Finding the best subgroup with differential treatment effect with multiple outcomes.

Precision medicine aims to identify specific patient subgroups that may benefit the most from a particular treatment than the whole population. Existing definitions for the best subgroup in subgroup analysis are based on a single outcome and do not consider multiple outcomes; specifically, outcomes of different types. In this article, we introduce a definition for the best subgroup under a multiple-outcome setting with continuous, binary, and censored time-to-event outcomes. Our definition provides a trade-off between the subgroup size and the conditional average treatment effects (CATE) in the subgroup with respect to each of the outcomes while taking the relative contribution of the outcomes into account. We conduct simulations to illustrate the proposed definition. By examining the outcomes of urinary tract infection and renal scarring in the RIVUR clinical trial, we identify a subgroup of children that would benefit the most from long-term antimicrobial prophylaxis.

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.

Predicting absolute risk for a person with missing risk factors.

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors.

G-estimation of structural nested mean models for interval-censored data using pseudo-observations.

Two large-scale randomized clinical trials compared fenofibrate and placebo in diabetic patients with pre-existing retinopathy (FIELD study) or risk factors (ACCORD trial) on an intention-to-treat basis and reported a significant reduction in the progression of diabetic retinopathy in the fenofibrate arms. However, their analyses involved complications due to intercurrent events, that is, treatment-switching and interval-censoring. This article addresses these problems involved in estimation of causal effects of long-term use of fibrates in a cohort study that followed patients with type 2 diabetes for 8 years. We propose structural nested mean models (SNMMs) of time-varying treatment effects and pseudo-observation estimators for interval-censored data. The first estimator for SNMMs uses a nonparametric maximum likelihood estimator (MLE) as a pseudo-observation, while the second estimator is based on MLE under a parametric piecewise exponential distribution. Through numerical studies with real and simulated datasets, the pseudo-observations estimators of causal effects using the nonparametric Wellner-Zhan estimator perform well even under dependent interval-censoring. Its application to the diabetes study revealed that the use of fibrates in the first 4 years reduced the risk of diabetic retinopathy but did not support its efficacy beyond 4 years.

Effects of anesthesia exposure on postnatal maturation of white matter in rhesus monkeys.

There is increasing concern about the potential effects of anesthesia exposure on the developing brain. The effects of relatively brief anesthesia exposures used repeatedly to acquire serial magnetic resonance imaging scans could be examined prospectively in rhesus macaques. We analyzed magnetic resonance diffusion tensor imaging (DTI) of 32 rhesus macaques (14 females, 18 males) aged 2 weeks to 36 months to assess postnatal white matter (WM) maturation. We investigated the longitudinal relationships between each DTI property and anesthesia exposure, taking age, sex, and weight of the monkeys into consideration. Quantification of anesthesia exposure was normalized to account for variation in exposures. Segmented linear regression with two knots provided the best model for quantifying WM DTI properties across brain development as well as the summative effect of anesthesia exposure. The resulting model revealed statistically significant age and anesthesia effects in most WM tracts. Our analysis indicated there were major effects on WM associated with low levels of anesthesia even when repeated as few as three times. Fractional anisotropy values were reduced across several WM tracts in the brain, indicating that anesthesia exposure may delay WM maturation, and highlight the potential clinical concerns with even a few exposures in young children.

Inference on subgroups identified based on a heterogeneous treatment effect in a post hoc analysis of a clinical trial.

Due to the many benefits of understanding treatment effect heterogeneity in a clinical trial, an exploratory post hoc subgroup analysis is often performed to find subpopulations of patients with conditional average treatment effect that suggests better treatment efficacy than in the overall population. A naive re-substitution approach uses all available data to identify a subgroup and then proceeds with estimation and inference using the same data set. This approach generally leads to an overly optimistic estimate of conditional average treatment effect. In this article, in a post hoc analysis, we estimate the target optimal subgroup through maximizing a utility function, from candidates systematically identified with a penalized regression. We then compare two resampling-based bias-correction methods, cross-validation and debiasing bootstrap, for obtaining approximately unbiased estimates and valid inference of conditional average treatment effect in the identified subgroup, with either an empirical or an augmented estimator. Our results show that both the cross-validation and the debiasing bootstrap methods reduce the re-substitution bias effectively. The cross-validation method appears to have less biased point estimates, smaller standard error estimates, but poorer coverages than the debiasing bootstrap method when using the empirical estimator and the sample size is moderate. Using the augmented estimator in the debiasing bootstrap method leads to less biased point estimates but poorer coverages. We conclude that bias correction should be a part of every exploratory post hoc subgroup analysis to eliminate re-substitution bias and to obtain a proper confidence interval for the estimated conditional average treatment effect in the selected subgroup.

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.

An imputation approach for a time-to-event analysis subject to missing outcomes due to noncoverage in disease registries.

Disease incidence data in a national-based cohort study would ideally be obtained through a national disease registry. Unfortunately, no such registry currently exists in the United States. Instead, the results from individual state registries need to be combined to ascertain certain disease diagnoses in the United States. The National Cancer Institute has initiated a program to assemble all state registries to provide a complete assessment of all cancers in the United States. Unfortunately, not all registries have agreed to participate. In this article, we develop an imputation-based approach that uses self-reported cancer diagnosis from longitudinally collected questionnaires to impute cancer incidence not covered by the combined registry. We propose a two-step procedure, where in the first step a mover-stayer model is used to impute a participant's registry coverage status when it is only reported at the time of the questionnaires given at 10-year intervals and the time of the last-alive vital status and death. In the second step, we propose a semiparametric working model, fit using an imputed coverage area sample identified from the mover-stayer model, to impute registry-based survival outcomes for participants in areas not covered by the registry. The simulation studies show the approach performs well as compared with alternative ad hoc approaches for dealing with this problem. We illustrate the methodology with an analysis that links the United States Radiologic Technologists study cohort with the combined registry that includes 32 of the 50 states.

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.

Generalized multi-SNP mediation intersection-union test.

To elucidate the molecular mechanisms underlying genetic variants identified from genome-wide association studies (GWAS) for a variety of phenotypic traits encompassing binary, continuous, count, and survival outcomes, we propose a novel and flexible method to test for mediation that can simultaneously accommodate multiple genetic variants and different types of outcome variables. Specifically, we employ the intersection-union test approach combined with the likelihood ratio test to detect mediation effect of multiple genetic variants via some mediator (e.g., the expression of a neighboring gene) on outcome. We fit high-dimensional generalized linear mixed models under the mediation framework, separately under the null and alternative hypothesis. We leverage Laplace approximation to compute the marginal likelihood of outcome and use coordinate descent algorithm to estimate corresponding parameters. Our extensive simulations demonstrate the validity of our proposed methods and substantial, up to 97%, power gains over alternative methods. Applications to real data for the study of Chlamydia trachomatis infection further showcase advantages of our methods. We believe our proposed methods will be of value and general interest in this post-GWAS era to disentangle the potential causal mechanism from DNA to phenotype for new drug discovery and personalized medicine.

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.

Host Genetic Risk Factors for Chlamydia trachomatis-Related Infertility in Women.

BACKGROUND: Chlamydia trachomatis (Ct) infection ascending to the upper genital tract can cause infertility. Direct association of genetic variants as contributors is challenging because infertility may not be diagnosed until years after infection. Investigating the intermediate trait of ascension bridges this gap. METHODS: We identified infertility genome-wide association study (GWAS) loci using deoxyribonucleic acid from Ct-seropositive cisgender women in a tubal factor infertility study and Ct-infected cisgender women from a longitudinal pelvic inflammatory disease cohort with known fertility status. Deoxyribonucleic acid and blood messenger ribonucleic acid from 2 additional female cohorts with active Ct infection and known endometrial infection status were used to investigate the impact of infertility single-nucleotide polymorphisms (SNPs) on Ct ascension. A statistical mediation test examined whether multiple infertility SNPs jointly influenced ascension risk by modulating expression of mediator genes. RESULTS: We identified 112 candidate infertility GWAS loci, and 31 associated with Ct ascension. The SNPs altered chlamydial ascension by modulating expression of 40 mediator genes. Mediator genes identified are involved in innate immune responses including type I interferon production, T-cell function, fibrosis, female reproductive tract health, and protein synthesis and degradation. CONCLUSIONS: We identified Ct-related infertility loci and their potential functional effects on Ct ascension.