Application of a sequential multiple assignment randomized trial (SMART) design in older patients with chronic lymphocytic leukemia.

BACKGROUND: Ibrutinib therapy is safe and effective in patients with chronic lymphocytic leukemia (CLL). Currently, ibrutinib is administered continuously until disease progression. Combination regimens with ibrutinib are being developed to deepen response which could allow for ibrutinib maintenance (IM) discontinuation. Among untreated older patients with CLL, clinical investigators had the following questions: (i) does ibrutinib + venetoclax + obinutuzumab (IVO) with IM have superior progression-free survival (PFS) compared with ibrutinib + obinutuzumab (IO) with IM, and (ii) does the treatment strategy of IVO + IM for patients without minimal residual disease complete response (MRD- CR) or IVO + IM discontinuation for patients with MRD- CR have superior PFS compared with IO + IM. DESIGN: Conventional designs randomize patients to IO with IM or IVO with IM to address the first objective, or randomize patients to each treatment strategy to address the second objective. A sequential multiple assignment randomized trial (SMART) design and analysis is proposed to address both objectives. RESULTS: A SMART design strategy is appropriate when comparing adaptive interventions, which are defined by an individual's sequence of treatment decisions and guided by intermediate outcomes, such as response to therapy. A review of common applications of SMART design strategies is provided. Specific to the SMART design previously considered for Alliance study A041702, the general structure of the SMART is presented, an approach to sample size and power calculations when comparing adaptive interventions embedded in the SMART with a time-to-event end point is fully described, and analyses plans are outlined. CONCLUSION: SMART design strategies can be used in cancer clinical trials with adaptive interventions to identify optimal treatment strategies. Further, standard software exists to provide sample size, power calculations, and data analysis for a SMART design.

Epidemiologic study of drinking water chlorination and Wisconsin female cancer mortality.

The association between gastrointestinal, urinary tract, brain, lung, and breast cancer mortality and drinking water trihalomethane exposure, as estimated by average daily chlorine dosage of water source 20 years past, was investigated for Wisconsin white females by use of a death certificate-based case-control study design. A total of 8,029 cancer deaths and 8,029 controls (noncancer deaths) matched on county of residence, year of death, and age were taken from mortality records of 28 counties for the years 1972-77. Data on characteristics and treatment of municipal water supplied to the residences of cases and controls were obtained from questionnaires sent to the water superintendents of the 202 waterworks associated with the sample. By the use of logistic regression analysis, odds ratios for site-specific cancer death associated with high, medium, and low chlorine-dosed water as compared to unchlorinated water exposure were determined; the control variables were urbanicity, marital status, and occupation. With the exception of cancer of the colon, no anatomic cancer site was significantly associated with any chlorine dose exposure category. For colon cancer, odds ratios of 1.51 [95% confidence interval (Cl) = 1.06-2.14], 1.53 (95% Cl=1.08-2.00, and 1.53 (95% Cl-1.11-2.11) were obtained for high-, medium-, and low-dose chlorination, respectively (P less than or equal to 0.02). For colon cancer cases and controls exposed to water sources affected by rural runoff, odds ratios of 3.30 (95% Cl=1.45-7.47), 3.60 (95% Cl=1.57-8.26), and 2.74 (95% Cl=1.10-6.88) were observed for high, medium, and low chlorine dosages 20 years past (P less than or equal to 0.025).

Cytogenetic features of human neuroblastomas and cell lines.

We reviewed the banded karyotypes of 24 human neuroblastomas and cell lines to identify any consistent chromosomal abnormalities. Six of the 10 primary tumors and one of the 14 cell lines were studied at this institution. Of the 24 neuroblastomas karyotyped, 20 were near-diploid, one was near-triploid, and 3 were near-tetraploid. One primary tumor had a diploid karyotype without numerical or structural rearrangements. The 20 cases with a karyotype in the diploid range were statistically analyzed for gain or loss of while chromosomes and for structural abnormalities of each chromosome arm. The short arm of chromosome 1 was preferentially involved in structural rearrangements, occurring in 14 cases (p less than 0.01). In 11 of these cases, the abnormality of chromosome 1 included deletion of bands 1p32 leads to 1pter, rendering the cells monosomic for this genetic material. Of the remaining three cases, one involved a reciprocal translocation of chromosomes 1p and 12q, another had insertion of genetic material at band 1p13, and the third had an extra dark band at 1p36. No other numerical or structural abnormalities occurred with sufficient frequency to reach statistical significance (p greater than 0.20). Six of the primary tumors or cell lines in the diploid range had double minute chromatin bodies, four cell lines had homogeneously staining regions, and two cell lines had either double minute chromatin bodies or homogeneously staining regions in subpopulations of cells. Hence, partial monosomy for the short arm of chromosome 1 was the most consistent cytogenetic abnormality in the human neuroblastomas studied.

