Sensitivity analysis of individual treatment effects: A robust conformal inference approach.

We propose a model-free framework for sensitivity analysis of individual treatment effects (ITEs), building upon ideas from conformal inference. For any unit, our procedure reports the Γ-value, a number which quantifies the minimum strength of confounding needed to explain away the evidence for ITE. Our approach rests on the reliable predictive inference of counterfactuals and ITEs in situations where the training data are confounded. Under the marginal sensitivity model of [Z. Tan, J. Am. Stat. Assoc. 101, 1619-1637 (2006)], we characterize the shift between the distribution of the observations and that of the counterfactuals. We first develop a general method for predictive inference of test samples from a shifted distribution; we then leverage this to construct covariate-dependent prediction sets for counterfactuals. No matter the value of the shift, these prediction sets (resp. approximately) achieve marginal coverage if the propensity score is known exactly (resp. estimated). We describe a distinct procedure also attaining coverage, however, conditional on the training data. In the latter case, we prove a sharpness result showing that for certain classes of prediction problems, the prediction intervals cannot possibly be tightened. We verify the validity and performance of the methods via simulation studies and apply them to analyze real datasets.

A neural mass model for disturbance of alpha rhythm in the minimal hepatic encephalopathy.

One of the early markers of minimal hepatic encephalopathy (MHE) is the disruption of alpha rhythm observed in electroencephalogram (EEG) signals. However, the underlying mechanisms responsible for this occurrence remain poorly understood. To address this gap, we develop a novel biophysical model MHE-AWD-NCM, encompassing the communication dynamics between a cortical neuron population (CNP) and an astrocyte population (AP), aimed at investigating the relationship between alpha wave disturbance (AWD) and mechanistical principles, specifically concerning astrocyte-neuronal communication in the context of MHE. In addition, we introduce the concepts of peak power density and peak frequency within the alpha band as quantitative measures of AWD. Our model faithfully reproduces the characteristic EEG phenomenology during MHE and shows how impairments of communication between CNP and AP could promote AWD. The results suggest that the disruptions in feedback neurotransmission from AP to CNP, along with the inhibition of GABA uptake by AP from the extracellular space, contribute to the observed AWD. Moreover, we found that the variation of external excitatory stimuli on CNP may play a key role in AWD in MHE. Finally, the sensitivity analysis is also performed to assess the relative significance of above factors in influencing AWD. Our findings align with the physiological observations and provide a more comprehensive understanding of the complex interplay of astrocyte-neuronal communication that underlies the AWD observed in MHE, which potentially may help to explore the targeted therapeutic interventions for the early stage of hepatic encephalopathy.

Differential genetic mutations and immune cell infiltration in high- and low-risk STAD: Implications for prognosis and immunotherapy efficacy.

This study investigates genetic mutations and immune cell dynamics in stomach adenocarcinoma (STAD), focusing on identifying prognostic markers and therapeutic targets. Analysis of TCGA-STAD samples revealed C > A as the most common single nucleotide variant (SNV) in both high and low-risk groups. Key mutated driver genes included TTN, TP53 and MUC16, with frame-shift mutations more prevalent in the low-risk group and missense mutations in the high-risk group. Interaction analysis of hub genes such as C1QA and CD68 showed significant correlations, impacting immune cell infiltration patterns. Using ssGSEA, we found higher immune cell infiltration (B cells, CD4+ T cells, CD8+ T cells, DC cells, NK cells) in the high-risk group, correlated with increased risk scores. xCell algorithm results indicated distinct immune infiltration levels between the groups. The study's risk scoring model proved effective in prognosis prediction and immunotherapy efficacy assessment. Key molecules like CD28, CD27 and SLAMF7 correlated significantly with risk scores, suggesting potential targets for high-risk STAD patients. Drug sensitivity analysis showed a negative correlation between risk scores and sensitivity to certain treatments, indicating potential therapeutic options for high-risk STAD patients. We also validated the carcinogenic role of RPL14 in gastric cancer through phenotypic experiments, demonstrating its influence on cancer cell proliferation, invasion and migration. Overall, this research provides crucial insights into the genetic and immune aspects of STAD, highlighting the importance of a risk scoring model for personalized treatment strategies and clinical decision-making in gastric cancer management.

