K. K. Gordon Lan

An aid to data monitoring in long-term clinical trials

Abstract In data monitoring of long-term clinical trials, it is routine to consider the question of whether a trial should be terminated before its scheduled end. Termination may seem reasonable either because it appears that the null hypothesis (H0) is likely to be disproved at the end of the trial or, even under optimistic assumptions, it is quite unlikely to be disproved. This idea has recently been formalized and characterized (with respect to Type 1 and Type 2 error) by Lan, Simon, and Halperin [Comm Stat in press]; their results provide a quantitative rationale for using as a monitoring tool, the conditional probability given current results and particular hypotheses that the treatment group will be superior (in the statistical sense) at the designed end of the trial. If the conditional probability under H0 is sufficiently high, rejection of H0 is indicated; if the conditional probability under Ha is sufficiently low, acceptance of H0 is indicated. Details of the implementation of this idea are considered for the case where the outcome variable is dichotomous and the statistic comparing the two groups at the trials end is simply the standardized observed difference in proportions of events. The case of simultaneous entry and no competing risk is considered in detail with subsequent discussion of the alterations required if staggered entry and/or competing risk are relevant; simplifications which are possible in the case of staggered entry are described. Unsurprisingly, our results depend on assumptions made about further experience. Possible approaches to the extrapolation problem thus created are briefly described.

Computations for Group Sequential Boundaries Using the Lan-DeMets Spending Function Method

We describe an interactive Fortran program which performs computations related to the design and analysis of group sequential clinical trials using Lan-DeMets spending functions. Many clinical trials include interim analyses of accumulating data and rely on group sequential methods to avoid consequent inflation of the type I error rate. The computations are appropriate for interim test statistics whose distribution or limiting distribution is multivariate normal with independent increments. Recent theoretical results indicate that virtually any design likely to be used in a clinical trial will fall into this category. Interim analyses need not be equally spaced, and their number need not be specified in advance. In addition to determining sequential boundaries using an alpha spending function, the program can perform power computations, compute probabilities associated with a given set of boundaries, and generate confidence intervals.

Statistical aspects of early termination in the beta-blocker heart attack trial

Abstract The Beta-Blocker Heart Attack Trial was a randomized double blind controlledtrial comparing propranolol with placebo in 3837 patients with a recent myocardial infarction. The trial was terminated on recommendation of the Policy and Data Monitoring Board 9 months before the scheduled closing date. The propranolol group, at the time of the decision, had a 26% lower mortality (z = 2.82). Many issues were considered in this decision. These included the magnitude of the overall results; consistency of results across subgroups, clinical centers, and cause of death; and completeness of follow-up. Two basic statistical methods were used in declaring the overall mortality results significant. The first method evaluated the current survival data taking into account the issue of repeated significance testing. The second method evaluated whether the observed trend was so impressive that the conclusion was unlikely to change even if the trial should continue to the scheduled end. These two methods, as well as other considerations led to the recommendation to discontinue the trial.

Changing Frequency of Interim Analysis in Sequential Monitoring

In clinical trial data monitoring, one can either introduce a discrete sequential boundary for a set of specified decision times or adopt a use function and then derive the boundary when data are monitored. If the use function approach is employed, one can adjust the frequency of data monitoring as long as the decision is not data-dependent. However, if the frequency of future data monitoring is affected by the observed data, then the probability of Type I error will no longer be preserved exactly. But the effect on the significance level and power is very small, perhaps negligible, as indicated by simulation results.

More flexible sequential and non-sequential designs in long-term clinical trial

In this paper, we describe decision making procedures as they exist in most clinical trials,review some recently suggested approaches to monitoring and clarify how these methods allow greater flexibility in monitoring and explicit specification of data monitoring methods in the protocol.

Information and information fractions for design and sequential monitoring of clinical trials

The use of information in sequential monitoring of clinical trials is described. Technically defined as the inverse of the variance of some estimate, the information in a trial depends on the type of data collected on the patients. We examine three common situations: comparison of two means, comparison of two survival curves, and comparison of two populations slopes from repeated measures data. In each case we discuss how to proceed when the information available at the planned end of the trial, the total information, is unknown. The amount of information at a given interim analysis divided by the total information is the information fraction. Some natural estimates of the information fraction and their relationships to calender time are presented. The concept of total information can also be useful for the design of trials collecting repeated measures data.

Monitoring boundaries for adverse effects in long-term clinical trials

The typical long-term trial has a data monitoring committee. A primary responsibility of this committee is maintenance of patient safety. In this role, this committee is likely to recommend stopping a trial when a new treatment appears worse than the control even when the difference is not statistically significant or if it appears that the new treatment will not be clearly beneficial. Several approaches, including the use of conditional power, can be used to help the monitoring committee decide if a study should be stopped early because of a harmful or insufficiently effective treatment. These monitoring approaches have altered the way in which we view one-sided or two-sided tests of significance.

Conditional Bias of Point Estimates Following a Group Sequential Test

Abstract Repeated significance testing in a sequential experiment not only increases the overall type I error rate of the false positive conclusion but also causes biases in estimating the unknown parameter. In general, the test statistics in a sequential trial can be properly approximated by a Brownian motion with a drift parameter at interim looks. The unadjusted maximum likelihood estimator can be potentially very biased due to the possible early stopping rule at any interim. In this paper, we investigate the conditional and marginal biases with focus on the conditional one upon the stopping time in estimating the Brownian motion drift parameter. It is found that the conditional bias may be very serious for existing point estimation methods, even if the unconditional bias is satisfactory. New conditional estimators are thus proposed, which can significantly reduce the conditional bias from unconditional estimators. The results of Monte-Carlo studies show that the proposed estimators can provide a much smaller conditional bias and MSE than the naive MLE and a Whitebeads bias reduced estimator.

Monitoring mortality at interim analyses while testing a composite endpoint at the final analysis

Mortality is often used as the clinical endpoint in clinical trials for acute diseases and takes precedence over any other outcome. A composite outcome such as death plus disease occurrence (or recurrence) or death plus hospitalization may also be considered, sometimes even as the primary outcome due to practical sample size issues. That is, a composite endpoint should have a higher event rate and thus a smaller sample size than for mortality alone to reach the same power. Two different scenarios are considered: in Scenario 1, the composite outcome is the primary endpoint and the mortality outcome is secondary; in Scenario 2, the mortality outcome is the primary endpoint and the composite outcome is secondary. In either scenario, the trial will be stopped if the simple mortality outcome shows an adverse effect or a significant benefit at an interim analysis, while the composite outcome will be tested at the final analysis if the mortality outcomes fails to show significance. These scenarios are typical in many trials sponsored by industry for regulatory approval. We refer to them as a switching the primary endpoint process. Two switching-endpoint procedures are proposed to calculate the efficacy boundary for the composite test statistic at the final analysis. The Bonferroni method is used in Method 1. In Method 2, the calculation is based upon the joint distribution of the test statistics for the simple mortality and the composite outcomes. A completed clinical trial, prospective randomized amlodipine survival evaluation (PRAISE-1), is used to illustrate the two switching-endpoint procedures. A simulation study shows that the two switching-endpoint procedures allow a trial to be stopped early due to a clinically relevant benefit in the mortality while preserving the overall alpha level.

Grouping and linear regression

With a large number of observations, the method of grouping is often employed to provide simpler graphs or tables. When one investigates the relationship between two variables, one usually groups based on the magnitude of the independent variable, and then plots the dependent variable averages against independent variable averages to get a clearer graph. If grouping is based on the magnitude of the dependent variable, the plot of group means as indicated above does not appropriately describe the relationship of the dependent variable to the independent variable. These results are demonstrated theoretically for the special case of bivariate normality (and thus linear regression), but would be expected to be similar for other distribution assumptions. An example is given from an epidemiological study.