Sensitivity analysis for matched observational studies with continuous exposures and binary outcomes

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g. RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data,more » providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.« less

Matching is a commonly used causal inference study design in observational studies. Through matching on measured confounders between different treatment groups, valid randomization inferences can be conducted under the no unmeasured confounding assumption, and sensitivity analysis can be further performed to assess robustness of results to potential unmeasured confounding. However, for many common matched designs, there is still a lack of valid downstream randomization inference and sensitivity analysis methods. Specifically, in matched observational studies with treatment doses (eg, continuous or ordinal treatments), with the exception of some special cases such as pair matching, there is no existing randomization inference or sensitivity analysis method for studying analogs of the sample average treatment effect (ie, Neyman-type weak nulls), and no existing valid sensitivity analysis approach for testing the sharp null of no treatment effect for any subject (ie, Fisher's sharp null) when the outcome is nonbinary. To fill these important gaps, we propose new methods for randomization inference and sensitivity analysis that can work for general matched designs with treatment doses, applicable to general types of outcome variables (eg, binary, ordinal, or continuous), and cover both Fisher's sharp null and Neyman-type weak nulls. We illustrate our methods via comprehensive simulation studies and a real data application. All the proposed methods have been incorporated into $\tt {R}$ package $\tt {doseSens}$.

This study uses Monte Carlo simulations to examine the ability of the two-stage least-squares (2SLS) estimator and two-stage residual inclusion (2SRI) estimators with varying forms of residuals to estimate the local average and population average treatment effect parameters in models with binary outcome, endogenous binary treatment, and single binary instrument. The rarity of the outcome and the treatment are varied across simulation scenarios. Results show that 2SLS generated consistent estimates of the LATE and biased estimates of the ATE across all scenarios. 2SRI approaches, in general, produce biased estimates of both LATE and ATE under all scenarios. 2SRI using generalized residuals minimizes the bias in ATE estimates. Use of 2SLS and 2SRI is illustrated in an empirical application estimating the effects of long-term care insurance on a variety of binary healthcare utilization outcomes among the near-elderly using the Health and Retirement Study.

Now a days the usage of electrical power is increasing enormously and it is also becoming highly impossible in imagining the world without the electricity. So here is one of the techniques for maintaining the continuous supply i.e., by generating the electrical power in the distribution premises. Distribution Generation has been growing rapidly in power systems due to their capable solution for the issues like power system deregulation, to meet the demand of electric power and shortages in the electric power transmission capacities. Concept of Distributed generation (DG) plays an effective key role in the distribution networks. Among many of their merits, real power loss reduction, THD reduction voltage sag and voltage swell reduction and voltage profile improvement can be the salient merits of DG. Improper location of DG sources in to the electrical power system would lead to the increase energy or power loss, and also jeopardize the system operation. In this paper, determination of DG location is done by using Sensitivity Analysis and corresponding DG size is found by using Particle Swarm Optimization (PSO) to mitigate the real power losses in the distribution networks. Standard IEEE 15 bus test system is chosen to test the proposed PSO — Sensitivity Analysis approach. The results so obtained show the enhancement of voltage profile, reduction of real power loss using MATLAB.

GIS multicriteria decision analysis (MCDA) methods are increasingly being used in landslide susceptibility mapping for the prediction of future hazards, decision making, as well as hazard mitigation plans. However, the uncertainties associated with MCDA techniques are inevitable and model outcomes are prone to multiple types of uncertainty. In this paper, the spatiality explicitly method is employed to assess the uncertainty associated with two methods of GIS-MCDA namely, Analytical Hierarchical Process (AHP) and Ordered Weighted Averaging (OWA). Our methodology consists of three stages. The first-stage analysis makes use of the AHP matrix weights for GIS-MCDA based landslide susceptibility mapping. This phase is based on a multicriteria evaluation which assesses the susceptibility areas and the landslide hazard potentiality by considering causal and diagnostic criteria. In the second stage the sensitivity and uncertainty analysis of the AHP weights is performed using Monte Carlo Simulation (MCS) and Global Sensitive Analysis (GSA). Finally, validation of results was performed using the existing landslide inventory. This paper carried out a GIS-MCDA uncertainty analysis and demonstrates a solution for the uncertainty modelling. Through the validation exercise with known existing landslides, the AHP clearly performed best. Results of this research demonstrate that further improvement of the accuracy of GIS-based MCDA can be achieved by employing the spatiality explicitly method and accordingly applying MCS and GSA for sensitivity analysis of the AHP weights.

