Time‐to‐event continual reassessment method incorporating treatment cycle information with application to an oncology phase I trial

Delayed dose limiting toxicities (i.e. beyond first cycle of treatment) is a challenge for phase I trials. The time‐to‐event continual reassessment method (TITE‐CRM) is a Bayesian dose‐finding design to address the issue of long observation time and early patient drop‐out. It uses a weighted binomial likelihood with weights assigned to observations by the unknown time‐to‐toxicity distribution, and is open to accrual continually. To avoid dosing at overly toxic levels while retaining accuracy and efficiency for DLT evaluation that involves multiple cycles, we propose an adaptive weight function by incorporating cyclical data of the experimental treatment with parameters updated continually. This provides a reasonable estimate for the time‐to‐toxicity distribution by accounting for inter‐cycle variability and maintains the statistical properties of consistency and coherence. A case study of a First‐in‐Human trial in cancer for an experimental biologic is presented using the proposed design. Design calibrations for the clinical and statistical parameters are conducted to ensure good operating characteristics. Simulation results show that the proposed TITE‐CRM design with adaptive weight function yields significantly shorter trial duration, does not expose patients to additional risk, is competitive against the existing weighting methods, and possesses some desirable properties.     

Utility‐Based Optimization of Combination Therapy Using Ordinal Toxicity and Efficacy in Phase I/II Trials

Summary An outcome‐adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biological agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda‐Ordaz model (1981, Biometrika 68 , 357–363) is used for the marginal outcome probabilities as functions of a dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method's sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size, and starting dose pair.     

BMA‐Mod: A Bayesian model averaging strategy for determining dose‐response relationships in the presence of model uncertainty

Successful pharmaceutical drug development requires finding correct doses. The issues that conventional dose‐response analyses consider, namely whether responses are related to doses, which doses have responses differing from a control dose response, the functional form of a dose‐response relationship, and the dose(s) to carry forward, do not need to be addressed simultaneously. Determining if a dose‐response relationship exists, regardless of its functional form, and then identifying a range of doses to study further may be a more efficient strategy. This article describes a novel estimation‐focused Bayesian approach (BMA‐Mod) for carrying out the analyses when the actual dose‐response function is unknown. Realizations from Bayesian analyses of linear, generalized linear, and nonlinear regression models that may include random effects and covariates other than dose are optimally combined to produce distributions of important secondary quantities, including test‐control differences, predictive distributions of possible outcomes from future trials, and ranges of doses corresponding to target outcomes. The objective is similar to the objective of the hypothesis‐testing based MCP‐Mod approach, but provides more model and distributional flexibility and does not require testing hypotheses or adjusting for multiple comparisons. A number of examples illustrate the application of the method.     

Hormone replacement therapy enhances IGF‐1 signaling in skeletal muscle by diminishing miR‐182 and miR‐223 expressions: a study on postmenopausal monozygotic twin pairs

MiRNAs are fine‐tuning modifiers of skeletal muscle regulation, but knowledge of their hormonal control is lacking. We used a co‐twin case–control study design, that is, monozygotic postmenopausal twin pairs discordant for estrogen‐based hormone replacement therapy (HRT) to explore estrogen‐dependent skeletal muscle regulation via miRNAs. MiRNA profiles were determined from vastus lateralis muscle of nine healthy 54–62‐years‐old monozygotic female twin pairs discordant for HRT (median 7 years). MCF‐7 cells, human myoblast cultures and mouse muscle experiments were used to confirm estrogen's causal role on the expression of specific miRNAs, their target mRNAs and proteins and finally the activation of related signaling pathway. Of the 230 miRNAs expressed at detectable levels in muscle samples, qPCR confirmed significantly lower miR‐182, miR‐223 and miR‐142‐3p expressions in HRT using than in their nonusing co‐twins. Insulin/IGF‐1 signaling emerged one common pathway targeted by these miRNAs. IGF‐1R and FOXO3A mRNA and protein were more abundantly expressed in muscle samples of HRT users than nonusers. In vitro assays confirmed effective targeting of miR‐182 and miR‐223 on IGF‐1R and FOXO3A mRNA as well as a dose‐dependent miR‐182 and miR‐223 down‐regulations concomitantly with up‐regulation of FOXO3A and IGF‐1R expression. Novel finding is the postmenopausal HRT‐reduced miRs‐182, miR‐223 and miR‐142‐3p expression in female skeletal muscle. The observed miRNA‐mediated enhancement of the target genes' IGF‐1R and FOXO3A expression as well as the activation of insulin/IGF‐1 pathway signaling via phosphorylation of AKT and mTOR is an important mechanism for positive estrogen impact on skeletal muscle of postmenopausal women.     

