Causal inference in the absence of positivity: The role of overlap weights.

How to analyze data when there is violation of the positivity assumption? Several possible solutions exist in the literature. In this paper, we consider propensity score (PS) methods that are commonly used in observational studies to assess causal treatment effects in the context where the positivity assumption is violated. We focus on and examine four specific alternative solutions to the inverse probability weighting (IPW) trimming and truncation: matching weight (MW), Shannon's entropy weight (EW), overlap weight (OW), and beta weight (BW) estimators. We first specify their target population, the population of patients for whom clinical equipoise, that is, where we have sufficient PS overlap. Then, we establish the nexus among the different corresponding weights (and estimators); this allows us to highlight the shared properties and theoretical implications of these estimators. Finally, we introduce their augmented estimators that take advantage of estimating both the propensity score and outcome regression models to enhance the treatment effect estimators in terms of bias and efficiency. We also elucidate the role of the OW estimator as the flagship of all these methods that target the overlap population. Our analytic results demonstrate that OW, MW, and EW are preferable to IPW and some cases of BW when there is a moderate or extreme (stochastic or structural) violation of the positivity assumption. We then evaluate, compare, and confirm the finite-sample performance of the aforementioned estimators via Monte Carlo simulations. Finally, we illustrate these methods using two real-world data examples marked by violations of the positivity assumption.

Accuracy of 12 Intraocular Lens Power Formulas After Corneal Myopic Refractive Surgery.

PURPOSE: To assess the predictive accuracy of new-generation online intraocular lens (IOL) power formulas in eyes with previous myopic laser refractive surgery (LRS) and to evaluate the influence of corneal asphericity on the predictive accuracy. METHODS: The authors retrospectively evaluated 52 patients (78 eyes) with a history of laser in situ keratomileusis (LASIK) or photorefractive keratectomy (PRK) who subsequently underwent cataract surgery. Refractive prediction errors were calculated for 12 no-history new online formulas: 8 formulas with post-LRS versions (Barrett True-K, EVO 2.0, Hoffer QST, and Pearl DGS) using keratometry and posterior/total keratometry measured by IOLMaster 700 and 4 formulas without post-LRS versions (Cooke K6 and Kane) using keratometry and total keratometry. The refractive prediction error, mean absolute error (MAE), and percentages of eyes with prediction errors of ±0.25, ±0.50, ±0.75, ±1.00, and ±1.50 diopters (D) were compared. RESULTS: The MAEs of the 12 formulas were significantly different (F = 83.66, P < .001). The MAEs ranged from 0.62 to 0.94 D and from 1.07 to 1.84 D in the formulas with and without post-LRS versions, respectively. The EVO formula produced the lowest MAE (0.60) and MedAE (0.47), followed by the Barrett True-K (0.69 and 0.50, respectively). Each percentage of eyes with refractive prediction error was also significantly different among the 12 formulas (P < .001). CONCLUSIONS: The EVO and Barrett True-K formulas demonstrate comparable performance to the other existing formulas in eyes with a history of myopic LASIK/PRK. Surgeons should use these formulas with post-LRS versions and input keratometric values whenever possible. [J Refract Surg. 2024;40(6):e354-e361.].

On exact randomization-based covariate-adjusted confidence intervals.

Randomization-based inference using the Fisher randomization test allows for the computation of Fisher-exact P-values, making it an attractive option for the analysis of small, randomized experiments with non-normal outcomes. Two common test statistics used to perform Fisher randomization tests are the difference-in-means between the treatment and control groups and the covariate-adjusted version of the difference-in-means using analysis of covariance. Modern computing allows for fast computation of the Fisher-exact P-value, but confidence intervals have typically been obtained by inverting the Fisher randomization test over a range of possible effect sizes. The test inversion procedure is computationally expensive, limiting the usage of randomization-based inference in applied work. A recent paper by Zhu and Liu developed a closed form expression for the randomization-based confidence interval using the difference-in-means statistic. We develop an important extension of Zhu and Liu to obtain a closed form expression for the randomization-based covariate-adjusted confidence interval and give practitioners a sufficiency condition that can be checked using observed data and that guarantees that these confidence intervals have correct coverage. Simulations show that our procedure generates randomization-based covariate-adjusted confidence intervals that are robust to non-normality and that can be calculated in nearly the same time as it takes to calculate the Fisher-exact P-value, thus removing the computational barrier to performing randomization-based inference when adjusting for covariates. We also demonstrate our method on a re-analysis of phase I clinical trial data.

Incorporating nonparametric methods for estimating causal excursion effects in mobile health with zero-inflated count outcomes.

In mobile health, tailoring interventions for real-time delivery is of paramount importance. Micro-randomized trials have emerged as the "gold-standard" methodology for developing such interventions. Analyzing data from these trials provides insights into the efficacy of interventions and the potential moderation by specific covariates. The "causal excursion effect," a novel class of causal estimand, addresses these inquiries. Yet, existing research mainly focuses on continuous or binary data, leaving count data largely unexplored. The current work is motivated by the Drink Less micro-randomized trial from the UK, which focuses on a zero-inflated proximal outcome, i.e., the number of screen views in the subsequent hour following the intervention decision point. To be specific, we revisit the concept of causal excursion effect, specifically for zero-inflated count outcomes, and introduce novel estimation approaches that incorporate nonparametric techniques. Bidirectional asymptotics are established for the proposed estimators. Simulation studies are conducted to evaluate the performance of the proposed methods. As an illustration, we also implement these methods to the Drink Less trial data.

A New Method to Minimize the Standard Deviation and Root Mean Square of the Prediction Error of Single-Optimized IOL Power Formulas.

Purpose: The purpose of this study was to develop a simplified method to approximate constants minimizing the standard deviation (SD) and the root mean square (RMS) of the prediction error in single-optimized intraocular lens (IOL) power calculation formulas. Methods: The study introduces analytical formulas to determine the optimal constant value for minimizing SD and RMS in single-optimized IOL power calculation formulas. These formulas were tested against various datasets containing biometric measurements from cataractous populations and included 10,330 eyes and 4 different IOL models. The study evaluated the effectiveness of the proposed method by comparing the outcomes with those obtained using traditional reference methods. Results: In optimizing IOL constants, minor differences between reference and estimated A-constants were found, with the maximum deviation at -0.086 (SD, SRK/T, and Vivinex) and -0.003 (RMS, PEARL DGS, and Vivinex). The largest discrepancy for third-generation formulas was -0.027 mm (SD, Haigis, and Vivinex) and 0.002 mm (RMS, Hoffer Q, and PCB00/SN60WF). Maximum RMS differences were -0.021 and +0.021, both involving Hoffer Q. Post-minimization, the largest mean prediction error was 0.726 diopters (D; SD) and 0.043 D (RMS), with the highest SD and RMS after adjustments at 0.529 D and 0.875 D, respectively, indicating effective minimization strategies. Conclusions: The study simplifies the process of minimizing SD and RMS in single-optimized IOL power predictions, offering a valuable tool for clinicians. However, it also underscores the complexity of achieving balanced optimization and suggests the need for further research in this area. Translational Relevance: The study presents a novel, clinically practical approach for optimizing IOL power calculations.

Prediction of low-addition segmented refractive intraocular lens position and deviation using anterior-segment optical coherence tomography.

This study aimed to develop and analyze the accuracy of predictive formulae for postoperative anterior chamber depth, tilt, and decentration of low-added-segment refractive intraocular lenses. This single-center, retrospective, observational study included the right eyes of 96 patients (mean age: 72.43 ± 6.58 years), who underwent a cataract surgery with implantation of a low-added segmented refractive intraocular lens at the Medical University Hospital between July 2019 and January 2021, and were followed up for more than 1 month postoperatively. The participants were divided into an estimation group to create a prediction formula and a validation group to verify the accuracy of the formula. Anterior segment optical coherence tomography (CASIA 2, Tomey Corporation, Japan) and swept-source optical coherence tomography biometry (IOL Master 700, Carl Zeiss Meditec AG) were used to measure the anterior ocular components. A predictive formula was devised for postoperative anterior chamber depth, intraocular lens tilt, and intraocular lens decentration (p <0.01) in the estimation group. A significant positive correlation was observed between the estimated values calculated using the prediction formula and the measured values for postoperative anterior chamber depth (r = 0.792), amount of intraocular lens tilt (r = 0.610), direction of intraocular lens tilt (r = 0.668), and amount of intraocular lens decentration (r = 0.431) (p < 0.01) in the validation group. In conclusion, our findings reveal that predicting the position of the low-added segmented refractive intraocular lens enables the prognosis of postoperative refractive values with a greater accuracy in determining the intraocular lens adaptation.