Cost-effectiveness of platelet glycoprotein IIb/IIIa inhibition with eptifibatide in patients with non-ST-elevation acute coronary syndromes.

BACKGROUND: In the PURSUIT trial, eptifibatide significantly reduced the 30-day incidence of death and myocardial infarction relative to placebo in 9461 patients with an acute coronary syndrome (unstable angina or non-Q-wave myocardial infarction). METHODS AND RESULTS: We conducted a 2-part prospective economic substudy of the 3522 US patients enrolled in PURSUIT: (1) an empirical intention-to-treat comparison of medical costs (hospital plus physician) up to 6 months after hospitalization and (2) a lifetime cost-effectiveness analysis. The base-case cost-effectiveness ratio was expressed as the 1996 US dollars required to add 1 life-year with eptifibatide therapy. The 2 treatment arms had equivalent resource consumption and medical costs (exclusive of the cost of the eptifibatide regimen) during the index (enrollment) hospitalization (P=0.78) and up to 6 months afterward (P=0.60). The average wholesale price of the eptifibatide regimen was $1217, but a typical hospital discounted price was $1014. The estimated life expectancy from randomization in the US patients was 15.96 years for eptifibatide and 15.85 years for placebo, an incremental difference of 0.111. The incremental cost-effectiveness ratio for eptifibatide therapy in US PURSUIT patients was $16 491 per year of life saved. This result was robust through a wide range of sensitivity analyses. The cost-utility ratio for eptifibatide (using time trade-off defined utilities) was $19 693 per added quality-adjusted life-year. CONCLUSIONS: Based on the results observed in the US PURSUIT patients, the routine addition of eptifibatide to standard care for non-ST-elevation acute coronary syndrome patients is economically attractive by conventional standards.

Statistical analysis of cytogenetic abnormalities in human cancer cells.

It is sometimes difficult to evaluate reports of "nonrandom" chromosome involvement in certain malignant diseases, since the "random" or expected distribution is seldom defined. Therefore, we have developed methods for the statistical analysis of cytogenetic abnormalities in human cancer cells with modal karyotypes in the diploid range (35-57 chromosomes). For this analysis, it is assumed that the expected gain or loss of each chromosome will occur with equal probability and structural abnormalities will involve each chromosome in proportion to its size. To perform this analysis, the total number of numerical and structural abnormalities is determined from the modal karyotypes of a series of histologically related tumors. The maximum expected values are determined by computer simulation for different levels of significance. Then the distributions of observed and expected abnormalities of each type are compared to identify nonrandom involvement. Preferential gain or loss is analyzed for each of the 24 different chromosomes, and preferential structural rearrangement is determined for each of the 48 chromosome arms. We have analyzed two series of karyotypic data to demonstrate the utility of this method. The rationale for the assumptions made as well as alternative approaches are discussed.

m-AMSA in refractory lymphoma. A phase II trial of the Eastern Cooperative Oncology Group.

m-AMSA (4'-[9'-acridinylamino]-methansulfon-m-anisidide) is an acridine derivative which has shown a wide spectrum of activity in preclinical testing. The mechanism of action is thought to be via interference with synthesis and integrity of DNA chains by intercalation between base pairs and external binding. Initial phase I clinical trials revealed granulocytopenia to be the dose limiting toxicity with occasional thrombocytopenia. Phlebitis, liver function abnormalities, and cardiac abnormalities have also been noted. Early reports suggested activity in leukemia and lymphoma. Based on these results ECOG evaluated m-AMSA in a phase II trial of Hodgkin's disease and non-Hodgkin's lymphoma.

Testing for differences in survival with delayed ascertainment.

During the interim stages of most large-scale clinical trials, knowledge that a patient is alive or dead is usually not up-to-date. This is due to the pattern of patient visits to hospitals as well as the administrative set-up used by the study to obtain information on vital status. On a two-armed study, if the process of ascertaining vital status is not the same in both treatment groups, then the standard method of testing based on the logrank statistic may not be applicable. Instead, an ad hoc modification to the logrank test, which artificially truncates follow-up prior to the time of analysis, is often used. These approaches have not been formally addressed in the literature. In the early stages of a clinical trial, severe bias or loss of power may result. For this situation, we propose a class of test statistics that extends the usual class of U statistics. Asymptotic normality is derived by reformulating the statistics in terms of counting processes and employing the theory of U statistics along with martingale techniques. For early interim analyses, a numerical study indicates that the new tests can be more powerful than the current practice when differential ascertainment is present. To illustrate the potential loss of information when lagging follow-up to control for ascertainment delays, we reanalyze an AIDS clinical trial with the truncated logrank and the new statistics.

Sequential methods for comparing years of life saved in the two-sample censored data problem.

This research develops nonparametric strategies for sequentially monitoring clinical trial data where detecting years of life saved is of interest. The recommended test statistic looks at integrated differences in survival estimates during the time frame of interest. In many practical situations, the test statistic presented has an independent increments covariance structure. Hence, with little additional work, we may apply these testing procedures using available methodology. In the case where an independent increments covariance structure is present, we suggest how clinical trial data might be monitored using these statistics in an information-based design. The resulting study design maintains the desired stochastic operating characteristics regardless of the shapes of the survival curves being compared. This offers an advantage over the popular log-rank-based design strategy since more restrictive assumptions relating to the behavior of the hazards are required to guarantee the planned power of the test. Recommendations for how to sequentially monitor clinical trial progress in the nonindependent increments case are also provided along with an example.

Efficient estimation of the distribution of quality-adjusted survival time.

Quality of life is an important aspect in evaluation of clinical trials of chronic diseases, such as cancer and AIDS. Quality-adjusted survival analysis is a method that combines both the quantity and quality of a patient's life into one single measure. In this paper, we discuss the efficiency of weighted estimators for the distribution of quality-adjusted survival time. Using the general representation theorem for missing data processes, we are able to derive an estimator that is more efficient than the one proposed in Zhao and Tsiatis (1997, Biometrika 84, 339-348). Simulation experiments are conducted to assess the small sample properties of this estimator and to compare it with the semiparametric efficiency bound. The value of this estimator is demonstrated from an application of the method to a data set obtained from a breast cancer clinical trial.

Evaluating surrogate markers of clinical outcome when measured with error.

In most clinical trials, markers are measured periodically with error. In the presence of measurement error, the naive method of using the observed marker values in the Cox model to evaluate the relationship between the marker and clinical outcome can produce biased estimates and lead to incorrect conclusions when evaluating a potential surrogate. We propose a two-stage approach to account for the measurement error and reduce the bias of the estimate. In the first stage, an empirical Bayes estimate of the time-dependent covariate is computed at each event time. In the second stage, these estimates are imputed in the Cox proportional hazards model to estimate the regression parameter of interest. We demonstrate through extensive simulations that this methodology reduces the bias of the regression estimate and correctly identifies good surrogate markers more often than the naive approach. An application evaluating CD4 count as a surrogate of disease progression in an AIDS clinical trial is presented.

Nonparametric survival estimation using prognostic longitudinal covariates.

One of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right-censored data. This research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual. We begin by defining a survival estimate which uses time-dependent covariates to more precisely get at the underlying survival curves in the presence of censoring. This estimate has a smaller asymptotic variance than the usual Kaplan-Meier in the presence of censoring and reduces to the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) in situations where the covariate is not prognostic or no censoring occurs. In addition, this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information. Because the Kaplan-Meier estimate is known to be biased in this situation due to informative censoring, we recommend use of our estimate.

Study duration for clinical trials with survival response and early stopping rule.

A comparative clinical trial with built-in sequential stopping rules allows earlier-than-scheduled stopping, should there be a significant indication of treatment difference. In a clinical trial where the major outcome is time (survival time or response) to a certain event such as failure, the design of the study should determine how long one needs to accrue patients and follow through until there is a sufficient number of events observed during the entire study duration. This paper proposes a unified design procedure for group sequential clinical trials with survival response. The time to event is assumed to be exponentially distributed, but the arguments extend naturally to the proportional hazards model after suitable transformation on the time scale. An example from the Eastern Cooperative Oncology Group (ECOG) is given to illustrate how this procedure can be implemented. The same example is used to explore the overall operating characteristics and the robustness of the proposed group sequential design.

Testing equality of survival functions of quality-adjusted lifetime.

We present a method for comparing the survival functions of quality-adjusted lifetime from two treatments. This test statistic becomes the ordinary log-rank test when quality-adjusted lifetime is the same as the survival time. Simulation experiments are conducted to examine the behavior of our proposed test statistic under both null and alternative hypotheses. In addition, we apply our method to a breast cancer trial for comparing the distribution of quality-adjusted lifetime between two treatment regimes.

Using auxiliary time-dependent covariates to recover information in nonparametric testing with censored data.

Murray and Tsiatis (1996) described a weighted survival estimate that incorporates prognostic time-dependent covariate information to increase the efficiency of estimation. We propose a test statistic based on the statistic of Pepe and Fleming (1989, 1991) that incorporates these weighted survival estimates. As in Pepe and Fleming, the test is an integrated weighted difference of two estimated survival curves. This test has been shown to be effective at detecting survival differences in crossing hazards settings where the logrank test performs poorly. This method uses stratified longitudinal covariate information to get more precise estimates of the underlying survival curves when there is censored information and this leads to more powerful tests. Another important feature of the test is that it remains valid when informative censoring is captured by the incorporated covariate. In this case, the Pepe-Fleming statistic is known to be biased and should not be used. These methods could be useful in clinical trials with heavy censoring that include collection over time of covariates, such as laboratory measurements, that are prognostic of subsequent survival or capture information related to censoring.

The use of simulation and bootstrap in information-based group sequential studies.

In this paper, we present an information-based design and monitoring procedure which applies to any type of model for any type of group sequential study provided there is a unique parameter of interest one can estimate efficiently. Simulation techniques are described to handle the design phase of this procedure. Since designs depend on potentially unreliable guesses of nuisance parameters, we propose a bootstrap method that uses the information available at the interim analysis times to generate projections and prediction intervals for the time at which the study will be fully powered. A monitoring board can use this information to decide whether a redesign of the trial is warranted. We also show how to use simulation to redesign studies in progress. We illustrate all of these techniques with data from AIDS Clinical Trial Group Protocol 021.

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.

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.

Causal inference on the difference of the restricted mean lifetime between two groups.

When comparing survival times between two treatment groups, it may be more appropriate to compare the restricted mean lifetime, i.e., the expectation of lifetime restricted to a time L, rather than mean lifetime in order to accommodate censoring. When the treatments are not assigned to patients randomly, as in observational studies, we also need to account for treatment imbalances in confounding factors. In this article, we propose estimators for the difference of the restricted mean lifetime between two groups that account for treatment imbalances in prognostic factors assuming a proportional hazards relationship. Large-sample properties of our estimators based on martingale theory for counting processes are also derived. Simulation studies were conducted to compare these estimators and to assess the adequacy of the large-sample approximations. Our methods are also applied to an observational database of acute coronary syndrome patients from Duke University Medical Center to estimate the treatment effect on the restricted mean lifetime over 5 years.

Multiple imputation methods for estimating regression coefficients in the competing risks model with missing cause of failure.

We propose a method to estimate the regression coefficients in a competing risks model where the cause-specific hazard for the cause of interest is related to covariates through a proportional hazards relationship and when cause of failure is missing for some individuals. We use multiple imputation procedures to impute missing cause of failure, where the probability that a missing cause is the cause of interest may depend on auxiliary covariates, and combine the maximum partial likelihood estimators computed from several imputed data sets into an estimator that is consistent and asymptotically normal. A consistent estimator for the asymptotic variance is also derived. Simulation results suggest the relevance of the theory in finite samples. Results are also illustrated with data from a breast cancer study.

Utilizing propensity scores to estimate causal treatment effects with censored time-lagged data.

Observational studies frequently are conducted to compare long-term effects of treatments. Without randomization, patients receiving one treatment are not guaranteed to be prognostically comparable to those receiving another treatment. Furthermore, the response of interest may be right-censored because of incomplete follow-up. Statistical methods that do not account for censoring and confounding may lead to biased estimates. This article presents a method for estimating treatment effects in nonrandomized studies with right-censored responses. We review the assumptions required to estimate average causal effects and derive an estimator for comparing two treatments by applying inverse weights to the complete cases. The weights are determined according to the estimated probability of receiving treatment conditional on covariates and the estimated treatment-specific censoring distribution. By utilizing martingale representations, the estimator is shown to be asymptotically normal and an estimator for the asymptotic variance is derived. Simulation results are presented to evaluate the properties of the estimator. These methods are applied to an observational data set of acute coronary syndrome patients from Duke University Medical Center to estimate the effect of a treatment strategy on the mean 5-year medical cost.