Shape restricted additive hazards models: Monotone, unimodal, and U-shape hazard functions.

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time-dependent covariate with monotone or U-shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

CRM and partial order CRM with adaptive rescaling for dose-finding in immunotherapy trials with a continuous outcome.

In many phase 1 oncology trials of immunotherapies, no dose-limiting toxicities are observed and the maximum tolerated dose cannot be identified. In these settings, dose-finding can be guided by a biomarker of response rather than the occurrences of dose-limiting toxicity. The recommended phase 2 dose can be defined as the dose with mean response equal to a prespecified value of a continuous response biomarker. To target the mean of a continuous biomarker, we build on the idea of the continual reassessment method and the quasi-Bernoulli likelihood. We extend the design to a problem of finding the recommended phase 2 dose combination in a trial with multiple immunotherapies.

Pregnancy-related factors may signal additional protection or risk of future cardiovascular diseases.

BACKGROUND: Cardiovascular disease (CVD) guidelines recommend using the Pooled Cohort Equation (PCE) to assess 10-year CVD risk based on traditional risk factors. Pregnancy-related factors have been associated with future CVD. We examined the contribution of two pregnancy-related factors, (1) history of a low birthweight (LBW) infant and (2) breastfeeding to CVD risk accounting for traditional risk factors as assessed by the PCE. METHODS: A nationally representative sample of women, ages 40-79, with a history of pregnancy, but no prior CVD, was identified using NHANES 1999-2006. Outcomes included (1) CVD death and (2) CVD death plus CVD surrogates. We used Cox proportional hazards models to adjust for PCE risk score. RESULTS: Among 3,758 women, 479 had a LBW infant and 1,926 reported breastfeeding. Mean follow-up time was 12.1 years. Survival models showed a consistent reduction in CVD outcomes among women with a history of breastfeeding. In cause-specific survival models, breastfeeding was associated with a 24% reduction in risk of CVD deaths (HR 0.76; 95% CI 0.45─1.27, p = 0.30) and a 33% reduction in risk of CVD deaths + surrogate CVD, though not statistically significant. (HR 0.77; 95% CI 0.52─1.14, p = 0.19). Survival models yielded inconclusive results for LBW with wide confidence intervals (CVD death: HR 0.98; 95% CI 0.47─2.05; p = 0.96 and CVD death + surrogate CVD: HR 1.29; 95% CI 0.74─2.25; p = 0.38). CONCLUSION: Pregnancy-related factors may provide important, relevant information about CVD risk beyond traditional risk factors. While further research with more robust datasets is needed, it may be helpful for clinicians to counsel women about the potential impact of pregnancy-related factors, particularly the positive impact of breastfeeding, on cardiovascular health.

Semiparametric analysis of a generalized linear model with multiple covariates subject to detection limits.

Studies on the health effects of environmental mixtures face the challenge of limit of detection (LOD) in multiple correlated exposure measurements. Conventional approaches to deal with covariates subject to LOD, including complete-case analysis, substitution methods, and parametric modeling of covariate distribution, are feasible but may result in efficiency loss or bias. With a single covariate subject to LOD, a flexible semiparametric accelerated failure time (AFT) model to accommodate censored measurements has been proposed. We generalize this approach by considering a multivariate AFT model for the multiple correlated covariates subject to LOD and a generalized linear model for the outcome. A two-stage procedure based on semiparametric pseudo-likelihood is proposed for estimating the effects of these covariates on health outcome. Consistency and asymptotic normality of the estimators are derived for an arbitrary fixed dimension of covariates. Simulations studies demonstrate good large sample performance of the proposed methods vs conventional methods in realistic scenarios. We illustrate the practical utility of the proposed method with the LIFECODES birth cohort data, where we compare our approach to existing approaches in an analysis of multiple urinary trace metals in association with oxidative stress in pregnant women.

Efficiency of Naive Estimators for Accelerated Failure Time Models under Length-Biased Sampling.