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero‐modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)–(b) and (b)–(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed‐effects regression model based on the hurdle version of the Poisson–Lindley distribution. In this framework, the zero‐modification is incorporated by assuming that a binary probability model determines which outcomes are zero‐valued, and a zero‐truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well‐established mixed‐effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian ‐value and the randomized quantile residuals were considered for model diagnostics.     

Deeply conserved susceptibility in a multi‐host,multi‐parasite system

Variation in susceptibility is ubiquitous in multi‐host, multi‐parasite assemblages, and can have profound implications for ecology and evolution in these systems. The extent to which susceptibility to parasites is phylogenetically conserved among hosts can be revealed by analysing diverse regional communities. We screened for haemosporidian parasites in 3983 birds representing 40 families and 523 species, spanning ~ 4500 m elevation in the tropical Andes. To quantify the influence of host phylogeny on infection status, we applied Bayesian phylogenetic multilevel models that included a suite of environmental, spatial, temporal, life history and ecological predictors. We found evidence of deeply conserved susceptibility across the avian tree; host phylogeny explained substantial variation in infection status, and results were robust to phylogenetic uncertainty. Our study suggests that susceptibility is governed, in part, by conserved, latent aspects of anti‐parasite defence. This demonstrates the importance of deep phylogeny for understanding present‐day ecological interactions.     

Heterogeneity and concordance in locus‐specific differentiation and introgression between species of towhees

The maintenance or breakdown of reproductive isolation is an observable outcome of secondary contact between species. In cases where hybrids beyond the F1 are formed, the representation of each species' ancestry can vary dramatically among genomic regions. This genomic heterogeneity in ancestry and introgression can offer insight into evolutionary processes, particularly if introgression is compared in multiple hybrid zones. Similarly, considerable heterogeneity exists across the genome in the extent to which populations and species have diverged, reflecting the combined effects of different evolutionary processes on genetic variation. We studied hybridization across two hybrid zones of two phenotypically well‐differentiated bird species in Mexico (Pipilo maculatus and P. ocai), to investigate genomic heterogeneity in differentiation and introgression. Using genotyping‐by‐sequencing (GBS) and hierarchical Bayesian models, we genotyped 460 birds at over 41 000 single nucleotide polymorphism (SNP) loci. We identified loci exhibiting extreme introgression relative to the genome‐wide expectation using a Bayesian genomic cline model. We also estimated locus‐specific F_ST and identified loci with exceptionally high genetic divergence between the parental species. We found some concordance of locus‐specific introgression in the two independent hybrid zones (6–20% of extreme loci shared across zones), reflecting areas of the genome that experience similar gene flow when the species interact. Additionally, heterogeneity in introgression and divergence across the genome revealed another subset of loci under the influence of locally specific factors. These results are consistent with a history in which reproductive isolation has been influenced by a common set of loci in both hybrid zones, but where local environmental and stochastic factors also lead to genomic differentiation.     

Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

Continual reassessment method for partial ordering

Summary Much of the statistical methodology underlying the experimental design of phase 1 trials in oncology is intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the maximally tolerated dose, the highest dose that can be administered with an acceptable level of toxicity. A fundamental assumption of these methods is monotonicity of the dose–toxicity curve. This is a reasonable assumption for single‐agent trials in which the administration of greater doses of the agent can be expected to produce dose‐limiting toxicities in increasing proportions of patients. When studying multiple agents, the assumption may not hold because the ordering of the toxicity probabilities could possibly be unknown for several of the available drug combinations. At the same time, some of the orderings are known and so we describe the whole situation as that of a partial ordering. In this article, we propose a new two‐dimensional dose‐finding method for multiple‐agent trials that simplifies to the continual reassessment method (CRM), introduced by O'Quigley, Pepe, and Fisher (1990, Biometrics 46 , 33–48), when the ordering is fully known. This design enables us to relax the assumption of a monotonic dose–toxicity curve. We compare our approach and some simulation results to a CRM design in which the ordering is known as well as to other suggestions for partial orders.     

Fair Innings and Time‐Relative Claims

Greg Bognar has recently offered a prioritarian justification for ‘fair innings’ distributive principles that would ration access to healthcare on the basis of patients' age. In this article, I agree that Bognar's principle is among the strongest arguments for age‐based rationing. However, I argue that this position is incomplete because of the possibility of ‘time‐relative' egalitarian principles that could complement the kind of lifetime egalitarianism that Bognar adopts. After outlining Bognar's position, and explaining the attraction of time‐relative egalitarianism, I suggest various ways in which these two kinds of principle could interact. Since various options have very different implications for age‐based rationing, proponents of such a rationing scheme must take a position on time‐relative egalitarianism to complement a lifetime prioritarian view like Bognar's.     

Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios

A Bayesian adaptive design is proposed for dose-finding in phase I/II clinical trials to incorporate the bivariate outcomes, toxicity and efficacy, of a new treatment. Without specifying any parametric functional form for the drug dose-response curve, we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy. After observing all the responses of each cohort of patients, the dosage for the next cohort is escalated, deescalated, or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities. A novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes. We conduct simulation studies to evaluate the operating characteristics of the proposed method. Under various scenarios, the new Bayesian design based on the toxicity-efficacy odds ratio trade-offs exhibits good properties and treats most patients at the desirable dose levels. The method is illustrated with a real trial design for a breast medical oncology study.     

A Bayesian phase 2 model based adaptive design to optimise antivenom dosing: Application to a dose-finding trial for a novel Russell’s viper antivenom in Myanmar

For most antivenoms there is little information from clinical studies to infer the relationship between dose and efficacy or dose and toxicity. Antivenom dose-finding studies usually recruit too few patients (e.g. fewer than 20) relative to clinically significant event rates (e.g. 5%). Model based adaptive dose-finding studies make efficient use of accrued patient data by using information across dosing levels, and converge rapidly to the contextually defined ‘optimal dose’. Adequate sample sizes for adaptive dose-finding trials can be determined by simulation. We propose a model based, Bayesian phase 2 type, adaptive clinical trial design for the characterisation of optimal initial antivenom doses in contexts where both efficacy and toxicity are measured as binary endpoints. This design is illustrated in the context of dose-finding for Daboia siamensis (Eastern Russell’s viper) envenoming in Myanmar. The design formalises the optimal initial dose of antivenom as the dose closest to that giving a pre-specified desired efficacy, but resulting in less than a pre-specified maximum toxicity. For Daboia siamensis envenoming, efficacy is defined as the restoration of blood coagulability within six hours, and toxicity is defined as anaphylaxis. Comprehensive simulation studies compared the expected behaviour of the model based design to a simpler rule based design (a modified ‘3+3’ design). The model based design can identify an optimal dose after fewer patients relative to the rule based design. Open source code for the simulations is made available in order to determine adequate sample sizes for future adaptive snakebite trials. Antivenom dose-finding trials would benefit from using standard model based adaptive designs. Dose-finding trials where rare events (e.g. 5% occurrence) are of clinical importance necessitate larger sample sizes than current practice. We will apply the model based design to determine a safe and efficacious dose for a novel lyophilised antivenom to treat Daboia siamensis envenoming in Myanmar.     

Fine‐scale substrate heterogeneity in green roof plant communities: The constraint of size

Heterogeneity–diversity relationship (HDR) is commonly shown to be positive in accordance with classic niche processes. However, recent soil‐based studies have often found neutral and even negative HDRs. Some of the suggested reasons for this discrepancy include the lack of resemblance between manipulated substrate and natural settings, the treated areas not being large enough to contain species' root span, and finally limited‐sized plots may not sustain focal species’ populations over time. Vegetated green roofs are a growing phenomenon in many cities that could be an ideal testing ground for this problem. Recent studies have focused on the ability of these roofs to sustain stable and diverse plant communities and substrate heterogeneity that would increase niches on the roof has been proposed as a method to attain this goal. We constructed an experimental design using green roof experimental modules (4 m²) where we manipulated mineral and organic substrate component heterogeneity in different subplots (0.25 m²) within the experimental module while maintaining the total sum of mineral and organic components. A local annual plant community was seeded in the modules and monitored over three growing seasons. We found that plant diversity and biomass were not affected by experimentally created substrate heterogeneity. In addition, we found that different treatments, as well as specific subplot substrates, had an effect on plant community assemblages during the first year but not during the second and third years. Substrate heterogeneity levels were mostly unchanged over time. The inability to retain plant community composition over the years despite the maintenance of substrate differences supports the hypothesis that maintenance of diversity is constrained at these spatial scales by unfavorable dispersal and increased stochastic events as opposed to predictions of classic niche processes.     

mTRAQ‐based quantification of potential endometrial carcinoma biomarkers from archived formalin‐fixed paraffin‐embedded tissues

Formalin‐fixed paraffin‐embedded (FFPE) tissues are the primary and preferred medium for archiving patients' samples. Here we demonstrate relative quantifications of protein biomarkers in extracts of laser microdissected epithelial cells from FFPE endometrial carcinoma tissues versus those from normal proliferative endometria by means of targeted proteomic analyses using LC–multiple reaction monitoring (MRM) MS with MRM Tags for Relative and Absolute Quantitation (mTRAQ) labeling. Comparable results of differential expressions for pyruvate kinase isoform M2 (PK‐M2) and polymeric Ig receptor were observed between analyses on laser microdissected epithelial cells from FFPE tissues and corresponding homogenates from frozen tissues of the same individuals that had previously been analyzed and reported. We also identified PK‐M2 in the normal proliferative phase of the endometrium. Other biomarkers in addition to PK‐M2 and polymeric Ig receptor were also observed but not consistently and/or were at levels below the threshold for quantification.     

Environmental heterogeneity,dispersal mode,and co‐occurrence in stream macroinvertebrates

Both environmental heterogeneity and mode of dispersal may affect species co‐occurrence in metacommunities. Aquatic invertebrates were sampled in 20–30 streams in each of three drainage basins, differing considerably in environmental heterogeneity. Each drainage basin was further divided into two equally sized sets of sites, again differing profoundly in environmental heterogeneity. Benthic invertebrate data were divided into three groups of taxa based on overland dispersal modes: passive dispersers with aquatic adults, passive dispersers with terrestrial winged adults, and active dispersers with terrestrial winged adults. The co‐occurrence of taxa in each dispersal mode group, drainage basin, and heterogeneity site subset was measured using the C‐score and its standardized effect size. The probability of finding high levels of species segregation tended to increase with environmental heterogeneity across the drainage basins. These patterns were, however, contingent on both dispersal mode and drainage basin. It thus appears that environmental heterogeneity and dispersal mode interact in affecting co‐occurrence in metacommunities, with passive dispersers with aquatic adults showing random patterns irrespective of environmental heterogeneity, and active dispersers with terrestrial winged adults showing increasing segregation with increasing environmental heterogeneity.     

Trait‐based tests of coexistence mechanisms

Recent functional trait studies have shown that trait differences may favour certain species (environmental filtering) while simultaneously preventing competitive exclusion (niche partitioning). However, phenomenological trait‐dispersion analyses do not identify the mechanisms that generate niche partitioning, preventing trait‐based prediction of future changes in biodiversity. We argue that such predictions require linking functional traits with recognised coexistence mechanisms involving spatial or temporal environmental heterogeneity, resource partitioning and natural enemies. We first demonstrate the limitations of phenomenological approaches using simulations, and then (1) propose trait‐based tests of coexistence, (2) generate hypotheses about which plant functional traits are likely to interact with particular mechanisms and (3) review the literature for evidence for these hypotheses. Theory and data suggest that all four classes of coexistence mechanisms could act on functional trait variation, but some mechanisms will be stronger and more widespread than others. The highest priority for future research is studies of interactions between environmental heterogeneity and trait variation that measure environmental variables at within‐community scales and quantify species' responses to the environment in the absence of competition. Evidence that similar trait‐based coexistence mechanisms operate in many ecosystems would simplify biodiversity forecasting and represent a rare victory for generality over contingency in community ecology.     

A systems‐based approach to investigate dose‐ and time‐dependent methylmercury‐induced gene expression response in C57BL/6 mouse embryos undergoing neurulation

BACKGROUND: Aberrations during neurulation due to genetic and/or environmental factors underlie a variety of adverse developmental outcomes, including neural tube defects (NTDs). Methylmercury (MeHg) is a developmental neurotoxicant and teratogen that perturbs a wide range of biological processes/pathways in animal models, including those involved in early gestation (e.g., cell cycle, cell differentiation). Yet, the relationship between these MeHg‐linked effects and changes in gestational development remains unresolved. Specifically, current information lacks mechanistic comparisons across dose or time for MeHg exposure during neurulation. These detailed investigations are crucial for identifying sensitive indicators of toxicity and for risk assessment applications. METHODS: Using a systems‐based toxicogenomic approach, we examined dose‐ and time‐dependent effects of MeHg on gene expression in C57BL/6 mouse embryos during cranial neural tube closure, assessing for significantly altered genes and associated Gene Ontology (GO) biological processes. Using the GO‐based application GO‐Quant, we quantitatively assessed dose‐ and time‐dependent effects on gene expression within enriched GO biological processes impacted by MeHg. RESULTS: We observed MeHg to significantly alter expression of 883 genes, including several genes (e.g., Vangl2, Celsr1, Ptk7, Twist, Tcf7) previously characterized to be crucial for neural tube development. Significantly altered genes were associated with development cell adhesion, cell cycle, and cell differentiation–related GO biological processes. CONCLUSIONS: Our results suggest that MeHg‐induced impacts within these biological processes during gestational development may underlie MeHg‐induced teratogenic and neurodevelopmental toxicity outcomes. Birth Defects Res (Part B) 89:188–200, 2010. © 2010 Wiley‐Liss, Inc.     

Model‐based integration of observed and expert‐based information for assessing the geographic and environmental distribution of freshwater species

Freshwater ecosystems harbor specialized and vulnerable biodiversity, and the prediction of potential impacts of freshwater biodiversity to environmental change requires knowledge of the geographic and environmental distribution of taxa. To date, however, such quantitative information about freshwater species distributions remains limited. Major impediments include heterogeneity in available species occurrence data, varying detectability of species in their aquatic environment, scarcity of contiguous freshwater‐specific predictors, and methods that support addressing these issues in a single framework. Here we demonstrate the use of a hierarchical Bayesian modeling (HBM) framework that combines disparate species occurrence information with newly‐developed 1 km freshwater‐specific predictors, to account for imperfect species detection and make fine‐grain (1 km) estimates of distributions in freshwater organisms. The approach integrates a Bernoulli suitability and a Binomial observability process into a hierarchical zero‐inflated Binomial model. The suitability process includes point presence observations, records of site visits, 1 km environmental predictors and expert‐derived species range maps integrated with a distance‐decay function along the within‐stream distance as covariates. The observability process uses repeated observations to estimate a probability of observation given that the species was present. The HBM accounts for the spatial autocorrelation in species habitat suitability projections using an intrinsic Gaussian conditional autoregressive model. We used this framework for three fish species native to different regions and habitats in North America. Model comparison shows that HBMs significantly outperformed non‐spatial GLMs in terms of AUC and TSS scores, and that expert information when appropriately included in the model can provide an important refinement. Such ancillary species information and an integrative, hierarchical Bayesian modeling framework can therefore be used to advance fine‐grain habitat suitability predictions and range size estimates in the freshwater realm. Our approach is extendable in terms of data availability and generality and can be used on other freshwater organisms and regions.     

A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR‐ and Proportion‐Data

In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non‐iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.     

Bayesian propensity scores for high‐dimensional causal inference: A comparison of drug‐eluting to bare‐metal coronary stents

High‐dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high‐dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high‐dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem.