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.

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.

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.

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.

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.

G-estimation of structural nested mean models for competing risks data using pseudo-observations.

This article provides methods of causal inference for competing risks data. The methods are formulated as structural nested mean models of causal effects directly related to the cumulative incidence function or subdistribution hazard, which reflect the survival experience of a subject in the presence of competing risks. The effect measures include causal risk differences, causal risk ratios, causal subdistribution hazard ratios, and causal effects of time-varying exposures. Inference is implemented by g-estimation using pseudo-observations, a technique to handle censoring. The finite-sample performance of the proposed estimators in simulated datasets and application to time-varying exposures in a cohort study of type 2 diabetes are also presented.

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.

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.

Antibacterial Use Is Associated with an Increased Risk of Hematologic and Gastrointestinal Adverse Events in Patients Treated with Gemcitabine for Stage IV Pancreatic Cancer.

BACKGROUND: Preclinical evidence has demonstrated that common intratumor bacteria metabolize the chemotherapeutic drug gemcitabine. The significance of this bacterial metabolism pathway, relative to the known metabolic pathways by host enzymes, is not known. We hypothesized that bacterial metabolism is clinically significant and that "knockdown" by antibacterial therapy has the unintended effect of increasing the effective dose of gemcitabine, thereby increasing the risk for gemcitabine-associated toxicities. MATERIALS AND METHODS: We reanalyzed the comparator arm of the MPACT trial (NCT01442974), made available through Project Data Sphere, LLC (CEO Roundtable on Cancer's Life Sciences Consortium, Cary, NC; www.projectdatasphere.org). In this arm, 430 patients with metastatic pancreatic adenocarcinoma were treated with gemcitabine. We used the Anderson-Gill survival model to compare the risk of developing an adverse event after antibacterial prescription with time unexposed to antibacterials. Adverse events of grade 3 and greater were considered at three levels of granularity: all aggregated into one endpoint, aggregated by class, and taken individually. Antibiotic exposures were analyzed in aggregate as well as by class. RESULTS: Antibacterial exposure was associated with an increased risk of adverse events (hazard ratio [HR]: 1.77; confidence interval [CI]: 1.46-2.14), any hematologic adverse event (HR: 1.64; CI: 1.26-2.13), and any gastrointestinal adverse event (HR: 2.14; CI: 1.12-4.10) but not a constitutional (HR: 1.33; CI: 0.611-2.90) or hepatologic adverse event (HR: 0.99; CI: 0.363-2.71). Among specific adverse events, antibacterial exposure was associated with an increased risk of anemia (HR: 3.16; CI: 1.59-6.27), thrombocytopenia (HR: 2.52; CI: 1.31-4.85), leukopenia (HR: 3.91; CI: 1.46-10.5), and neutropenia (HR: 1.53; CI: 1.07-2.17) but not any other specific adverse events. CONCLUSION: Antibacterial exposure was associated with an increased risk of gemcitabine-associated, dose-limiting adverse events, including aggregate hematologic and gastrointestinal events, as well as four specific hematologic adverse events, suggesting that intratumor bacteria may be responsible for a clinically significant portion of gemcitabine metabolism. Alternative avenues of evidence will be necessary to confirm this preliminary finding and assess its generalizability. There is plentiful opportunity for similar analyses on other clinical trial data sets, where gemcitabine or other biomimetic small molecules were used. IMPLICATIONS FOR PRACTICE: Patients treated with gemcitabine for metastatic pancreatic ductal adenocarcinoma have an increased rate of gemcitabine-associated toxicity during and after antibiotic therapy. This observation is consistent with preclinical evidence that intratumor bacteria metabolize gemcitabine to an inactive form. Further research is needed to determine whether this observation merits any changes in clinical practice.

The Influence of Screening, Misclassification, and Reporting Biases on Reported Chlamydia Case Rates Among Young Women in the United States, 2000 Through 2017.

BACKGROUND: National chlamydia case rate trends are difficult to interpret because of biases from partial screening coverage, imperfect diagnostic tests, and underreporting. We examined the extent to which these time-varying biases could influence reported annual chlamydia case rates. METHODS: Annual reported case rates among women aged 15 through 24 years from 2000 through 2017 were obtained from the Centers for Disease Control and Prevention's National Center for HIV/AIDS, Viral Hepatitis, STD, and TB Prevention AtlasPlus tool. Estimates of reporting completeness, diagnostic test sensitivity and specificity, and screening coverage were derived from literature review and expert opinion. We adjusted annual reported case rates for incomplete reporting, imperfect diagnostic tests, and partial screening coverage through a series of corrections, and calculated annual adjusted case rates of correctly diagnosed chlamydia. RESULTS: Adjusted chlamydia case rates among young women were higher than reported case rates throughout the study period. Reported case rates increased over the study period, but adjusted rates declined from 12,900 to 7900 cases per 100,000 person-years between 2000 and 2007. After 2007, adjusted case rates declined to 7500 cases per 100,000 person-years in 2017. Bias from partial screening coverage had a larger impact on case rate magnitude and trend shape than bias from imperfect diagnostic tests or underreporting. CONCLUSIONS: Reported chlamydia case rates may be substantially lower than true chlamydia case rates because of incomplete reporting, imperfect diagnostic tests, and partial screening coverage. Because the magnitude of these biases has declined over time, the differences between reported and adjusted case rates have narrowed, revealing a sharp decline in adjusted case rates even as reported case rates have risen. The decline in adjusted case rates suggests that the rise in reported case rates should not be interpreted strictly as increasing chlamydia incidence, as the observed rise can be explained by improvements in screening coverage, diagnostic tests, and reporting.

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.

A review of the use of time-varying covariates in the Fine-Gray subdistribution hazard competing risk regression model.

In survival analysis, time-varying covariates are covariates whose value can change during follow-up. Outcomes in medical research are frequently subject to competing risks (events precluding the occurrence of the primary outcome). We review the types of time-varying covariates and highlight the effect of their inclusion in the subdistribution hazard model. External time-dependent covariates are external to the subject, can effect the failure process, but are not otherwise involved in the failure mechanism. Internal time-varying covariates are measured on the subject, can effect the failure process directly, and may also be impacted by the failure mechanism. In the absence of competing risks, a consequence of including internal time-dependent covariates in the Cox model is that one cannot estimate the survival function or the effect of covariates on the survival function. In the presence of competing risks, the inclusion of internal time-varying covariates in a subdistribution hazard model results in the loss of the ability to estimate the cumulative incidence function (CIF) or the effect of covariates on the CIF. Furthermore, the definition of the risk set for the subdistribution hazard function can make defining internal time-varying covariates difficult or impossible. We conducted a review of the use of time-varying covariates in subdistribution hazard models in articles published in the medical literature in 2015 and in the first 5 months of 2019. Seven percent of articles published included a time-varying covariate. Several inappropriately described a time-varying covariate as having an association with the risk of the outcome.

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).

Diagnostic accuracy of acute infarcts in multiple cerebral circulations for cardioembolic stroke: Literature review and meta-analysis.

OBJECTIVE: To determine the diagnostic value of acute infarcts in multiple cerebral circulations (AIMCC) on MRI diffusion-weighted imaging (DWI) for cardioembolism (CE) stroke subtype in adult patients hospitalized with acute ischemic stroke, we conducted a systematic literature review and meta-analysis. METHODS: MEDLINE was searched via PubMed for articles reporting patients hospitalized with acute ischemic stroke with MRI DWI categorized as AIMCC vs other and use of Trial of Org 10172 in Acute Stroke Treatment (TOAST) Criteria for cardioembolism subtype. Measures of diagnostic accuracy were calculated from the retrieved studies. RESULTS: Seven eligible articles comprised 5813 patients. Bivariate random effects models estimated sensitivity 0.19 (95% CI, 0.13 to 0.27), specificity 0.89 (0.86 to 0.91), positive predictive value 0.37 (0.30 to 0.45), negative predictive value 0.76 (0.7 to 0.82), positive likelihood ratio 1.70 (1.13 to 2.57) and negative likelihood ratio 0.91 (0.83 to 1). INTERPRETATION: The pattern of AIMCC on DWI is of limited diagnostic value. It is not sufficiently accurate to exclude cardiac pathology by a negative test nor does a positive test indicate a major increase in the probability of identifying a potential cardioembolic source.

Propensity-score matching with competing risks in survival analysis.

Propensity-score matching is a popular analytic method to remove the effects of confounding due to measured baseline covariates when using observational data to estimate the effects of treatment. Time-to-event outcomes are common in medical research. Competing risks are outcomes whose occurrence precludes the occurrence of the primary time-to-event outcome of interest. All non-fatal outcomes and all cause-specific mortality outcomes are potentially subject to competing risks. There is a paucity of guidance on the conduct of propensity-score matching in the presence of competing risks. We describe how both relative and absolute measures of treatment effect can be obtained when using propensity-score matching with competing risks data. Estimates of the relative effect of treatment can be obtained by using cause-specific hazard models in the matched sample. Estimates of absolute treatment effects can be obtained by comparing cumulative incidence functions (CIFs) between matched treated and matched control subjects. We conducted a series of Monte Carlo simulations to compare the empirical type I error rate of different statistical methods for testing the equality of CIFs estimated in the matched sample. We also examined the performance of different methods to estimate the marginal subdistribution hazard ratio. We recommend that a marginal subdistribution hazard model that accounts for the within-pair clustering of outcomes be used to test the equality of CIFs and to estimate subdistribution hazard ratios. We illustrate the described methods by using data on patients discharged from hospital with acute myocardial infarction to estimate the effect of discharge prescribing of statins on cardiovascular death.

On the self-triggering Cox model for recurrent event data.

Recurrent event data frequently occur in longitudinal studies when subjects experience more than one event during the observation period. Often, the occurrence of subsequent events is associated with the experience of previous events. Such dependence is commonly ignored in the application of standard recurrent event methodology. In this paper, we utilize a Cox-type regression model with time-varying triggering effect depending on the number and timing of previous events to enhance both model fit and prediction. Parameter estimation and statistical inference is achieved via the partial likelihood. A statistical test procedure is provided to assess the existence of the triggering effects. We demonstrate our approach via comprehensive simulation studies and a real data analysis on chronic pseudomonas infections in young cystic fibrosis patients. Our model provides significantly better predictions than standard recurrent event models.

Analyzing discrete competing risks data with partially overlapping or independent data sources and nonstandard sampling schemes, with application to cancer registries.

This paper demonstrates the flexibility of a general approach for the analysis of discrete time competing risks data that can accommodate complex data structures, different time scales for different causes, and nonstandard sampling schemes. The data may involve a single data source where all individuals contribute to analyses of both cause-specific hazard functions, overlapping datasets where some individuals contribute to the analysis of the cause-specific hazard function of only one cause while other individuals contribute to analyses of both cause-specific hazard functions, or separate data sources where each individual contributes to the analysis of the cause-specific hazard function of only a single cause. The approach is modularized into estimation and prediction. For the estimation step, the parameters and the variance-covariance matrix can be estimated using widely available software. The prediction step utilizes a generic program with plug-in estimates from the estimation step. The approach is illustrated with three prognostic models for stage IV male oral cancer using different data structures. The first model uses only men with stage IV oral cancer from population-based registry data. The second model strategically extends the cohort to improve the efficiency of the estimates. The third model improves the accuracy for those with a lower risk of other causes of death, by bringing in an independent data source collected under a complex sampling design with additional other-cause covariates. These analyses represent novel extensions of existing methodology, broadly applicable for the development of prognostic models capturing both the cancer and noncancer aspects of a patient's health.

On the choice of time scales in competing risks predictions.

In the standard analysis of competing risks data, proportional hazards models are fit to the cause-specific hazard functions for all causes on the same time scale. These regression analyses are the foundation for predictions of cause-specific cumulative incidence functions based on combining the estimated cause-specific hazard functions. However, in predictions arising from disease registries, where only subjects with disease enter the database, disease-related mortality may be more naturally modeled on the time since diagnosis time scale while death from other causes may be more naturally modeled on the age time scale. The single time scale methodology may be biased if an incorrect time scale is employed for one of the causes and an alternative methodology is not available. We propose inferences for the cumulative incidence function in which regression models for the cause-specific hazard functions may be specified on different time scales. Using the disease registry data, the analysis of other cause mortality on the age scale requires left truncating the event time at the age of disease diagnosis, complicating the analysis. In addition, standard Martingale theory is not applicable when combining regression models on different time scales. We establish that the covariate conditional predictions are consistent and asymptotically normal using empirical process techniques and propose consistent variance estimators for constructing confidence intervals. Simulation studies show that the proposed two time scales method performs well, outperforming the single time-scale predictions when the time scale is misspecified. The methods are illustrated with stage III colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of National Cancer Institute.

Nonparametric binary instrumental variable analysis of competing risks data.

In both observational studies and randomized trials with noncompliance, unmeasured confounding may exist which may bias treatment effect estimates. Instrumental variables (IV) are a popular technique for addressing such confounding, enabling consistent estimation of causal effects. This paper proposes nonparametric IV estimators for censored time to event data that may be subject to competing risks. A simple, plug-in estimator is introduced using nonparametric estimators of the cumulative incidence function, with confidence intervals derived using asymptotic theory. To provide an overall test of the treatment effect, an integrated weighted difference statistic is suggested, which is applicable to data with and without competing risks. Simulation studies demonstrate that the methods perform well with realistic samples sizes. The methods are applied to assess the effect of infant or maternal antiretroviral therapy on transmission of HIV from mother to child via breastfeeding using data from a large, recently completed randomized trial in Malawi where noncompliance with assigned treatment may confound treatment effect estimates.