Illustrating the Impact of a Time-Varying Covariate With an Extended Kaplan-Meier Estimator

The American Statistician (Impact Factor: 0.92). 02/2005; 59(November):301-307. DOI: 10.1198/000313005X70371
Source: RePEc


In clinical endpoint trials, the association between a baseline covariate and the risk of an endpoint is often measured by the hazard ratio as calculated by a Cox regression model, and illustrated by Kaplan-Meier curves comparing cohorts defined by levels of the covariate. The Cox regression model is easily extended to the case of time-varying covariates; however, there is no clear approach for similarly extending the standard Kaplan-Meier estimator. Various ad hoc procedures that have been used in the medical literature are seriously flawed. This article discusses an extended Kaplan-Meier estimator that can be used with time-varying covariates and illustrates this method using data from a long-term clinical trial.

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    • "To illustrate the impact of EPP, we utilised a proportional hazards model fitted to patients classified as good-prognosis according to EORTC prognostic scoring (in brief with two or less of the following characteristics: WBC X8.3 Â 10 9 l À 1 ; ECOGX1; histological diagnosis probable/possible; male gender; non-epithelioid histology) (Curran et al, 1998). Extended Kaplan–Meier estimates (Snapinn et al, 2005) were calculated and plotted. A sensitivity analysis of the effect of EPP was conducted using the landmark analysis (Freedman et al, 1992) for comparison with the time-dependent model results. "
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    ABSTRACT: Background: Although the prognosis of most patients presenting with malignant pleural mesothelioma (MPM) is poor, a small proportion survives long term. We investigated factors associated with survival in a large patient series. Methods: All patients registered with the NSW Dust Diseases Board (2002–2009) were included in an analysis of prognostic factors using Kaplan–Meier and Cox regression analysis. On the basis of these analyses, we developed a risk score (Prognostic Index (PI)). Results: We identified 910 patients: 90% male; histology (epithelioid 60% biphasic 13% sarcomatoid 17%); stage (Tx-I-II 48% III-IV 52%); and calretinin expression (91%). Treatment: chemotherapy(CT) 44%, and extrapleural-pneumonectomy (EPP) 6%. Median overall survival (OS) was 10.0 months. Longer OS was associated with: age <70 (13.5 vs 8.5 months; P<0.001); female gender (12.0 vs 9.9 months; P<0.001); epithelioid subtype (13.3 vs 6.2 months; P<0.001); ECOG status 0 (27.4 vs 9.7 months; P=0.015), calretinin expression (10.9 vs 5.5 months; P<0.001); neutrophil–lymphocyte ratio (NLR) <5 (11.9 vs 7.5 months; P<0.001); platelet count <400 (11.5 vs 7.2 months; P<0.001); and normal haemoglobin (16.4 vs 8.8 months; P<0.001). On time-dependent analysis, patients receiving pemetrexed-based chemotherapy (HR=0.83; P=0.048) or EPP (HR=0.41; P<0.001) had improved survival. Age, gender, histology, calretinin and haematological factors remained significant on multivariate analysis. In all, 24% of patients survived >20 months: 16% of these receiving EPP, and 66% CT. The PI offered improved prognostic discrimination over one of the existing prognostic models (EORTC). Conclusions: We identified calretinin expression, age, gender, histological subtype, platelet count and haemoglobin level as independent prognostic factors. Patients undergoing EPP or pemetrexed-based chemotherapy demonstrated better survival, but 84% and 34% of long survivors, respectively, did not receive radical surgery or chemotherapy.
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    • "The Cox model calculates a hazard ratio associated with noncompliance under the assumption that this hazard ratio is constant over time. In order to explore visually whether or not this assumption is true, we create extended Kaplan-Meier curves that compare endpoint rates for cohorts defined by time-varying covariates [16]. These curves are somewhat difficult to interpret but are consistent with the Cox regression method. "
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    ABSTRACT: Noncompliance with study medications is an important issue in the design of endpoint clinical trials. Including noncompliant patient data in an intention-to-treat analysis could seriously decrease study power. Standard methods for calculating sample size account for noncompliance, but all assume that noncompliance is noninformative, i.e., that the risk of discontinuation is independent of the risk of experiencing a study endpoint. Using data from several published clinical trials (OPTIMAAL, LIFE, RENAAL, SOLVD-Prevention and SOLVD-Treatment), we demonstrate that this assumption is often untrue, and we discuss the effect of informative noncompliance on power and sample size.
    Preview · Article · Aug 2004 · Current controlled trials in cardiovascular medicine
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    ABSTRACT: Taking advantage of the proximity between Temple's Statistics Department and many large pharmaceutical companies, a number of successful professional relationships developed and grew. A special partnership was formed between Temple's Biostatistics Research Center and Merck's Research Laboratories. This led to a number of summer graduate student internships that resulted in the identification of interesting dissertation topics and numerous award winning Ph.D. dissertations, most leading to successful publication in statistics journals. It also led to the creation of the very successful annual Merck- Temple Conferences, the 12th having been run in October 2004. These conferences attracted leading statisticians as speakers and were well attended. We feel that such partnerships will be of increased importance in the future due to the increasing complexity of drug and vaccine development requiring collaboration in development and application of novel experimental designs and methods of analysis. We will provide an overview of this successful partnership and illustrate, with cases, the mutual benefits of this professional relationship.
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