In prevalent cohort studies where subjects are recruited at a cross-section, the time to an event may be subject to length-biased sampling, with the observed data being either the forward recurrence time, or the backward recurrence time, or their sum. In the regression setting, assuming a semiparametric accelerated failure time model for the underlying event time, where the intercept parameter is absorbed into the nuisance parameter, it has been shown that the model remains invariant under these observed data set-ups and can be fitted using standard methodology for accelerated failure time model estimation, ignoring the length-bias. However, the efficiency of these estimators is unclear, owing to the fact that the observed covariate distribution, which is also length-biased, may contain information about the regression parameter in the accelerated life model. We demonstrate that if the true covariate distribution is completely unspecified, then the naive estimator based on the conditional likelihood given the covariates is fully efficient for the slope.

Competing risks predictions with different time scales under the additive risk model.

In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

A parametric approach to relaxing the independence assumption in relative survival analysis.

With known cause of death (CoD), competing risk survival methods are applicable in estimating disease-specific survival. Relative survival analysis may be used to estimate disease-specific survival when cause of death is either unknown or subject to misspecification and not reliable for practical usage. This method is popular for population-based cancer survival studies using registry data and does not require CoD information. The standard estimator is the ratio of all-cause survival in the cancer cohort group to the known expected survival from a general reference population. Disease-specific death competes with other causes of mortality, potentially creating dependence among the CoD. The standard ratio estimate is only valid when death from disease and death from other causes are independent. To relax the independence assumption, we formulate dependence using a copula-based model. Likelihood-based parametric method is used to fit the distribution of disease-specific death without CoD information, where the copula is assumed known and the distribution of other cause of mortality is derived from the reference population. We propose a sensitivity analysis, where the analysis is conducted across a range of assumed dependence structures. We demonstrate the utility of our method through simulation studies and an application to French breast cancer data.

Accounting for Preinvasive Conditions in Analysis of Invasive Cancer Risk: Application to Breast Cancer.

BACKGROUND: Preinvasive cancer conditions are often actively treated to minimize progression to life-threatening invasive cancers, but this creates challenges for analysis of invasive cancer risk. Conventional methods of treating preinvasive conditions as censoring events or targeting at the composite outcome could both lead to bias. METHODS: We propose two solutions: one that provides exact estimates of risk based on distributional assumptions about progression, and one that provides risk bounds corresponding to extreme cases of no or complete progression. We compare these approaches through simulations and an analysis of the Sister Study data in the context of ductal carcinoma in situ (DCIS) and invasive breast cancer. RESULTS: Simulations suggested important biases with conventional approaches, whereas the proposed estimate is consistent when progression parameters are correctly specified, and the risk bounds are robust in all scenarios. With Sister Study, the estimated lifetime risks for invasive breast cancer are 0.220 and 0.269 with DCIS censored or combined. Without detailed progression information, a sensitivity analysis suggested lifetime risk falls between the bounds of 0.214 and 0.269 across assumptions of 10%-95% of DCIS patients progressing to invasive cancer in an average of 1-10 years. CONCLUSIONS: When estimating invasive cancer risk while preinvasive conditions are actively treated, it is important to consider the implied assumptions and potential biases of conventional approaches. Although still not perfect, we proposed two practical solutions that provide improved understanding of the underlying mechanism of invasive cancer.

Causal Proportional Hazards Estimation with a Binary Instrumental Variable.

Instrumental variables (IV) are a useful tool for estimating causal effects in the presence of unmeasured confounding. IV methods are well developed for uncensored outcomes, particularly for structural linear equation models, where simple two-stage estimation schemes are available. The extension of these methods to survival settings is challenging, partly because of the nonlinearity of the popular survival regression models and partly because of the complications associated with right censoring or other survival features. Motivated by the Prostate, Lung, Colorectal and Ovarian (PLCO) Cancer screening trial, we develop a simple causal hazard ratio estimator in a proportional hazards model with right censored data. The method exploits a special characterization of IV which enables the use of an intuitive inverse weighting scheme that is generally applicable to more complex survival settings with left truncation, competing risks, or recurrent events. We rigorously establish the asymptotic properties of the estimators, and provide plug-in variance estimators. The proposed method can be implemented in standard software, and is evaluated through extensive simulation studies. We apply the proposed IV method to a data set from the Prostate, Lung, Colorectal and Ovarian cancer screening trial to delineate the causal effect of flexible sigmoidoscopy screening on colorectal cancer survival which may be confounded by informative noncompliance with the assigned screening regimen.