Causal associations of immune cell phenotypes with migraine: A mendelian randomization study.

The interaction between the immune system and the brain, crucial for blood-brain barrier integrity, is a potential factor in migraine development. Although there's evidence of a connection between immune dysregulation and migraine, a clear causal link has been lacking. To bridge this knowledge gap, we performed a two-sample Mendelian randomization (MR) analysis of 731 immune cell phenotypes to determine their causality with migraine, of which parameters included fluorescence, cell abundance, count, and morphology. Sensitivity and pleiotropy checks validated our findings. After applying a false discovery rate correction, our MR study identified 35 of 731 immune phenotypes with a significant causal link to migraine (p < 0.05). Of these, 24 showed a protective effect (inverse variance weighting : p < 0.05, odds ratio <1), and 11 were risk factors (inverse variance weighting : p < 0.05, odds ratio >1). Although limited by population sample size and potential population-specific genetic variations, our study uncovers a significant genetic link between certain immune cell markers and migraine, providing new insights into the disorder's pathophysiology. These discoveries are crucial for developing targeted biomarkers and personalized treatments. The research enhances our understanding of immune cells' role in migraine and may substantially improve patient outcomes and lessen its socio-economic impact.

Parameter Sensitivity of Transient Community Dynamics.

AbstractTransient dynamics have always intrigued ecologists, but current rapid environmental change (inducing transients even in previously undisturbed systems) has highlighted their importance more than ever. Here, I introduce a method for analyzing the sensitivity of transient ecological dynamics to parameter perturbations. The question the method answers is: how would the community dynamics have unfolded for some time horizon had the parameters been slightly different? I apply the method to three empirically parameterized models: competition between native forbs and exotic grasses in California, a host-parasitoid system, and an experimental chemostat predator-prey model. These applications showcase the ecological insights one can gain from models using transient sensitivity analysis. First, one can find parameters and their combinations whose perturbations disproportionately affect a system. Second, one can identify particular windows of time during which the predicted deviation from the unperturbed trajectories is especially large and utilize this information for management purposes. Third, there is an inverse relationship between transient and long-term sensitivities whenever the interacting populations are ecologically similar; paradoxically, the smaller the immediate response of the system, the more extreme its long-term response will be.

A Bayesian semiparametric approach for inference on the population partly conditional mean from longitudinal data with dropout.

Studies of memory trajectories using longitudinal data often result in highly nonrepresentative samples due to selective study enrollment and attrition. An additional bias comes from practice effects that result in improved or maintained performance due to familiarity with test content or context. These challenges may bias study findings and severely distort the ability to generalize to the target population. In this study, we propose an approach for estimating the finite population mean of a longitudinal outcome conditioning on being alive at a specific time point. We develop a flexible Bayesian semiparametric predictive estimator for population inference when longitudinal auxiliary information is known for the target population. We evaluate the sensitivity of the results to untestable assumptions and further compare our approach to other methods used for population inference in a simulation study. The proposed approach is motivated by 15-year longitudinal data from the Betula longitudinal cohort study. We apply our approach to estimate lifespan trajectories in episodic memory, with the aim to generalize findings to a target population.

A controlled effects approach to assessing immune correlates of protection.

