Anastasios A. Tsiatis

A JOINT MODEL FOR SURVIVAL AND LONGITUDINAL DATA MEASURED WITH ERROR

The relationship between a longitudinal covariate and a failure time process can be assessed using the Cox proportional hazards regression model. We consider the problem of estimating the parameters in the Cox model when the longitudinal covariate is measured infrequently and with measurement error. We assume a repeated measures random effects model for the covariate process. Estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process. This approach uses the available information optimally because we use both the covariate and survival data simultaneously. Parameters are estimated using the expectation-maximization algorithm. We argue that such a method is superior to naive methods where one maximizes the partial likelihood of the Cox model using the observed covariate values. It also improves on two-stage methods where, in the first stage, empirical Bayes estimates of the covariate process are computed and then used as time-dependent covariates in a second stage to find the parameters in the Cox model that maximize the partial likelihood.

The analysis of multiple endpoints in clinical trials

Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.

Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS

Abstract A question that has received a great deal of attention in evaluating new treatments in acquired immune deficiency syndrome (AIDS) clinical trials is that of finding a good surrogate marker for clinical progression. The identification of such a marker may be useful in assessing the efficacy of new therapies in a shorter period. The number of CD4-lymphocyte counts has been proposed as such a potential marker for human immune virus (HIV) trials because of its observed correlation with clinical outcome. But to evaluate the role of CD4 counts as a potential surrogate marker, we must better understand the relationship of clinical outcome to an individuals CD4 count history over time. The Cox proportional hazards regression model is used to study the relationship between CD4 counts as a time-dependent covariate and survival. Because the CD4 counts are measured only periodically and with substantial measurement error and biological variation, standard methods for estimating the parameters in the Cox mod...

Exact significance testing to establish treatment equivalence with ordered categorical data.

This communication concerns the problem of establishing the therapeutic equivalence of two treatments that are being compared on the basis of ordered categorical data. The problem is formulated as a significance test in which the null hypothesis specifies a treatment difference. An efficient numerical algorithm for computing the exact significance level is provided, along with a simple method for obtaining the asymptotic significance level. Both methods are applied to a clinical trial of a new agent versus an active control. Guidelines for when to use the exact procedure and when to rely on asymptotic theory are provided.

A randomized controlled trial of a reduced daily dose of zidovudine in patients with the acquired immunodeficiency syndrome

Abstract Background. The initially tested dose of zidovudine for the treatment of patients with advanced disease caused by the human immunodeficiency virus type 1 (HIV) was 1500 mg. Although this dose is effective, it is associated with substantial toxicity. Methods. To evaluate the efficacy and safety of a reduced dose, we conducted a randomized controlled trial in 524 subjects who had had a first episode of Pneumocystis carinii pneumonia. The subjects were assigned to receive zidovudine in either a dose of 250 mg taken orally every four hours (the standard-treatment group, n = 262) or a dose of 200 mg taken orally every four hours for four weeks and thereafter 100 mg taken every four hours (the low-dose group, n = 262). Results. The median length of follow-up was 25.6 months. At 18 months the estimated survival rates were 52 percent for the standard-treatment group and 63 percent for the low-dose group (P = 0.012 by the log-rank test). At 24 months the estimated survival rates were 27 percent for the st...

Approximately Optimal One-Parameter Boundaries for Group Sequential Trials

We present a class of group sequential tests, indexed by a single parameter, that yields approximately optimal results. We also provide tables of key values to help in the design of group sequential tests that meet selected specifications.

Correcting for non-compliance in randomized trials using rank preserving structural failure time models

We propose correcting for non-compliance in randomized trials by estimating the parameters of a class of semi-parametric failure time models, the rank preserving structural failure time models, using a class of rank estimators. These models are the structural or strong version of the “accelerated failure time model with time-dependent covariates” of Cox and Oakes (1984). In this paper we develop a large sample theory for these estimators, derive the optimal estimator within this class, and briefly consider the construction of “partially adaptive” estimators whose efficiency may approach that of the optimal estimator. We show that in the absence of censoring the optimal estimator attains the semiparametric efficiency bound for the model.

Cost-Effectiveness of Defibrillator Therapy or Amiodarone in Chronic Stable Heart Failure: Results From the Sudden Cardiac Death in Heart Failure Trial (SCD-HeFT)

Background— In the Sudden Cardiac Death in Heart Failure Trial (SCD-HeFT), implantable cardioverter-defibrillator (ICD) therapy significantly reduced all-cause mortality rates compared with medical therapy alone in patients with stable, moderately symptomatic heart failure, whereas amiodarone had no benefit on mortality rates. We examined long-term economic implications of these results. Methods and Results— Medical costs were estimated by using hospital billing data and the Medicare Fee Schedule. Our base case cost-effectiveness analysis used empirical clinical and cost data to estimate the lifetime incremental cost of saving an extra life-year with ICD therapy relative to medical therapy alone. At 5 years, the amiodarone arm had a survival rate equivalent to that of the placebo arm and higher costs than the placebo arm. For ICD relative to medical therapy alone, the base case lifetime cost-effectiveness and cost-utility ratios (discounted at 3%) were

Quality of Life with Defibrillator Therapy or Amiodarone in Heart Failure

38 389 per life-year saved (LYS) and

Exact confidence intervals following a group sequential test.

41 530 per quality-adjusted LYS, respectively. A cost-effectiveness ratio <