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category.

Proportional rates models are frequently used for the analysis of recurrent event data with multiple event categories. When some of the event categories are missing, a conventional approach is to either exclude the missing data for a complete-case analysis or employ a parametric model for the missing event type. It is well known that the complete-case analysis is inconsistent when the missingness depends on covariates, and the parametric approach may incur bias when the model is misspecified. In this paper, we aim to provide a more robust approach using a rate proportion method for the imputation of missing event types. We show that the log-odds of the event type can be written as a semiparametric generalized linear model, facilitating a theoretically justified estimation framework. Comprehensive simulation studies were conducted demonstrating the improved performance of the semiparametric method over parametric procedures. Multiple types of Pseudomonas aeruginosa infections of young cystic fibrosis patients were analyzed to demonstrate the feasibility of our proposed approach.

Infant gut microbiome composition is associated with non-social fear behavior in a pilot study.

Experimental manipulation of gut microbes in animal models alters fear behavior and relevant neurocircuitry. In humans, the first year of life is a key period for brain development, the emergence of fearfulness, and the establishment of the gut microbiome. Variation in the infant gut microbiome has previously been linked to cognitive development, but its relationship with fear behavior and neurocircuitry is unknown. In this pilot study of 34 infants, we find that 1-year gut microbiome composition (Weighted Unifrac; lower abundance of Bacteroides, increased abundance of Veillonella, Dialister, and Clostridiales) is significantly associated with increased fear behavior during a non-social fear paradigm. Infants with increased richness and reduced evenness of the 1-month microbiome also display increased non-social fear. This study indicates associations of the human infant gut microbiome with fear behavior and possible relationships with fear-related brain structures on the basis of a small cohort. As such, it represents an important step in understanding the role of the gut microbiome in the development of human fear behaviors, but requires further validation with a larger number of participants.

Consistency of the CRM when the dose-toxicity curve is not monotone and its application to the POCRM.

The continual reassessment method (CRM) is a well-known design for dose-finding trials with the goal of estimating the maximum tolerated dose (MTD), the dose with a given probability of toxicity. The standard assumption is that the probability of toxicity monotonically increases with dose. We show that the CRM can still be consistent and correctly identify the MTD even when the dose-toxicity curve is not monotone as long as there is monotonicity of the true toxicity probabilities right below and right above the true MTD. In the case of multiple therapies, where it is unclear how to order combinations of dose levels of multiple therapies, our findings provide insight into the performance of the partial order CRM (POCRM). To select the correct dose combination at the end of a trial, the POCRM does not have to select a monotone ordering of drug combinations. We illustrate the connection between our results for the CRM with a nonmonotone dose-toxicity curve and the POCRM via simulations.

Canonical correlation analysis for elliptical copulas.

Canonical correlation analysis (CCA) is a common method used to estimate the associations between two different sets of variables by maximizing the Pearson correlation between linear combinations of the two sets of variables. We propose a version of CCA for transelliptical distributions with an elliptical copula using pairwise Kendall's tau to estimate a latent scatter matrix. Because Kendall's tau relies only on the ranks of the data this method does not make any assumptions about the marginal distributions of the variables, and is valid when moments do not exist. We establish consistency and asymptotic normality for canonical directions and correlations estimated using Kendall's tau. Simulations indicate that this estimator outperforms standard CCA for data generated from heavy tailed elliptical distributions. Our method also identifies more meaningful relationships when the marginal distributions are skewed. We also propose a method for testing for non-zero canonical correlations using bootstrap methods. This testing procedure does not require any assumptions on the joint distribution of the variables and works for all elliptical copulas. This is in contrast to permutation tests which are only valid when data are generated from a distribution with a Gaussian copula. This method's practical utility is shown in an analysis of the association between radial diffusivity in white matter tracts and cognitive tests scores for six-year-old children from the Early Brain Development Study at UNC-Chapel Hill. An R package implementing this method is available at github.com/blangworthy/transCCA.

Estimation of causal quantile effects with a binary instrumental variable and censored data.