An immune correlate of risk (CoR) is an immunologic biomarker in vaccine recipients associated with an infectious disease clinical endpoint. An immune correlate of protection (CoP) is a CoR that can be used to reliably predict vaccine efficacy (VE) against the clinical endpoint and hence is accepted as a surrogate endpoint that can be used for accelerated approval or guide use of vaccines. In randomized, placebo-controlled trials, CoR analysis is limited by not assessing a causal vaccine effect. To address this limitation, we construct the controlled risk curve of a biomarker, which provides the causal risk of an endpoint if all participants are assigned vaccine and the biomarker is set to different levels. Furthermore, we propose a causal CoP analysis based on controlled effects, where for the important special case that the biomarker is constant in the placebo arm, we study the controlled vaccine efficacy curve that contrasts the controlled risk curve with placebo arm risk. We provide identification conditions and formulae that account for right censoring of the clinical endpoint and two-phase sampling of the biomarker, and consider G-computation estimation and inference under a semiparametric model such as the Cox model. We add modular approaches to sensitivity analysis that quantify robustness of CoP evidence to unmeasured confounding. We provide an application to two phase 3 trials of a dengue vaccine indicating that controlled risk of dengue strongly varies with 50$\%$ neutralizing antibody titer. Our work introduces controlled effects causal mediation analysis to immune CoP evaluation.

Estimating the relative importance of epidemiological and behavioural parameters for epidemic mpox transmission: a modelling study.

BACKGROUND: Many European countries experienced outbreaks of mpox in 2022, and there was an mpox outbreak in 2023 in the Democratic Republic of Congo. There were many apparent differences between these outbreaks and previous outbreaks of mpox; the recent outbreaks were observed in men who have sex with men after sexual encounters at common events, whereas earlier outbreaks were observed in a wider population with no identifiable link to sexual contacts. These apparent differences meant that data from previous outbreaks could not reliably be used to parametrise infectious disease models during the 2022 and 2023 mpox outbreaks, and modelling efforts were hampered by uncertainty around key transmission and immunity parameters. METHODS: We developed a stochastic, discrete-time metapopulation model for mpox that allowed for sexual and non-sexual transmission and the implementation of non-pharmaceutical interventions, specifically contact tracing and pre- and post-exposure vaccinations. We calibrated the model to case data from Berlin and used Sobol sensitivity analysis to identify parameters that mpox transmission is especially sensitive to. We also briefly analysed the sensitivity of the effectiveness of non-pharmaceutical interventions to various efficacy parameters. RESULTS: We found that variance in the transmission probabilities due to both sexual and non-sexual transmission had a large effect on mpox transmission in the model, as did the level of immunity to mpox conferred by a previous smallpox vaccination. Furthermore, variance in the number of pre-exposure vaccinations offered was the dominant contributor to variance in mpox dynamics in men who have sex with men. If pre-exposure vaccinations were not available, both the accuracy and timeliness of contact tracing had a large impact on mpox transmission in the model. CONCLUSIONS: Our results are valuable for guiding epidemiological studies for parameter ascertainment and identifying key factors for success of non-pharmaceutical interventions.

Assessing the causal relationship between immune cells and prostatitis: evidence from bidirectional mendelian randomization analysis.

Prostatitis represents a common disease of the male genitourinary system, significantly impacting the physical and mental health of male patients. While numerous studies have suggested a potential link between immune cell activity and prostatitis, the exact causal role of immune cells in prostatitis remains uncertain. This study aims to explore the causal relationship between immune cell characteristics and prostatitis using a bidirectional Mendelian randomization approach. This study utilizes data from the public GWAS database and employs bidirectional Mendelian randomization analysis to investigate the causal relationship between immune cells and prostatitis. The causal relationship between 731 immune cell features and prostatitis was primarily investigated through inverse variance weighting (IVW), complemented by MR-Egger regression, a simple model, the weighted median method, and a weighted model. Ultimately, the results underwent sensitivity analysis to assess the heterogeneity, horizontal pleiotropy, and stability of Single Nucleotide Polymorphisms (SNPs) in immune cells and prostatitis. MR analysis revealed 17 immune cells exhibiting significant causal effects on prostatitis. In contrast, findings from reverse MR indicated a significant causal relationship between prostatitis and 13 immune cells. Our study utilizes bidirectional Mendelian Randomization to establish causal relationships between specific immune cell phenotypes and prostatitis, highlighting the reciprocal influence between immune system behavior and the disease. Our findings suggest targeted therapeutic approaches and the importance of including diverse populations for broader validation and personalized treatment strategies.

A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects.

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models.

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Cost-effectiveness analysis of emicizumab prophylaxis in patients with haemophilia A in India.

