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K K Lan

Publications and source records attributed to K K Lan.

At least 19 recordsLinked to original sources
PubMed1995

Sequential monitoring of survival data with the Wilcoxon statistic.

When a spending function is used in sequential data monitoring of a clinical trial, it is important to know the information fraction at the times of interim analysis. In a maximum duration designed study, the information fraction is unknown when data are monitored, and it has to be estimated. The modified Wilcoxon statistic developed by Peto and Peto and modified by Prentice is often used to compare two survival curves in a clinical trial. We give guidelines for estimating the information fraction in a maximum duration trial when this statistic is employed. When there is a relatively low event rate or the survival time is approximately exponential, the information fraction for the Peto-Peto-Prentice Wilcoxon statistic is very close to that of the popular logrank statistic. In other cases, it would be helpful to estimate the information fraction as a function of elapsed calendar time. We discuss both group sequential and continuous monitoring.

Biometry↗
PubMed1994

Use of surrogate information time for monitoring the effect of treatment on the change in a response variable in clinical trials.

We discuss the monitoring of clinical trials data and propose two surrogates for total information for use with the spending function approach where there are repeated measurements and we wish to compare the rates of change in a response variable under different treatments. These surrogates are applied to a setting similar to the Lung Health Study. Although the surrogates do not require estimation of the variance parameters, they do require some knowledge of the ratio R of the within- to the between-individual variances. The effects of overestimating and underestimating R are illustrated. In situations of uncertainty we recommend overestimating R, to provide a conservative estimate of information time at each interim analysis.

Adult↗
PubMed1993

Use of spending functions for occasional or continuous monitoring of data in clinical trials.

In many clinical trials, data are monitored periodically by an external data monitoring committee (DMC). Usually the frequency of these interim 'looks' at the data is prespecified. However, the progress of a clinical trial is unpredictable; often the schedule of looks must be modified. The Lan-DeMets procedure provides a spending function approach which does not require prespecification of the frequency or timing of interim looks. The procedure was developed based on the principle of a continuous Brownian motion process. In this paper we employ more elementary concepts to describe a procedure which is based upon the continuous monitoring of emerging data. The approach is flexible in that it applies to both continuous data monitoring and occasional interim monitoring. Examples are given from real clinical trials.

Bias↗
PubMed1993

Sequential monitoring of clinical trials: the role of information and Brownian motion.

Sequential monitoring has been a topic of major interest in clinical trials methodology over the past two decades. This paper presents a unified conceptual framework for sequential monitoring that covers a wide variety of monitoring procedures in a wide variety of clinical trial settings. The central elements of this framework consist of a suitable concept of statistical information and a scheme for using this concept as a basis for summarizing the accumulating results of a trial in a standardized form, through a stochastic process that can be shown to approximate classical Brownian motion. The ideas are developed in a simple step-by-step fashion and illustrated by several practical examples.

Biophysical Phenomena↗
PubMed1992

A comparison of sample size methods for the logrank statistic.

Several methods are available for sample size calculation for clinical trials when survival curves are to be compared using the logrank statistic. We discuss advantages and disadvantages of some of these methods, and present simulation results under exponential, proportional hazards and non-proportional hazard situations.

Clinical Trials as Topic↗
PubMed1992

Sequential monitoring for comparison of changes in a response variable in clinical studies.

The spending function approach proposed by Lan and DeMets (1983, Biometrika 70, 659-663) for sequential monitoring of clinical trials is applied to situations where comparison of changes in a continuous response variable between two groups is the primary concern. Death, loss to follow-up, and missed visits could cause follow-up measurements to be right-censored or missing for some participants. Furthermore, the probability of being censored may be dependent on the parameter value of the response variable (informative censoring). We propose to compare treatment effects by comparing areas under the expected response change curves between the two groups. When the response curves are linear as a function of time in both groups, this comparison is equivalent to comparing the rates of change in the response variable. Covariances of the sequential test statistics are derived. Conditions for having independent increments are presented. For studies designed to evaluate long-term treatment effects, spending functions obtained by shifting the usual spending functions (Kim and DeMets, 1987, Biometrika 74, 149-154) to the right and then rescaling to the remaining interval are also proposed. Such a shifted spending function is applied to the monitoring plan for the Lung Health Study (Anthonisen, 1989, American Review of Respiratory Diseases 140, 871-872).

Adult↗
PubMed1990

Implementation of group sequential logrank tests in a maximum duration trial.