Effects of intraocular pressure change on intraocular lens power calculation in primary open-angle glaucoma and ocular hypertension.

This study aimed to assess the effect of intraocular pressure (IOP) changes on biometry and intraocular lens (IOL) power calculation in patients diagnosed with primary open-angle glaucoma (POAG) and ocular hypertension (OHT). This prospective non-randomized cohort study enrolled patients with diagnosed POAG and OHT, presenting with IOP levels exceeding 25 mmHg. Thai Clinical Trials Registry number was TCTR20180912007. Optical biometry, encompassing measurements such as corneal thickness (CCT), keratometry, anterior chamber depth (ACD), and axial length, was conducted before and after IOP reduction. The IOL power was also determined using the SRK/T formula. The main outcomes measured were alterations in biometry and IOL power. Correlations between IOP, biometric parameters, and IOL power were analyzed. In total, 28 eyes were included in the study, with a mean patient age of 65.71±10.2 years. After IOP reduction, all biometric parameters, except CCT and ACD, exhibited a decrease without reaching statistical significance (all p>0.05). Meanwhile, IOL power showed a slight increase of 0.214±0.42 diopters (P = 0.035). The correlation between IOP and biometric parameters was found to be weak. However, there was a moderate correlation between IOP and IOL power (r2 = 0.267). Notably, IOL power tended to increase by more than 0.5 diopters when IOP decreased by more than 10 mmHg (p < 0.001). In conclusion, changes in IOP among patients with POAG and OHT do not significantly impact biometry and IOL power calculations. Nonetheless, it may be prudent to consider a slight adjustment in IOL power when IOP is lowered by more than 10 mmHg.

Efficient testing of the biomarker positive and negative subgroups in a biomarker-stratified trial.

In many randomized placebo-controlled trials with a biomarker defined subgroup, it is believed that this subgroup has the same or higher treatment effect compared with its complement. These subgroups are often referred to as the biomarker positive and negative subgroups. Most biomarker-stratified pivotal trials are aimed at demonstrating a significant treatment effect either in the biomarker positive subgroup or in the overall population. A major shortcoming of this approach is that the treatment can be declared effective in the overall population even though it has no effect in the biomarker negative subgroup. We use the isotonic assumption about the treatment effects in the two subgroups to construct an efficient way to test for a treatment effect in both the biomarker positive and negative subgroups. A substantial reduction in the required sample size for such a trial compared with existing methods makes evaluating the treatment effect in both the biomarker positive and negative subgroups feasible in pivotal trials especially when the prevalence of the biomarker positive subgroup is less than 0.5.

Efficient data integration under prior probability shift.

Conventional supervised learning usually operates under the premise that data are collected from the same underlying population. However, challenges may arise when integrating new data from different populations, resulting in a phenomenon known as dataset shift. This paper focuses on prior probability shift, where the distribution of the outcome varies across datasets but the conditional distribution of features given the outcome remains the same. To tackle the challenges posed by such shift, we propose an estimation algorithm that can efficiently combine information from multiple sources. Unlike existing methods that are restricted to discrete outcomes, the proposed approach accommodates both discrete and continuous outcomes. It also handles high-dimensional covariate vectors through variable selection using an adaptive least absolute shrinkage and selection operator penalty, producing efficient estimates that possess the oracle property. Moreover, a novel semiparametric likelihood ratio test is proposed to check the validity of prior probability shift assumptions by embedding the null conditional density function into Neyman's smooth alternatives (Neyman, 1937) and testing study-specific parameters. We demonstrate the effectiveness of our proposed method through extensive simulations and a real data example. The proposed methods serve as a useful addition to the repertoire of tools for dealing dataset shifts.

Causal inference for time-to-event data with a cured subpopulation.

When studying the treatment effect on time-to-event outcomes, it is common that some individuals never experience failure events, which suggests that they have been cured. However, the cure status may not be observed due to censoring which makes it challenging to define treatment effects. Current methods mainly focus on estimating model parameters in various cure models, ultimately leading to a lack of causal interpretations. To address this issue, we propose 2 causal estimands, the timewise risk difference and mean survival time difference, in the always-uncured based on principal stratification as a complement to the treatment effect on cure rates. These estimands allow us to study the treatment effects on failure times in the always-uncured subpopulation. We show the identifiability using a substitutional variable for the potential cure status under ignorable treatment assignment mechanism, these 2 estimands are identifiable. We also provide estimation methods using mixture cure models. We applied our approach to an observational study that compared the leukemia-free survival rates of different transplantation types to cure acute lymphoblastic leukemia. Our proposed approach yielded insightful results that can be used to inform future treatment decisions.

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components.

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

Comparative review of novel model-assisted designs for phase I/II clinical trials.

In recent years, both model-based and model-assisted designs have emerged to efficiently determine the optimal biological dose (OBD) in phase I/II trials for immunotherapy and targeted cellular agents. Model-based designs necessitate repeated model fitting and computationally intensive posterior sampling for each dose-assignment decision, limiting their practical application in real trials. On the other hand, model-assisted designs employ simple statistical models and facilitate the precalculation of a decision table for use throughout the trial, eliminating the need for repeated model fitting. Due to their simplicity and transparency, model-assisted designs are often preferred in phase I/II trials. In this paper, we systematically evaluate and compare the operating characteristics of several recent model-assisted phase I/II designs, including TEPI, PRINTE, Joint i3+3, BOIN-ET, STEIN, uTPI, and BOIN12, in addition to the well-known model-based EffTox design, using comprehensive numerical simulations. To ensure an unbiased comparison, we generated 10,000 dosing scenarios using a random scenario generation algorithm for each predetermined OBD location. We thoroughly assess various performance metrics, such as the selection percentages, average patient allocation to OBD, and overdose percentages across the eight designs. Based on these assessments, we offer design recommendations tailored to different objectives, sample sizes, and starting dose locations.

Direct and indirect treatment effects in the presence of semicompeting risks.

Semicompeting risks refer to the phenomenon that the terminal event (such as death) can censor the nonterminal event (such as disease progression) but not vice versa. The treatment effect on the terminal event can be delivered either directly following the treatment or indirectly through the nonterminal event. We consider 2 strategies to decompose the total effect into a direct effect and an indirect effect under the framework of mediation analysis in completely randomized experiments by adjusting the prevalence and hazard of nonterminal events, respectively. They require slightly different assumptions on cross-world quantities to achieve identifiability. We establish asymptotic properties for the estimated counterfactual cumulative incidences and decomposed treatment effects. We illustrate the subtle difference between these 2 decompositions through simulation studies and two real-data applications in the Supplementary Materials.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Sparse Group Penalties for bi-level variable selection.

Many data sets exhibit a natural group structure due to contextual similarities or high correlations of variables, such as lipid markers that are interrelated based on biochemical principles. Knowledge of such groupings can be used through bi-level selection methods to identify relevant feature groups and highlight their predictive members. One of the best known approaches of this kind combines the classical Least Absolute Shrinkage and Selection Operator (LASSO) with the Group LASSO, resulting in the Sparse Group LASSO. We propose the Sparse Group Penalty (SGP) framework, which allows for a flexible combination of different SGL-style shrinkage conditions. Analogous to SGL, we investigated the combination of the Smoothly Clipped Absolute Deviation (SCAD), the Minimax Concave Penalty (MCP) and the Exponential Penalty (EP) with their group versions, resulting in the Sparse Group SCAD, the Sparse Group MCP, and the novel Sparse Group EP (SGE). Those shrinkage operators provide refined control of the effect of group formation on the selection process through a tuning parameter. In simulation studies, SGPs were compared with other bi-level selection methods (Group Bridge, composite MCP, and Group Exponential LASSO) for variable and group selection evaluated with the Matthews correlation coefficient. We demonstrated the advantages of the new SGE in identifying parsimonious models, but also identified scenarios that highlight the limitations of the approach. The performance of the techniques was further investigated in a real-world use case for the selection of regulated lipids in a randomized clinical trial.

Changes in ocular biometrics following cycloplegic refraction in strabismic and amblyopic children.

This study was aimed to analyze ocular biometric changes following cycloplegia in pediatric patients with strabismus and amblyopia. Cycloplegia is routinely used to measure refractive error accurately by paralyzing accommodation. However, effects on axial length (AL), anterior chamber depth (ACD), keratometry (Km), and white-to-white distance (WTW) are not well studied in this population. This retrospective study examined 797 patients (1566 eyes) undergoing cycloplegic refraction at a Samsung Kangbuk hospital pediatric ophthalmology clinic from 2010 to 2023. Ocular biometry was measured before and after instilling 1% cyclopentolate and 0.5% phenylephrine/0.5% tropicamide. Patients were categorized by strabismus diagnosis, age, refractive error and amblyopia status. Differences in AL, ACD, Km, WTW, and refractive error pre- and post-cycloplegia were analyzed using paired t tests. ACD (3.44 ±â€…0.33 vs 3.58 ±â€…0.29 mm, P < .05) and WTW (12.09 ±â€…0.42 vs 12.30 ±â€…0.60 mm, P < .05) increased significantly after cycloplegia in all groups except other strabismus subgroup (Cs) in both parameters and youngest subgroup (G1) in ACD. Refractive error demonstrated a hyperopic shift from -0.48 ±â€…3.00 D to -0.06 ±â€…3.32 D (P < .05) in overall and a myopic shift from -6.97 ±â€…4.27 to -8.10 ±â€…2.26 in high myopia (HM). Also, AL and Km did not change significantly. In conclusion, cycloplegia impacts ocular biometrics in children with strabismus and amblyopia, significantly increasing ACD and WTW. Refractive error shifts hyperopically in esotropia subgroup (ET) and myopically in high myopia subgroup (HM), eldest subgroup (G3) relating more to anterior segment changes than AL/Km. Understanding cycloplegic effects on biometry is important for optimizing refractive correction in these patients.

[Evaluation of the accuracy of modern intraocular lens calculation formulas when optical biometry is not possible]. / Otsenka tochnosti sovremennykh formul rascheta intraokulyarnykh linz pri nevozmozhnosti vypolneniya opticheskoi biometrii.

PURPOSE: This study evaluates the accuracy of modern intraocular lens (IOL) calculation formulas using axial length (AL) data obtained by ultrasound biometry (UBM) compared to the third-generation SRK/T calculator. MATERIAL AND METHODS: The study included 230 patients (267 eyes) with severe lens opacities that prevented optical biometry, who underwent phacoemulsification (PE) with IOL implantation. IOL power calculation according to the SRK/T formula was based on AL and anterior chamber depth obtained by UBM (Tomey Biometer Al-100) and keratometry on the Topcon KR 8800 autorefractometer. To adapt AL for new generation calculators - Barrett Universal II (BUII), Hill RBF ver. 3.0 (RBF), Kane and Ladas Super Formula (LSF) - the retinal thickness (0.20 mm) was added to the axial length determined by UBM, and then the optical power of the artificial lens was calculated. The mean error and its modulus value were used as criteria for the accuracy of IOL calculation. RESULTS: A significant difference (p=0.008) in the mean IOL calculation error was found between the formulas. Pairwise analysis revealed differences between SRK/T (-0.32±0.58 D) and other formulas - BUII (-0.16±0.52 D; p=0.014), RBF (-0.17±0.51 D; p=0.024), Kane (-0.17±0.52 D; p=0.029), but not with the LSF calculator (-0.19±0.53 D; p=0.071). No significant differences between the formulas were found in terms of mean error modulus (p=0.238). New generation calculators showed a more frequent success in hitting target refraction (within ±1.00 D in more than 95% of cases) than the SRK/T formula (86%). CONCLUSION: The proposed method of adding 0.20 mm to the AL determined by UBM allows using this parameter in modern IOL calculation formulas and improving the refractive results of PE, especially in eyes with non-standard anterior segment structure.