Longitudinal studies with binary outcomes characterized by informative right censoring are commonly encountered in clinical, basic, behavioral, and health sciences. Approaches developed to analyze data with binary outcomes were mainly tailored to clustered or longitudinal data with missing completely at random or at random. Studies that focused on informative right censoring with binary outcomes are characterized by their imbedded computational complexity and difficulty of implementation. Here we present a new maximum likelihood-based approach with repeated binary measures modeled in a generalized linear mixed model as a function of time and other covariates. The longitudinal binary outcome and the censoring process determined by the number of times a subject is observed share latent random variables (random intercept and slope) where these subject-specific random effects are common to both models. A simulation study and sensitivity analysis were conducted to test the model under different assumptions and censoring settings. Our results showed accuracy of the estimates generated under this model when censoring was fully informative or partially informative with dependence on the slopes. A successful implementation was undertaken on a cohort of renal transplant patients with blood urea nitrogen as a binary outcome measured over time to indicate normal and abnormal kidney function until the emanation of graft rejection that eventuated in informative right censoring. In addition to its novelty and accuracy, an additional key feature and advantage of the proposed model is its viability of implementation on available analytical tools and widespread application on any other longitudinal dataset with informative censoring.

In the presence of unmeasured spatial confounding, spatial models can increase bias of exposure effect estimates compared to nonspatial models (bias exacerbation), leading to debate regarding their use. For continuous exposures, this issue predominantly occurs when exposures are purely spatially varying (eg, air pollution), whereas spatial models can mitigate bias for individual-level factors with nonspatial variability (eg, blood pressure). However, in the common setting of binary exposures, the potential for bias exacerbation and the optimal choice of spatial method have not been well characterized. Focusing on point-referenced data, through simulation and a real-world application, we compared approaches for controlling unmeasured spatial confounding for binary exposures, including spatial spline models, matching, and combinations of matching and penalized spline (PS) models (all targeting average treatment effect). Additionally, we generalized the exposure-PS (E-PS) model to accommodate binary exposures, which selects degrees of smoothing to explain variability in the exposure. Like continuous exposures, spatial methods were able to eliminate bias for individual-level binary exposures. Unlike continuous exposures, bias was also reduced for purely spatial binary exposures, provided spatial spline adjustment was sufficiently flexible. Generalized E-PS and the combination of nearest neighbor matching with replacement and PS generally resulted in the largest bias reductions.

The difference in restricted mean survival time has been increasingly used as an alternative measure to the hazard ratio in survival analysis. Although some statistical methods have been developed for estimating the difference in restricted mean survival time adjusted for measured confounders in observational studies, the impact of unmeasured confounding on the estimate has rarely been assessed. We develop a novel sensitivity analysis for the estimate of the difference in restricted mean survival time with respect to unmeasured confounding. After formulating the sensitivity analysis problem as an optimization problem, we explain how to obtain the sensitivity range of the difference in restricted mean survival time efficiently and assess its uncertainty using the percentile bootstrap confidence interval. Analytic results are provided for some important survival settings. Simulation studies show that the proposed methods perform well in various settings. We illustrate the proposed sensitivity analysis method by analyzing data from the German Breast Cancer Study Group study.