To control the Type I error probability in a group sequential procedure using the logrank test, it is important to know the information times (fractions) at the times of interim analyses conducted for purposes of data monitoring. For the logrank test, the information time at an interim analysis is the fraction of the total number of events to be accrued in the entire trial. In a maximum information trial design, the trial is concluded when a prespecified total number of events has been accrued. For such a design, therefore, the information time at each interim analysis is known. However, many trials are designed to accrue data over a fixed duration of follow-up on a specified number of patients. This is termed a maximum duration trial design. Under such a design, the total number of events to be accrued is unknown at the time of an interim analysis. For a maximum duration trial design, therefore, these information times need to be estimated. A common practice is to assume that a fixed fraction of information will be accrued between any two consecutive interim analyses, and then employ a Pocock or O'Brien-Fleming boundary. In this article, we describe an estimate of the information time based on the fraction of total patient exposure, which tends to be slightly negatively biased (i.e., conservative) if survival is exponentially distributed. We then present a numerical exploration of the robustness of this estimate when nonexponential survival applies. We also show that the Lan-DeMets (1983, Biometrika 70, 659-663) procedure for constructing group sequential boundaries with the desired level of Type I error control can be computed using the estimated information fraction, even though it may be biased. Finally, we discuss the implications of employing a biased estimate of study information for a group sequential procedure.

Biometry↗
PubMed1989

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.

Biometry↗
PubMed1988

The B-value: a tool for monitoring data.

This paper considers the problem of monitoring slowly accruing data from a nonsequentially designed experiment. We describe the use of the B-value, which is a transformed Z-value, for the calculation of conditional power. In data monitoring, interim Z-values do not allow simple projections to the end of the study. Moreover, because of their popular association with P-values, Z-values are often misinterpreted. If observed trends are viewed as the realization of a Brownian motion process, the B-value and its decomposition allow simple extrapolations to the end of the study under a variety of hypotheses. Applications are presented to one- and two-sample Z-tests, the two-sample Wilcoxon rank sum test, and the log-rank test.

Biometry↗
PubMed1987

Stochastic curtailing for comparison of slopes in longitudinal studies.

In some clinical trials, rate of change of a physiological function is used as a surrogate for a more serious outcome. We assume an expected change linear in time for each study participant with variation in slopes and intercepts from individual to individual and repeated measures over time for each individual. We also assume that deviations of response for an individual from expected response have zero mean, constant variance, and are uncorrelated. Under these assumptions we describe ways in which stochastic curtailing as defined by Lan, Simon, and Halperin (Commun Stat Seq Anal 1:207-219, 1982) can be implemented in a two-treatment trial for one-sided comparison of slopes in the two groups. Staggered entry is taken into account, as is the possibility that some of an individual's responses are not available; this is assumed to be random. The analysis assumes the number of participants in each group is large and that most individuals have at least two measurements (including baseline value). The possibility that rate of change is not constant and its consequences are discussed.

Clinical Trials as Topic↗
PubMed1986

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.

Clinical Trials as Topic↗
PubMed1985

Rank tests for survival analysis: a comparison by analogy with games.

Several commonly used two-sample linear rank tests for censored data have been shown to be closely linked in mathematical structure. This pedagogical paper elucidates the relationships among the tests by introducing a videogame played between a boys' team and a girls' team with different rules of payment by the consecutive losers considered. Depending on the rule of payment, the total amount of money the girls win as a team becomes the Wilcoxon statistic, the Savage statistic, or their generalizations under censoring.

Adolescent↗
PubMed1984

Exercise-induced ischemia in mildly symptomatic patients with coronary-artery disease and preserved left ventricular function. Identification of subgroups at risk of death during medical therapy.

To determine prospectively whether the severity of reversible left ventricular ischemia provides prognostic information in mildly symptomatic patients with coronary-artery disease and preserved left ventricular function at rest (ejection fraction greater than 40 per cent), we studied 117 patients by means of exercise electrocardiography and radionuclide angiography. No patient had stenosis of the left main coronary artery. Mortality during subsequent medical therapy was significantly associated (by univariate life-table analysis) with three-vessel coronary-artery disease and the magnitude of the ejection fraction during exercise. In patients with three-vessel disease who had both ST-segment depression of 1 mm or more and a decrease in ejection fraction during exercise, in association with an exercise tolerance of 120 W or less, the probability of survival at four years was only 71 +/- 11 per cent (S.E.). All deaths occurred in this subgroup. Thus, objective evidence of left ventricular ischemia during exercise and exercise capacity identify one subgroup of minimally symptomatic patients with three-vessel disease with an excellent prognosis and another subgroup at relatively high risk of dying during subsequent medical therapy.

Adult↗
PubMed1984

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

The Beta-Blocker Heart Attack Trial was a randomized double blind controlled trial 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.

Adrenergic beta-Antagonists↗
PubMed1982

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.

Blood Pressure↗