INTRODUCTION: Emicizumab is the initial subcutaneously administered bispecific antibody approved as a prophylactic treatment for patients with haemophilia A (PwHA). AIM: This study assessed the economic evaluation of emicizumab treatment for non-inhibitor severe haemophilia A (HA) patients in India. METHODS: A Markov model evaluated the cost-effectiveness of emicizumab prophylaxis compared to on-demand therapy (ODT), low-dose prophylaxis (LDP; 1565 IU/kg/year), intermediate-dose prophylaxis (IDP; 3915 IU/kg/year) and high-dose prophylaxis (HDP; 7125 IU/kg/year) for HA patients without factor VIII inhibitors. Inputs from HAVEN-1 and HAVEN-3 trials included transition probabilities of different bleeding types. Costs and benefits were discounted at a 3.5% annual rate. RESULTS: In the base-case analysis, emicizumab was cost-effective compared to HDP, with an incremental cost-effectiveness ratio (ICER) per quality-adjusted life-years (QALY) of Indian rupees (INR) 27,869. Compared to IDP, ODT and LDP, emicizumab prophylaxis could be considered a cost-effective option if the paying threshold is >1 per capita gross domestic product (GDP) with ICER/QALY values of INR 264,592, INR 255,876 and INR 305,398, respectively. One-way sensitivity analysis (OWSA) highlighted emicizumab cost as the parameter with the greatest impact on ICERs. Probabilistic sensitivity analysis (PSA) indicated that emicizumab had a 94.7% and 49.4% probability of being cost-effective at willingness-to-pay (WTP) thresholds of three and two-times per capita GDP. CONCLUSION: Emicizumab prophylaxis is cost-effective compared to HDP and provides value for money compared to ODT, IDP, and LDP for severe non-inhibitor PwHA in India. Its long-term humanistic, clinical and economic benefits outweigh alternative options, making it a valuable choice in resource-constrained settings.

A mathematical model for wound healing in the reef-building coral Pocillopora damicornis.

Coral reefs, among the most diverse ecosystems on Earth, currently face major threats from pollution, unsustainable fishing practices , and perturbations in environmental parameters brought on by climate change. Corals also sustain regular wounding from other sea life and human activity. Recent reef restoration practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs, a practice known as microfragmentation. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response to wounding similar to that observed in mammalian species. Utilizing prior models of wound healing in mammalian species as the mathematical basis, we formulated a mechanistic model of wound healing, including observations of the immune response and tissue repair in scleractinian corals for the species Pocillopora damicornis. The model consists of four differential equations which track changes in remaining wound debris, number of cells involved in inflammation, number of cells involved in proliferation, and amount of wound closure through re-epithelialization. The model is fit to experimental wound size data from linear and circular shaped wounds on a live coral fragment. Mathematical methods, including numerical simulations and local sensitivity analysis, were used to analyze the resulting model. The parameter space was also explored to investigate drivers of other possible wound outcomes. This model serves as a first step in generating mathematical models for wound healing in corals that will not only aid in the understanding of wound healing as a whole, but also help optimize reef restoration practices and predict recovery behavior after major wounding events.

The central role of the identifying assumption in population size estimation.

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data. If an appropriate identifying assumption cannot be found for a data set, no estimate of the population size should be produced based on that data set, as models with different identifying assumptions can produce arbitrarily different population size estimates-even with identical observed data fits. Approaches to multiple-systems estimation often do not explicitly specify identifying assumptions. This makes it difficult to decouple the specification of the model for the observed data from the identifying assumption and to provide justification for the identifying assumption. We present a re-framing of the multiple-systems estimation problem that leads to an approach that decouples the specification of the observed-data model from the identifying assumption, and discuss how common models fit into this framing. This approach takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study estimating the number of civilian casualties in the Kosovo war.

Multiply robust estimators in longitudinal studies with missing data under control-based imputation.

Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n-1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

Sensitivity analysis with iterative outlier detection for systematic reviews and meta-analyses.

Meta-analysis is a widely used tool for synthesizing results from multiple studies. The collected studies are deemed heterogeneous when they do not share a common underlying effect size; thus, the factors attributable to the heterogeneity need to be carefully considered. A critical problem in meta-analyses and systematic reviews is that outlying studies are frequently included, which can lead to invalid conclusions and affect the robustness of decision-making. Outliers may be caused by several factors such as study selection criteria, low study quality, small-study effects, and so on. Although outlier detection is well-studied in the statistical community, limited attention has been paid to meta-analysis. The conventional outlier detection method in meta-analysis is based on a leave-one-study-out procedure. However, when calculating a potentially outlying study's deviation, other outliers could substantially impact its result. This article proposes an iterative method to detect potential outliers, which reduces such an impact that could confound the detection. Furthermore, we adopt bagging to provide valid inference for sensitivity analyses of excluding outliers. Based on simulation studies, the proposed iterative method yields smaller bias and heterogeneity after performing a sensitivity analysis to remove the identified outliers. It also provides higher accuracy on outlier detection. Two case studies are used to illustrate the proposed method's real-world performance.

Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects.

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically - for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal - with a view to inform nonparametric inference.

Distributional imputation for the analysis of censored recurrent events.

Longitudinal clinical trials for which recurrent events endpoints are of interest are commonly subject to missing event data. Primary analyses in such trials are often performed assuming events are missing at random, and sensitivity analyses are necessary to assess robustness of primary analysis conclusions to missing data assumptions. Control-based imputation is an attractive approach in superiority trials for imposing conservative assumptions on how data may be missing not at random. A popular approach to implementing control-based assumptions for recurrent events is multiple imputation (MI), but Rubin's variance estimator is often biased for the true sampling variability of the point estimator in the control-based setting. We propose distributional imputation (DI) with corresponding wild bootstrap variance estimation procedure for control-based sensitivity analyses of recurrent events. We apply control-based DI to a type I diabetes trial. In the application and simulation studies, DI produced more reasonable standard error estimates than MI with Rubin's combining rules in control-based sensitivity analyses of recurrent events.

Validating Health Economic Models With the Probabilistic Analysis Check dashBOARD.

OBJECTIVES: Health economic (HE) models are often considered as "black boxes" because they are not publicly available and lack transparency, which prevents independent scrutiny of HE models. Additionally, validation efforts and validation status of HE models are not systematically reported. Methods to validate HE models in absence of their full underlying code are therefore urgently needed to improve health policy making. This study aimed to develop and test a generic dashboard to systematically explore the workings of HE models and validate their model parameters and outcomes. METHODS: The Probabilistic Analysis Check dashBOARD (PACBOARD) was developed using insights from literature, health economists, and a data scientist. Functionalities of PACBOARD are (1) exploring and validating model parameters and outcomes using standardized validation tests and interactive plots, (2) visualizing and investigating the relationship between model parameters and outcomes using metamodeling, and (3) predicting HE outcomes using the fitted metamodel. To test PACBOARD, 2 mock HE models were developed, and errors were introduced in these models, eg, negative costs inputs, utility values exceeding 1. PACBOARD metamodeling predictions of incremental net monetary benefit were validated against the original model's outcomes. RESULTS: PACBOARD automatically identified all errors introduced in the erroneous HE models. Metamodel predictions were accurate compared with the original model outcomes. CONCLUSIONS: PACBOARD is a unique dashboard aiming at improving the feasibility and transparency of validation efforts of HE models. PACBOARD allows users to explore the working of HE models using metamodeling based on HE models' parameters and outcomes.

How Many Monte Carlo Samples are Needed for Probabilistic Cost-Effectiveness Analyses?

OBJECTIVES: Probabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (eg, individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. METHODS: We show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev's inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described 2 methods to confirm, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. RESULTS: When N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead to misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. CONCLUSIONS: The number of parameter samples in probabilistic cost-effectiveness analyses should not be arbitrarily selected. We describe 3 methods to ensure that enough parameter samples are used in probabilistic cost-effectiveness analyses.