistent and asymptotically normal maximum likelihood estimators. We then relax the unrealistic assumption of continuous-time observation by considering natural discretizations based on a combination of Riemann-sum, finite difference, and thresholding approximations. The resulting estimators are also proven to be consistent and asymptotically normal under a general set of conditions, allowing for both finite and infinite jump activity in the driving L\'evy process. When discretizing the estimators, allowing for irregularly spaced observations is of great practical importance. In this respect, CAR($p$) models are not just relevant for "true" continuous-time processes: a CAR($p$) specification provides a natural continuous-time interpolation for modeling irregularly spaced data - even if the observed process is inherently discrete. As a practically relevant application, we consider the setting where the multivariate observation is known to possess a graphical structure. We refer to such a process as GrCAR and discuss the corresponding drift estimators and their properties. The finite sample behavior of all theoretical asymptotic results is empirically assessed by extensive simulation experiments.
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