The Tipan River, a tributary of Son River in Madhya Pradesh, India, is characterized by diverse geomorphic features such as pediment-pediplain complexes, low to moderately dissected hills, and an intricate river network. The soil of region ranges from clayey to loamy, underlain by geological formations including basalt, granite gneiss, limestone, and fine-grained sandstone. To address urgent need for sustainable groundwater management, this study integrates the Analytical Hierarchy Process (AHP) with Geographic Information System (GIS) tools to delineate groundwater potential zones (GWPZs). Eight hydrological parameters - rainfall, geology, geomorphology, soil, land use/land cover (LULC), slope, drainage density, and lineament density—were selected based on their relevance to groundwater occurrence and recharge. These were weighted through AHP using Saaty's 1–9 scale, with consistency verified (CI = 0.055, CR = 0.039). A weighted overlay analysis in ArcGIS Pro produced a GWPZ map, classifying basin into four classes: Poor (3.58%), Moderate (20.62%), Good (47.59%), and Very Good (28.21%). High groundwater potential was found in areas with gentle slopes, loamy soils, pediment-pediplain features, and high rainfall. The map's accuracy was validated using Receiver Operating Characteristic (ROC). Area Under Curve (AUC) value of 0.789, indicates strong predictive performance. Sensitivity analysis through the map removal method highlighted geology, geomorphology, and soil as the most influential parameters, while LULC showed minimal impact. This AHP-GIS approach offers a robust and replicable framework for groundwater assessment, supporting sustainable water resource planning in Tipan River Basin. Keywords: Tipan River Basin, Analytical Hierarchy Process, Geographic Information System, Groundwater Potential Zones, Sensitivity Analysis

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data assumptions. This is because measurements from subjects who provide the data after numerous failed attempts may differ from those who provide the measurement after fewer attempts. Previous models for these designs were parametric and/or did not allow sensitivity analysis. For the former, there are always concerns about model misspecification and for the latter, sensitivity analysis is essential when conducting inference in the presence of missing data. Here, we propose a new approach which minimizes issues with model misspecification by using Bayesian nonparametrics for the observed data distribution. We also introduce a novel approach for identification and sensitivity analysis. We re-analyze the repeated attempts data from a clinical trial involving patients with severe mental illness and conduct simulations to better understand the properties of ourapproach.

Non-inferiority trials are motivated in the context of clinical research where a proven active treatment exists and placebo-controlled trials are no longer acceptable for ethical reasons. Instead, active-controlled trials are conducted where a treatment is compared to an established treatment with the objective of demonstrating that it is non-inferior to this treatment. We review and compare the methodologies for calculating sample sizes and suggest appropriate methods to use. We demonstrate how the simplest method of using the anticipated response is predominantly consistent with simulations. In the context of trials with binary outcomes with expected high proportions of positive responses, we show how the sample size is quite sensitive to assumptions about the control response. We recommend when designing such a study that sensitivity analyses be performed with respect to the underlying assumptions and that the Bayesian methods described in this article be adopted to assess sample size.

This article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

Pesticide transfers in agricultural catchments are responsible for diffuse but major risks to water quality. Spatialized pesticide transfer models are useful tools to assess the impact of the structure of the landscape on water quality. Before considering using these tools in operational contexts, quantifying their uncertainties is a preliminary necessary step. In this study, we explored how global sensitivity analysis can be applied to the recent PESHMELBA pesticide transfer model to quantify uncertainties on transfer simulations. We set up a virtual catchment based on a real one and we compared different approaches for sensitivity analysis that could handle the specificities of the model: high number of input parameters, limited size of sample due to computational cost and spatialized output. We compared Sobol' indices obtained from Polynomial Chaos Expansion, HSIC dependence measures and feature importance measures obtained from Random Forest surrogate model. Results showed the consistency of the different methods and they highlighted the relevance of Sobol' indices to capture interactions between parameters. Sensitivity indices were first computed for each landscape element (site sensitivity indices). Second, we proposed to aggregate them at the hillslope and the catchment scale in order to get a summary of the model sensitivity and a valuable insight into the model hydrodynamical behaviour. The methodology proposed in this paper may be extended to other modular and distributed hydrological models as there has been a growing interest in these methods in recent years.

Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis