Robust covariate-adjusted log-rank statistics and corresponding sample size formula for recurrent events data.
ABSTRACT: Recurrent events data are frequently encountered in clinical trials. This article develops robust covariate-adjusted log-rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula. The proposed log-rank tests are robust with respect to different data-generating processes and are adjusted for predictive covariates. It reduces to the Kong and Slud (1997, Biometrika 84, 847-862) setting in the case of a single event. The sample size formula is derived based on the asymptotic normality of the covariate-adjusted log-rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context. When the effect size is small and the baseline covariates do not contain significant information about event times, it reduces to the same form as that of Schoenfeld (1983, Biometrics 39, 499-503) for cases of a single event or independent event times within a subject. We carry out simulations to study the control of type I error and the comparison of powers between several methods in finite samples. The proposed sample size formula is illustrated using data from an rhDNase study.
Project description:A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.
Project description:The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: [Formula: see text], Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ([Formula: see text]), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is?<?80%, PACS when?>?80% but?<?100%, and SCM when the expected power is 100%.
Project description:In the course of hypertension, cardiovascular disease events (e.g., stroke, heart failure) occur frequently and recurrently. The scientific interest in such study may lie in the estimation of treatment effect while accounting for the correlation among event times. The correlation among recurrent event times come from two sources: subject-specific heterogeneity (e.g., varied lifestyles, genetic variations, and other unmeasurable effects) and event dependence (i.e., event incidences may change the risk of future recurrent events). Moreover, event incidences may change the disease progression so that there may exist event-varying covariate effects (the covariate effects may change after each event) and event effect (the effect of prior events on the future events). In this article, we propose a Bayesian regression model that not only accommodates correlation among recurrent events from both sources, but also explicitly characterizes the event-varying covariate effects and event effect. This model is especially useful in quantifying how the incidences of events change the effects of covariates and risk of future events. We compare the proposed model with several commonly used recurrent event models and apply our model to the motivating lipid-lowering trial (LLT) component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) (ALLHAT-LLT).
Project description:Receptor activator of NF-kB (RANK) pathway regulates bone remodeling and is involved in breast cancer (BC) progression. Genetic polymorphisms affecting RANK-ligand (RANKL) and osteoprotegerin (OPG) have been previously associated with BC risk and bone metastasis (BM)-free survival, respectively. In this study we conducted a retrospective analysis of the association of five missense RANK SNPs with clinical characteristics and outcomes in BC patients with BM. SNP rs34945627 had an allelic frequency of 12.5% in BC patients, compared to 1.2% in the control group (P = 0.005). SNP rs34945627 was not associated with any clinicopathological characteristics, but patients presenting SNP rs34945627 had decreased disease-free survival (DFS) (log-rank P = 0.039, adjusted HR 2.29, 95% CI 1.04-5.08, P = 0.041), and overall survival (OS) (log-rank P = 0.019, adjusted HR 4.32, 95% CI 1.55-12.04, P = 0.005). No differences were observed regarding bone disease-free survival (log-rank P = 0.190, adjusted HR 1.68, 95% CI 0.78-3.66, P = 0.187), time to first skeletal-related event (log-rank P = 0.753, adjusted HR 1.28, 95% CI 1.42-3.84; P = 0.665), or time to bone progression (log-rank P = 0.618, adjusted HR 0.511, 95% CI 0.17-1.51; P = 0.233). Our analysis shows that RANK SNP rs34945627 has a high allelic frequency in patients with BC and BM, and is associated with decreased DFS and OS.
Project description:The comparative effectiveness of percutaneous closure of patent foramen ovale (PFO) plus medical therapy versus medical therapy alone for cryptogenic stroke is uncertain.The authors performed the first pooled analysis of individual participant data from completed randomized trials comparing PFO closure versus medical therapy in patients with cryptogenic stroke.The analysis included data on 2 devices (STARFlex [umbrella occluder] [NMT Medical, Inc., Boston, Massachusetts] and Amplatzer PFO Occluder [disc occluder] [AGA Medical/St. Jude Medical, St. Paul, Minnesota]) evaluated in 3 trials. The primary composite outcome was stroke, transient ischemic attack, or death; the secondary outcome was stroke. We used log-rank tests and unadjusted and covariate-adjusted Cox regression models to compare device closure versus medical therapy.Among 2,303 patients, closure was not significantly associated with the primary composite outcome. The difference became significant after covariate adjustment (hazard ratio [HR]: 0.68; p = 0.049). For the outcome of stroke, all comparisons were statistically significant, with unadjusted and adjusted HRs of 0.58 (p = 0.043) and 0.58 (p = 0.044), respectively. In analyses limited to the 2 disc occluder device trials, the effect of closure was not significant for the composite outcome, but was for the stroke outcome (unadjusted HR: 0.39; p = 0.013). Subgroup analyses did not identify significant heterogeneity of treatment effects. Atrial fibrillation was more common among closure patients.Among patients with PFO and cryptogenic stroke, closure reduced recurrent stroke and had a statistically significant effect on the composite of stroke, transient ischemic attack, and death in adjusted but not unadjusted analyses.
Project description:Time-to-event outcomes with cyclic time-varying covariates are frequently encountered in biomedical studies that involve multiple or repeated administrations of an intervention. In this paper, we propose approaches to generating event times for Cox proportional hazards models with both time-invariant covariates and a continuous cyclic and piecewise time-varying covariate. Values of the latter covariate change over time through cycles of interventions and its relationship with hazard differs before and after a threshold within each cycle. The simulations of data are based on inverting the cumulative hazard function and a log link function for relating the hazard function to the covariates. We consider closed-form derivations with the baseline hazard following the exponential, Weibull, or Gompertz distribution. We propose two simulation approaches: one based on simulating survival data under a single-dose regimen first before data are aggregated over multiple-dosing cycles and another based on simulating survival data directly under a multiple-dose regimen. We consider both fixed intervals and varying intervals of the drug administration schedule. The method's validity is assessed in simulation experiments. The results indicate that the proposed procedures perform well in generating data that conform to their cyclic nature and assumptions of the Cox proportional hazards model.
Project description:Recurrent event data arise frequently in many longitudinal follow-up studies. Hence, evaluating covariate effects on the rates of occurrence of such events is commonly of interest. Examples include repeated hospitalizations, recurrent infections of HIV, and tumor recurrences. In this article, we consider semiparametric regression methods for the occurrence rate function of recurrent events when the covariates may be measured with errors. In contrast to the existing works, in our case the conventional assumption of independent censoring is violated since the recurrent event process is interrupted by some correlated events, which is called informative drop-out. Further, some covariates may be measured with errors. To accommodate for both informative censoring and measurement error, the occurrence of recurrent events is modelled through an unspecified frailty distribution and accompanied with a classical measurement error model. We propose two corrected approaches based on different ideas, and we show that they are numerically identical when estimating the regression parameters. The asymptotic properties of the proposed estimators are established, and the finite sample performance is examined via simulations. The proposed methods are applied to the Nutritional Prevention of Cancer trial for assessing the effect of the plasma selenium treatment on the recurrence of squamous cell carcinoma.
Project description:We implemented six confounding adjustment methods: (1) covariate-adjusted regression, (2) propensity score (PS) regression, (3) PS stratification, (4) PS matching with two calipers, (5) inverse probability weighting and (6) doubly robust estimation to examine the associations between the body mass index (BMI) z-score at 3 years and two separate dichotomous exposure measures: exclusive breastfeeding v. formula only (n=437) and cesarean section v. vaginal delivery (n=1236). Data were drawn from a prospective pre-birth cohort study, Project Viva. The goal is to demonstrate the necessity and usefulness, and approaches for multiple confounding adjustment methods to analyze observational data. Unadjusted (univariate) and covariate-adjusted linear regression associations of breastfeeding with BMI z-score were -0.33 (95% CI -0.53, -0.13) and -0.24 (-0.46, -0.02), respectively. The other approaches resulted in smaller n (204-276) because of poor overlap of covariates, but CIs were of similar width except for inverse probability weighting (75% wider) and PS matching with a wider caliper (76% wider). Point estimates ranged widely, however, from -0.01 to -0.38. For cesarean section, because of better covariate overlap, the covariate-adjusted regression estimate (0.20) was remarkably robust to all adjustment methods, and the widths of the 95% CIs differed less than in the breastfeeding example. Choice of covariate adjustment method can matter. Lack of overlap in covariate structure between exposed and unexposed participants in observational studies can lead to erroneous covariate-adjusted estimates and confidence intervals. We recommend inspecting covariate overlap and using multiple confounding adjustment methods. Similar results bring reassurance. Contradictory results suggest issues with either the data or the analytic method.
Project description:Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.