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This paper reconsiders several results of historical and current importance to nonparametric estimation of the survival distribution for failure in the presence of right-censored observation times, demonstrating in particular how Volterra integral equations help inter-connect the resulting estimators. The paper begins by considering Efron's self-consistency equation, introduced in a seminal 1967 Berkeley symposium paper. Novel insights provided in the current work include the observations that (i) the self-consistency equation leads directly to an anticipating Volterra integral equation whose solution is given by a product-limit estimator for the censoring survival function; (ii) a definition used in this argument immediately establishes the familiar product-limit estimator for the failure survival function; (iii) the usual Volterra integral equation for the product-limit estimator of the failure survival function leads to an immediate and simple proof that it can be represented as an inverse probability of censoring weighted estimator; (iv) a simple identity characterizes the relationship between natural inverse probability of censoring weighted estimators for the survival and distribution functions of failure; (v) the resulting inverse probability of censoring weighted estimators, attributed to a highly influential 1992 paper of Robins and Rotnitzky, were implicitly introduced in Efron's 1967 paper in its development of the redistribution-to-the-right algorithm. All results developed herein allow for ties between failure and/or censored observations.

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BACKGROUND: Percutaneous catheter ablation (CA) to achieve pulmonary vein isolation is an effective treatment for drug-refractory paroxysmal and persistent atrial fibrillation (AF). However, recurrence rates after a single AF ablation procedure remain elevated. Conventional management after CA ablation has mostly been based on clinical AF recurrence. However, continuous recordings with insertable cardiac monitors (ICMs) and patient-triggered mobile app transmissions post-CA can now be used to detect early recurrences of subclinical AF (SCAF). We hypothesize that early intervention following CA based on personalized ICM data can prevent the substrate progression that promotes the onset and maintenance of atrial arrhythmias. METHODS: This is a randomized, double-blind (to SCAF data), single-tertiary center clinical trial in which 120 patients with drug-refractory paroxysmal or persistent AF are planned to undergo CA with an ICM. Randomization will be to an intervention arm (n = 60) consisting of ICM-guided early intervention based on SCAF and patient-triggered mobile app transmissions versus a control arm (n = 60) consisting of a standard intervention protocol based on clinical AF recurrence validated by the ICM. Primary endpoint is AF burden, which will be assessed from ICMs at 15 months post-AF ablation. Secondary endpoints include healthcare utilization, functional capacity, and quality of life. CONCLUSION: We believe that ICM-guided early intervention will provide a novel, personalized approach to post-AF ablation management that will result in a significant reduction in AF burden, healthcare utilization, and improvements in functional capacity and quality of life.

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OBJECTIVE: In this study, the authors assessed return on investment (ROI) associated with a forensic assertive community treatment (FACT) program. METHODS: A retrospective secondary data analysis of a randomized controlled trial comprising 70 legal-involved patients with severe mental illness was conducted in Rochester, New York. Patients were randomly assigned to receive either FACT or outpatient psychiatric treatment including intensive case management. Unit of service costs associated with psychiatric emergency department visits, psychiatric inpatient days, and days in jail were obtained from records of New York State Medicaid and the Department of Corrections. The total dollar value difference between the two trial arms calculated on a per-patient-per-year (PPPY) basis constituted the return from the FACT intervention. The FACT investment cost was defined by the total additional PPPY cost associated with FACT implementation relative to the control group. ROI was calculated by dividing the return by the investment cost. RESULTS: The estimated return from FACT was $27,588 PPPY (in 2019 dollars; 95% confidence interval [CI]=$3,262-$51,913), which was driven largely by reductions in psychiatric inpatient days, and the estimated investment cost was $18,440 PPPY (95% CI=$15,215-$21,665), implying an ROI of 1.50 (95% CI=0.35-2.97) for FACT. CONCLUSIONS: The Rochester FACT program was associated with approximately $1.50 return for every $1 spent on its implementation, even without considering potential returns from other sources, including reductions in acute medical care, crime-related damages, and public safety costs. ROI estimates were highly dependent on context-specific factors, particularly Medicaid reimbursement rates for assertive community treatment and hospital stays.

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We propose and study an augmented variant of the estimator proposed by Wang, Tchetgen Tchetgen, Martinussen, and Vansteelandt.