The causal effect of a treatment is of fundamental interest in the social, biological, and health sciences. Instrumental variable (IV) methods are commonly used to determine causal treatment effects in the presence of unmeasured confounding. In this work, we study a new binary IV framework with randomly censored outcomes where we propose to quantify the causal treatment effect by the concept of complier quantile causal effect (CQCE). The CQCE is identifiable under weaker conditions than the complier average causal effect when outcomes are subject to censoring, and it can provide useful insight into the dynamics of the causal treatment effect. Employing the special characteristic of the binary IV and adapting the principle of conditional score, we uncover a simple weighting scheme that can be incorporated into the standard censored quantile regression procedure to estimate CQCE. We develop robust nonparametric estimation of the derived weights in the first stage, which permits stable implementation of the second stage estimation based on existing software. We establish rigorous asymptotic properties for the proposed estimator, and confirm its validity and satisfactory finite-sample performance via extensive simulations. The proposed method is applied to a bone marrow transplant dataset to evaluate the causal effect of rituximab in diffuse large B-cell lymphoma patients.

Early Follow-up After Colorectal Surgery Reduces Postdischarge Emergency Department Visits.

BACKGROUND: Thirty-day readmissions, emergency department visits, and observation stays are common after colorectal surgery (9%-25%, 8%-12%, and 3%-5%), yet it is unknown to what extent planned postdischarge care can decrease the frequency of emergency department visits. OBJECTIVE: This study's aim was to determine whether early follow-up with the surgical team reduces 30-day emergency department visits. DESIGN: This retrospective cohort study used a central data repository of clinical and administrative data for 2013 through 2018. SETTING: This study was conducted in a large statewide health care system (10 affiliated hospitals, >300 practices). PATIENTS: All adult patients undergoing colorectal surgery were included unless they had a length of stay <1 day or died during the index hospitalization. INTERVENTION: Early (<10 days after discharge) versus late (≥10 days) follow-up at the outpatient surgery clinic, or no outpatient surgery clinic follow-up, was assessed. MAIN OUTCOME MEASURES: The primary outcome measured was the time to 30-day postdischarge emergency department visit. RESULTS: Our cohort included 3442 patients undergoing colorectal surgery; 38% of patients had an early clinic visit. Overall, 11% had an emergency department encounter between 11 and 30 days after discharge. Those with early follow-up had decreased emergency department encounters (adjusted HR 0.13; 95% CI, 0.08-0.22). An early clinic visit within 10 days, compared to 14 days, prevented an additional 142 emergency department encounters. Nationwide, this could potentially prevent 8433 unplanned visits each year with an estimated cost savings of $49 million annually. LIMITATIONS: We used retrospective data and were unable to assess for health care utilization outside our health system. CONCLUSIONS: Early follow-up within 10 days of adult colorectal surgery is associated with decreased subsequent emergency department encounters. See Video Abstract at http://links.lww.com/DCR/B330. EL SEGUIMIENTO TEMPRANO DESPUÉS DE LA CIRUGÍA COLORRECTAL REDUCE LAS VISITAS AL SERVICIO DE URGENCIAS POSTERIOR AL ALTA: Los readmisión a los treinta días, las visitas al servicio de urgencias y las estancias de observación son comunes después de la cirugía colorrectal, 9-25%, 8-12% y 3-5%, respectivamente. Sin embargo, se desconoce en qué medida la atención planificada posterior al alta puede disminuir la frecuencia de las visitas al servicio de urgencias.Determinar si el seguimiento temprano con el equipo quirúrgico reduce las visitas a 30 días al servicio de urgencias.Este estudio de cohorte retrospectivo utilizó un depósito central de datos clínicos y administrativos para 2013-2018.Gran sistema de salud estatal (10 hospitales afiliados,> 300 consultorios).Se incluyeron todos los pacientes adultos de cirugía colorrectal a menos que tuvieran una estadía <1 día o murieran durante el índice de hospitalización.Temprano (<10 días después del alta) versus tardío (≥10 días) o sin seguimiento en la clínica de cirugía ambulatoria.Tiempo para la visita al servicio de urgencias a 30 días después del alta.Nuestra cohorte incluyó 3.442 pacientes de cirugía colorrectal; El 38% de los pacientes tuvieron una visita temprana a clínica. En total, el 11% tuvo un encuentro con el servicio de urgencias entre 11 y 30 días después de ser dado de alta. Aquellos con seguimiento temprano disminuyeron las visitas al servicio de urgencias (HR 0,13; IC del 95%: 0,08 a 0,22). Además, una visita temprana a la clínica en un plazo de 10 días, en comparación con 14 días, evitó 142 encuentros adicionales en el servicio de urgencias. A nivel nacional, esto podría prevenir 8.433 visitas no planificadas cada año con un ahorro estimado de $ 49 millones anuales.Utilizamos datos retrospectivos y no pudimos evaluar la utilización de la atención médica fuera de nuestro sistema de salud.El seguimiento temprano dentro de los 10 días de la cirugía colorrectal en adultos se asocia con una disminución de los encuentros posteriores en el servicio de urgencias. Consulte Video Resumen en http://links.lww.com/DCR/B330. (Traducción-Dr. Gonzalo Hagerman).

Bias testing, bias correction, and confounder selection using an instrumental variable model.

Instrumental variable (IV) analysis can be used to address bias due to unobserved confounding when estimating the causal effect of a treatment on an outcome of interest. However, if a proposed IV is correlated with unmeasured confounders and/or weakly correlated with the treatment, the standard IV estimator may be more biased than an ordinary least squares (OLS) estimator. Several methods have been proposed that compare the bias of the IV and OLS estimators relying on the belief that measured covariates can be used as proxies for the unmeasured confounder. Despite these developments, there is lack of discussion about approaches that can be used to formally test whether the IV estimator may be less biased than the OLS estimator. Thus, we have developed a testing framework to compare the bias and a criterion to select informative measured covariates for bias comparison and regression adjustment. We also have developed a bias-correction method, which allows one to use an invalid IV to correct the bias of the OLS or IV estimator. Numerical studies demonstrate that the proposed methods perform well with realistic sample sizes.

Numerical evaluation of spray position for improved nasal drug delivery.

Topical intra-nasal sprays are amongst the most commonly prescribed therapeutic options for sinonasal diseases in humans. However, inconsistency and ambiguity in instructions show a lack of definitive knowledge on best spray use techniques. In this study, we have identified a new usage strategy for nasal sprays available over-the-counter, that registers an average 8-fold improvement in topical delivery of drugs at diseased sites, when compared to prevalent spray techniques. The protocol involves re-orienting the spray axis to harness inertial motion of particulates and has been developed using computational fluid dynamics simulations of respiratory airflow and droplet transport in medical imaging-based digital models. Simulated dose in representative models is validated through in vitro spray measurements in 3D-printed anatomic replicas using the gamma scintigraphy technique. This work breaks new ground in proposing an alternative user-friendly strategy that can significantly enhance topical delivery inside human nose. While these findings can eventually translate into personalized spray usage instructions and hence merit a change in nasal standard-of-care, this study also demonstrates how relatively simple engineering analysis tools can revolutionize everyday healthcare. Finally, with respiratory mucosa as the initial coronavirus infection site, our findings are relevant to intra-nasal vaccines that are in-development, to mitigate the COVID-19 pandemic.

Ensemble estimation and variable selection with semiparametric regression models.

We consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components, with an efficient estimator of the regression parameter available for each component. An optimal weighted combination of the component estimators, named an ensemble estimator, may be employed as an overall estimate of the regression parameter, and may be fully efficient under uncorrelatedness conditions. This approach is useful when the full likelihood function may be difficult to maximize, but the components are easy to maximize. It covers settings where the nuisance parameter may be estimated at different rates in the component likelihoods. As a motivating example we consider proportional hazards regression with prospective doubly censored data, in which the likelihood factors into a current status data likelihood and a left-truncated right-censored data likelihood. Variable selection is important in such regression modelling, but the applicability of existing techniques is unclear in the ensemble approach. We propose ensemble variable selection using the least squares approximation technique on the unpenalized ensemble estimator, followed by ensemble re-estimation under the selected model. The resulting estimator has the oracle property such that the set of nonzero parameters is successfully recovered and the semiparametric efficiency bound is achieved for this parameter set. Simulations show that the proposed method performs well relative to alternative approaches. Analysis of an AIDS cohort study illustrates the practical utility of the method.