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J M Lachin

Publications and source records attributed to J M Lachin.

At least 19 recordsLinked to original sources
PubMed2000

Statistical considerations in the intent-to-treat principle.

This paper describes some of the statistical considerations in the intent-to-treat design and analysis of clinical trials. The pivotal property of a clinical trial is the assignment of treatments to patients at random. Randomization alone, however, is not sufficient to provide an unbiased comparison of therapies. An additional requirement is that the set of patients contributing to an analysis provides an unbiased assessment of treatment effects, or that any missing data are ignorable. A sufficient condition to provide an unbiased comparison is to obtain complete data on all randomized subjects. This can be achieved by an intent-to-treat design wherein all patients are followed until death or the end of the trial, or until the outcome event is reached in a time-to-event trial, irrespective of whether the patient is still receiving or complying with the assigned treatment. The properties of this strategy are contrasted with those of an efficacy subset analysis in which patients and observable patient data are excluded from the analysis on the basis of information obtained postrandomization. I describe the potential bias that can be introduced by such postrandomization exclusions and the pursuant effects on type I error probabilities. Especially in a large study, the inflation in type I error probability can be severe, 0.50 or higher, even when the null hypothesis is true. Standard statistical methods for the analysis of censored or incomplete observations all require the assumption of missing at random to some degree, and none of these methods adjust for the potential bias introduced by post hoc subset selection. Nor is such adjustment possible unless one posits a model that relates the missing observations to other observed information for each subject-models that are inherently untestable. Further, the subset selection bias is confounded with the subset-specific treatment effect, and the two components are not identifiable without additional untestable assumptions. Methods for sensitivity analysis to assess the impact of bias in the efficacy subset analysis are described. It is generally believed that the efficacy subset analysis has greater power than the intent-to-treat analysis. However, even when the efficacy subset analysis is assumed to be unbiased, or have a true type I error probability equal to the desired level alpha, situations are described where the intent-to-treat analysis in fact has greater power than the efficacy subset analysis. The intent-to-treat design, wherein all possible patients continue to be followed, is especially powerful when an effective treatment arrests progression of disease during its administration. Thus, a patient benefits long after the patient becomes noncompliant or the treatment is terminated. In such cases, a landmark analysis using the observations from the last patient evaluation is likely to prove more powerful than life-table or longitudinal analyses. Examples are described.

Bias↗
PubMed2000

A flexible stochastic curtailing procedure for the log-rank test.

For safety and ethical reasons, a data monitoring committee of a clinical trial may wish to assess the futility of continuing a trial if the currently available data at an interim look show no beneficial effect due to treatment, especially when accompanied by mounting evidence of treatment emergent adverse effects. Stochastic curtailing whereby conditional power is evaluated given currently observed data is one way of evaluating futility. In clinical trials that look at "time-to-event" as the primary outcome, difference between treatment groups with respect to the primary outcome is commonly evaluated using the log-rank test. Although the unconditional power function for the log-rank test has been described previously, its conditional power has not been widely investigated. We describe a method for evaluating conditional power when the log-rank test is used to assess the difference between the survival distributions of two treatment groups with respect to some failure-time outcome. The method is useful under a wide range of assumptions regarding the underlying survival distribution, patient entry distribution, losses to follow-up, and (if applicable) noncompliance, drop-ins, lag in treatment effect, and stratification. This level of applicability is attained by generalizing a flexible Markov chain approach to unconditional power computation, described previously, to compute conditional power.

Clinical Trials as Topic↗
PubMed1999

Worst-rank score analysis with informatively missing observations in clinical trials.

Many randomized clinical trials schedule subjects to undergo some assessment at a fixed time (or times) after the initiation of treatment. Often, these follow-up measurements may be missing for some subjects because a disease-related event occurred prior to the time of the follow-up observation. For example, a study of congestive heart failure may schedule patients to undergo exercise testing at 12 weeks, but this measurement may be missing for those who died of heart disease during the study. In such cases, the measurements are informatively missing because mortality from heart disease and a decline in exercise both indicate progression of the underlying disease. It is inappropriate, therefore, to treat these missing observations as missing-at-random and ignore them in the analysis. In one approach to this problem, investigators have included such patients in the analysis of the follow-up data by assigning a rank that represents a "worst-rank score" relative to those actually observed. Some, however, have criticized this procedure as having the potential to produce biased results. In this paper, we explore the statistical properties of such an analysis. We show under a specific model that the imputation of a worst-rank score for informatively missing observations provides an unbiased test against a restricted alternative. We also describe generalizations that employ the actual times of the informative event. We present an example from a study of congestive heart failure. Last, we discuss the implications of this approach and of other methods.

Cardiotonic Agents↗
PubMed1997

Group sequential monitoring of distribution-free analyses of repeated measures.