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Screening for chronic diseases, such as cancer, is an important public health priority, but traditionally only the frequency or rate of screening has received attention. In this work, we study the importance of adhering to recommended screening policies and develop new methodology to better optimize screening policies when adherence is imperfect. We consider a progressive disease model with four states (healthy, undetectable preclinical, detectable preclinical, clinical), and overlay this with a stochastic screening-behavior model using the theory of renewal processes that allows us to capture imperfect adherence to screening programs in a transparent way. We show that decreased adherence leads to reduced efficacy of screening programs, quantified here using elements of the lead time distribution (i.e., the time between screening diagnosis and when diagnosis would have occurred clinically in the absence of screening). Under the assumption of an inverse relationship between prescribed screening frequency and individual adherence, we show that the optimal screening frequency generally decreases with increasing levels of non-adherence. We apply this model to an example in breast cancer screening, demonstrating how accounting for imperfect adherence affects the recommended screening frequency.

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The use of cumulative incidence functions for characterizing the risk of one type of event in the presence of others has become increasingly popular over the past two decades. The problems of modeling, estimation and inference have been treated using parametric, nonparametric and semi-parametric methods. Efforts to develop suitable extensions of machine learning methods, such as regression trees and ensemble methods, have begun comparatively recently. In this paper, we propose a novel approach to estimating cumulative incidence curves in a competing risks setting using regression trees and associated ensemble estimators. The proposed methods use augmented estimators of the Brier score risk as the primary basis for building and pruning trees, and lead to methods that are easily implemented using existing R packages. Data from the Radiation Therapy Oncology Group (trial 9410) is used to illustrate these new methods.

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Q-learning is a regression-based approach that is widely used to formalize the development of an optimal dynamic treatment strategy. Finite dimensional working models are typically used to estimate certain nuisance parameters, and misspecification of these working models can result in residual confounding and/or efficiency loss. We propose a robust Q-learning approach which allows estimating such nuisance parameters using data-adaptive techniques. We study the asymptotic behavior of our estimators and provide simulation studies that highlight the need for and usefulness of the proposed method in practice. We use the data from the "Extending Treatment Effectiveness of Naltrexone" multi-stage randomized trial to illustrate our proposed methods.

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BACKGROUND: Metastases are the leading cause of breast cancer-related deaths. The tumor microenvironment impacts cancer progression and metastatic ability. Fibrillar collagen, a major extracellular matrix component, can be studied using the light scattering phenomenon known as second-harmonic generation (SHG). The ratio of forward- to backward-scattered SHG photons (F/B) is sensitive to collagen fiber internal structure and has been shown to be an independent prognostic indicator of metastasis-free survival time (MFS). Here we assess the effects of heterogeneity in the tumor matrix on the possible use of F/B as a prognostic tool. METHODS: SHG imaging was performed on sectioned primary tumor excisions from 95 untreated, estrogen receptor-positive, lymph node negative invasive ductal carcinoma patients. We identified two distinct regions whose collagen displayed different average F/B values, indicative of spatial heterogeneity: the cellular tumor bulk and surrounding tumor-stroma interface. To evaluate the impact of heterogeneity on F/B's prognostic ability, we performed SHG imaging in the tumor bulk and tumor-stroma interface, calculated a 21-gene recurrence score (surrogate for OncotypeDX®, or S-ODX) for each patient and evaluated their combined prognostic ability. RESULTS: We found that F/B measured in tumor-stroma interface, but not tumor bulk, is prognostic of MFS using three methods to select pixels for analysis: an intensity threshold selected by a blinded observer, a histogram-based thresholding method, and an adaptive thresholding method. Using both regression trees and Random Survival Forests for MFS outcome, we obtained data-driven prediction rules that show F/B from tumor-stroma interface, but not tumor bulk, and S-ODX both contribute to predicting MFS in this patient cohort. We also separated patients into low-intermediate (S-ODX < 26) and high risk (S-ODX ≥26) groups. In the low-intermediate risk group, comprised of patients not typically recommended for adjuvant chemotherapy, we find that F/B from the tumor-stroma interface is prognostic of MFS and can identify a patient cohort with poor outcomes. CONCLUSIONS: These data demonstrate that intratumoral heterogeneity in F/B values can play an important role in its possible use as a prognostic marker, and that F/B from tumor-stroma interface of primary tumor excisions may provide useful information to stratify patients by metastatic risk.

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Machine learning (ML) provides a broad framework for addressing high-dimensional prediction problems in classification and regression. While ML is often applied for imaging problems in medical physics, there are many efforts to apply these principles to biological data toward questions of radiation biology. Here, we provide a review of radiogenomics modeling frameworks and efforts toward genomically guided radiotherapy. We first discuss medical oncology efforts to develop precision biomarkers. We next discuss similar efforts to create clinical assays for normal tissue or tumor radiosensitivity. We then discuss modeling frameworks for radiosensitivity and the evolution of ML to create predictive models for radiogenomics.

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This paper proposes a novel paradigm for building regression trees and ensemble learning in survival analysis. Generalizations of the CART and Random Forests algorithms for general loss functions, and in the latter case more general bootstrap procedures, are both introduced. These results, in combination with an extension of the theory of censoring unbiased transformations applicable to loss functions, underpin the development of two new classes of algorithms for constructing survival trees and survival forests: Censoring Unbiased Regression Trees and Censoring Unbiased Regression Ensembles. For a certain "doubly robust" censoring unbiased transformation of squared error loss, we further show how these new algorithms can be implemented using existing software (e.g., CART, random forests). Comparisons of these methods to existing ensemble procedures for predicting survival probabilities are provided in both simulated settings and through applications to four datasets. It is shown that these new methods either improve upon, or remain competitive with, existing implementations of random survival forests, conditional inference forests, and recursively imputed survival trees.

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Many longitudinal studies with a binary outcome measure involve a fraction of subjects with a homogeneous response profile. In our motivating data set, a study on the rate of human immunodeficiency virus (HIV) self-testing in a population of men who have sex with men (MSM), a substantial proportion of the subjects did not self-test during the follow-up study. The observed data in this context consist of a binary sequence for each subject indicating whether or not that subject experienced any events between consecutive observation time points, so subjects who never self-tested were observed to have a response vector consisting entirely of zeros. Conventional longitudinal analysis is not equipped to handle questions regarding the rate of events (as opposed to the odds, as in the classical logistic regression model). With the exception of discrete mixture models, such methods are also not equipped to handle settings in which there may exist a group of subjects for whom no events will ever occur, i.e. a so-called "never-responder" group. In this article, we model the observed data assuming that events occur according to some unobserved continuous-time stochastic process. In particular, we consider the underlying subject-specific processes to be Poisson conditional on some unobserved frailty, leading to a natural focus on modeling event rates. Specifically, we propose to use the power variance function (PVF) family of frailty distributions, which contains both the gamma and inverse Gaussian distributions as special cases and allows for the existence of a class of subjects having zero frailty. We generalize a computational algorithm developed for a log-gamma random intercept model (Conaway, 1990. A random effects model for binary data. Biometrics46, 317-328) to compute the exact marginal likelihood, which is then maximized to obtain estimates of model parameters. We conduct simulation studies, exploring the performance of the proposed method in comparison with competitors. Applying the PVF as well as a Gaussian random intercept model and a corresponding discrete mixture model to our motivating data set, we conclude that the group assigned to receive follow-up messages via SMS was self-testing at a significantly lower rate than the control group, but that there is no evidence to support the existence of a group of never-testers.

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As more patients are supported for longer periods by a left ventricular assist device (LVAD), hospital readmission is becoming a growing problem. However, data about temporal changes in readmission rates and causes for patients with prolonged LVAD support are limited. We aimed to evaluate rates, causes, and predictors of any and long-term readmission after LVAD placement at our institution. We followed 177 HeartMate II LVAD patients for a mean of 1.90 ± 1.33 years post initial discharge after implantation. A marginal rate model was used to evaluate readmission rates, accounting for mortality. During the first year, the readmission rate was 1.79 (95% confidence interval 1.51 to 2.10) readmissions per year. The readmission rate was 1.54 (95% confidence interval 1.07 to 1.93) 2 to 3 years after initial discharge. There was a further decrease in readmission rate in the 3- to 4-year interval. The most common causes of readmission during the first year and even after 3 to 4 years of LVAD support were bleeding (excluding intracranial bleeding) and infection. Female gender was associated with an increased risk of readmission in multivariable analyses, while blood urea nitrogen was predictive of long-term readmissions. In conclusion, readmission after LVAD implantation is common, but readmission rates decrease during long-term follow-up. Bleeding and infection remain leading causes of readmission during longer follow-up and strategies to decrease these complications may reduce readmission rates. Female patients and patients with renal dysfunction have increased risk of readmission and further studies are needed to improve outcomes in these groups.

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Assessment of the regularity of a sequence of events over time is important for clinical decision-making as well as informing public health policy. Our motivating example involves determining the effect of an intervention on the regularity of HIV self-testing behavior among high-risk individuals when exact self-testing times are not recorded. Assuming that these unobserved testing times follow a renewal process, the goals of this work are to develop suitable methods for estimating its distributional parameters when only the presence or absence of at least one event per subject in each of several observation windows is recorded. We propose two approaches to estimation and inference: a likelihood-based discrete survival model using only time to first event; and a potentially more efficient quasi-likelihood approach based on the forward recurrence time distribution using all available data. Regularity is quantified and estimated by the coefficient of variation (CV) of the interevent time distribution. Focusing on the gamma renewal process, where the shape parameter of the corresponding interevent time distribution has a monotone relationship with its CV, we conduct simulation studies to evaluate the performance of the proposed methods. We then apply them to our motivating example, concluding that the use of text message reminders significantly improves the regularity of self-testing, but not its frequency. A discussion on interesting directions for further research is provided.

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OBJECTIVE: Forensic assertive community treatment (FACT) is an adaptation of the assertive community treatment model and is designed to serve justice-involved adults with serious mental illness. This study compared the effectiveness of a standardized FACT model and enhanced treatment as usual in reducing jail and hospital use and in promoting engagement in outpatient mental health services. METHODS: Seventy adults with psychotic disorders who were arrested for misdemeanor crimes and who were eligible for conditional discharge were recruited from the Monroe County, New York, court system. Participants were randomly assigned to receive either FACT (N=35) or enhanced treatment as usual (N=35) for one year. Criminal justice and mental health service utilization outcomes were measured by using state and county databases. RESULTS: Forty-nine participants (70%) completed the full one-year intervention period. Nineteen (27%) were removed early by judicial order, one was removed by county health authorities, and one died of a medical illness. Intent-to-treat analysis for all 70 participants showed that those receiving the FACT intervention had fewer mean±SD convictions (.4±.7 versus .9±1.3, p=.023), fewer mean days in jail (21.5±25.9 versus 43.5±59.2, p=.025), fewer mean days in the hospital (4.4±15.1 versus 23.8±64.2, p=.025), and more mean days in outpatient mental health treatment (305.5±92.1 versus 169.4±139.6, p<.001) compared with participants who received treatment as usual. CONCLUSIONS: The Rochester FACT model was associated with fewer convictions for new crimes, less time in jail and hospitals, and more time in outpatient treatment among justice-involved adults with psychotic disorders compared with treatment as usual.

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Medicare Part D has been successful in providing affordable prescription drug coverage with relatively high levels of beneficiary reported satisfaction. We use nationally representative survey data to examine whether racial/ethnic disparities exist in reported Part D satisfaction and plan evaluations. Compared to non-Hispanic White Medicare beneficiaries, Hispanic beneficiaries are considerably more likely to report to switch to a new plan in the next year and, among beneficiaries auto-enrolled in a Part D plan, are less likely to be very satisfied with the currently enrolled plan. The findings of ethnic disparities in both Medicare Part D plan satisfaction and the intent to switch plans call for future quality and equity improvement efforts to address these disparities.

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This paper considers linear regression with missing covariates and a right censored outcome. We first consider a general two-phase outcome sampling design, where full covariate information is only ascertained for subjects in phase two and sampling occurs under an independent Bernoulli sampling scheme with known subject-specific sampling probabilities that depend on phase one information (e.g., survival time, failure status and covariates). The semiparametric information bound is derived for estimating the regression parameter in this setting. We also introduce a more practical class of augmented estimators that is shown to improve asymptotic efficiency over simple but inefficient inverse probability of sampling weighted estimators. Estimation for known sampling weights and extensions to the case of estimated sampling weights are both considered. The allowance for estimated sampling weights permits covariates to be missing at random according to a monotone but unknown mechanism. The asymptotic properties of the augmented estimators are derived and simulation results demonstrate substantial efficiency improvements over simpler inverse probability of sampling weighted estimators in the indicated settings. With suitable modification, the proposed methodology can also be used to improve augmented estimators previously used for missing covariates in a Cox regression model.

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Previous studies have shown that women with continuous-flow left ventricular assist devices (LVADs) are at greater risk of neurologic events. However, the relation between neurologic events and subsequent outcomes by gender is not well understood. We aimed to identify gender differences in the risk of neurologic events in patients with LVAD and the impact of time-dependent neurologic event on all-cause mortality by gender. Our study included 34 women and 157 men who received a HeartMate II LVAD at the University of Rochester Medical Center, Rochester, New York, from May 5, 2008, to June 5, 2014. Neurologic event was defined as a transient ischemic attack or cerebrovascular accident (hemorrhagic or ischemic). During a median follow-up of 25 months, 16 women (47%) and 20 men (13%) had neurologic events. Among patients with neurologic events, 7 women (44%) and 9 men (45%) died. Women had a 4.67-fold greater risk of neurologic events (hazard ratio [HR] 4.67, 95% confidence interval [CI] 2.26 to 9.66, p <0.001) compared with men. Women with neurologic events had an increased risk of all-cause mortality compared to women without neurologic event (HR 4.84, 95% CI 1.33 to 17.55, p = 0.017). Similarly, men with neurologic events had an increased risk of all-cause mortality compared to men without neurologic event (HR 4.20, 95% CI 1.93 to 9.17, p <0.001, interaction p = 0.854). In conclusion, among patients with LVAD, women are at greater risk of neurologic event compared to men. Both women and men after LVAD have similar high risk of all-cause mortality after neurologic events.

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Estimating a patient's mortality risk is important in making treatment decisions. Survival trees are a useful tool and employ recursive partitioning to separate patients into different risk groups. Existing 'loss based' recursive partitioning procedures that would be used in the absence of censoring have previously been extended to the setting of right censored outcomes using inverse probability censoring weighted estimators of loss functions. In this paper, we propose new 'doubly robust' extensions of these loss estimators motivated by semiparametric efficiency theory for missing data that better utilize available data. Simulations and a data analysis demonstrate strong performance of the doubly robust survival trees compared with previously used methods. Copyright © 2016 John Wiley & Sons, Ltd.

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Two-part random effects models (Olsen and Schafer,(1) Tooze et al.(2)) have been applied to repeated measures of semi-continuous data, characterized by a mixture of a substantial proportion of zero values and a skewed distribution of positive values. In the original formulation of this model, the natural logarithm of the positive values is assumed to follow a normal distribution with a constant variance parameter. In this article, we review and consider three extensions of this model, allowing the positive values to follow (a) a generalized gamma distribution, (b) a log-skew-normal distribution, and (c) a normal distribution after the Box-Cox transformation. We allow for the possibility of heteroscedasticity. Maximum likelihood estimation is shown to be conveniently implemented in SAS Proc NLMIXED. The performance of the methods is compared through applications to daily drinking records in a secondary data analysis from a randomized controlled trial of topiramate for alcohol dependence treatment. We find that all three models provide a significantly better fit than the log-normal model, and there exists strong evidence for heteroscedasticity. We also compare the three models by the likelihood ratio tests for non-nested hypotheses (Vuong(3)). The results suggest that the generalized gamma distribution provides the best fit, though no statistically significant differences are found in pairwise model comparisons.

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Bayesian meta-analysis is an increasingly important component of clinical research, with multivariate meta-analysis a promising tool for studies with multiple endpoints. Model assumptions, including the choice of priors, are crucial aspects of multivariate Bayesian meta-analysis (MBMA) models. In a given model, two different prior distributions can lead to different inferences about a particular parameter. A simulation study was performed in which the impact of families of prior distributions for the covariance matrix of a multivariate normal random effects MBMA model was analyzed. Inferences about effect sizes were not particularly sensitive to prior choice, but the related covariance estimates were. A few families of prior distributions with small relative biases, tight mean squared errors, and close to nominal coverage for the effect size estimates were identified. Our results demonstrate the need for sensitivity analysis and suggest some guidelines for choosing prior distributions in this class of problems. The MBMA models proposed here are illustrated in a small meta-analysis example from the periodontal field and a medium meta-analysis from the study of stroke. Copyright © 2015 John Wiley & Sons, Ltd.

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