In many clinical trials the principal analysis consists of a 1 degree of freedom test based on an aggregate summary statistic for a set of repeated measures. Various methods have been proposed for the marginal analysis of such repeated measures that entail estimates of a measure of treatment group difference (the treatment effect) at each of K repeated measures and a consistent estimate of the covariance matrix, where asymptotically these estimates are normally distributed. One can then obtain an overall large sample 1-d.f. test of group differences, such as by taking the average of these K estimates. These methods include the Wei-Lachin family of multivariate rank tests and a corresponding multivariate analysis using the Mann-Whitney difference estimator as a measure of treatment group differences. Other methods, such as O'Brien's non-parametric test, are based on a single summary score for each patient, such as the within-patient mean value. These, and other such methods, allow for some observations to be missing at random. Herein I employ sequential data augmentation to conduct group sequential analyses using a 1 degree of freedom test from a multivariate Mann-Whitney analysis and for the O'Brien rank test. Su and Lachin used this method to perform group sequential analyses of a vector of Hodges-Lehmann estimators. By augmentating the data from the sequential looks in a single analysis, one obtains an estimate of the covariance of the estimates at each look, from which one obtains an estimate of the correlations among the sequential 1-d.f. test statistics. I describe a simple secant algorithm to determine the group sequential boundaries based on recursive integration of the standard multivariate normal distribution with the estimated correlation matrix. Although the boundary obtains readily using the method of Slud and Wei, the more flexible method of Lan and DeMets may be preferred. The true information fraction at each look, needed to apply the spending function method of Lan and DeMets, however, is unknown. Thus, I also describe the use of a surrogate measure of information.

Algorithms↗
PubMed1996

The efficacy of tolrestat in the treatment of diabetic peripheral neuropathy. A meta-analysis of individual patient data.

OBJECTIVE: The aim of this meta-analysis was to review the existent evidence on the effectiveness of tolrestat in the treatment of diabetic peripheral neuropathy. RESEARCH DESIGN AND METHODS: Individual patient data on 738 subjects from the three randomized clinical trials published on this topic were analyzed using changes in motor nerve conduction velocities (NCVs) as endpoints. Nerves investigated included median, ulnar, tibial, and peroneal. RESULTS: The pooled analysis of NCV taken as a continuous measurement showed a significant treatment effect, the magnitude of this benefit being approximately equal to 1 m/s for all the nerves investigated. When looking at the proportion of patients experiencing a loss of NCV of at least 1 or 2 m/s in at least two out of the four nerves investigated, it emerged that treatment reduced by > 40% the risk of such outcomes after adjusting for patients' characteristics. The odds ratios relative to the placebo group were 1.82 (1.30-2.52) and 1.70 (1.15-2.48) for a decrease of 1 and 2 m/s, that is, placebo-treated patients have an 82 and 70% increased risk for a loss of nerve function of 1 and 2 m/s, respectively. No statistically significant difference in treatment effect emerged after stratification according to baseline motor NCV and glycated hemoglobin levels. CONCLUSIONS: After a treatment duration ranging between 24-52 weeks, patients treated with tolrestat had a reduced risk for developing nerve function loss compared with placebo-treated patients. Future long-term trials are needed to evaluate the impact of the treatment on more clinically meaningful endpoints such as the development of foot complications.

Aldehyde Reductase↗
PubMed1995

Martingales without tears.

This pedagogical paper presents a casual introduction to martingales, or fair gambling processes. Our objective is to describe the concept of a martingale and its application to common statistical tests used in the analysis of survival data, but without the mathematical rigor required for formal proofs. We use heuristic arguments to demonstrate that the logrank statistic evaluated over followup time is a fair gambling process, and introduce some mathematical notation and terminology along the way. We then employ the counting process approach to show that the logrank statistic computed over followup time can be expressed as the difference of two martingale transforms, and thus is a martingale. These ideas are first time introduced in the context of a discrete time process, and are then generalized to a continuous time process. With slight modifications, the same idea extends from the logrank to other weighted Mantel-Haenszel statistics computed over time.

Female↗
PubMed1995

Nonparametric test of stochastic ordering for multiple longitudinal measures.

We present a nonparametric approach that tests whether multiple longitudinal measures tend in the same direction over time. It is not required that each measure have the same number of serial observations, or that the observations be evenly spaced. The test and related estimators of group differences are based on the multivariate rank test of Wei and Lachin (1) and multivariate Mann-Whitney shift estimators of Thall and Lachin (2) and Lachin (3). An example is given using a subset of exercise data from a clinical trial of vesnarinone in congestive heart failure.

Cardiotonic Agents↗
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↗
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

The use of response-adaptive designs in clinical trials.

Response-adaptive designs in clinical trials are schemes for patient assignment to treatment, the goal of which is to place more patients on the better treatment based on patient responses already accrued in the trial. While ethically attractive at first glance, these designs have had very little use in practice; yet the statistical literature is rich on this subject. We discuss procedures and properties of these designs. Particular focus is given to the randomized play-the-winner rule of Wei and Durham, which was used in the ECMO trial. We also discuss reasons for the lack of use of these models, and areas of current and future research to address the weaknesses of these methods. We conclude that these designs may be applicable in some situations and describe conditions under which such a trial may be feasible.

Clinical Trials as Topic↗
PubMed1992

Some large-sample distribution-free estimators and tests for multivariate partially incomplete data from two populations.

The most common instance of multivariate observations is the case of repeated measures over time. The two most widely used methods for the analysis of K repeated measures for two groups are the K degrees of freedom (d.f.) T2 MANOVA F-test and the within-subjects 1 degree of freedom ANOVA F-test. Both require complete samples from normally distributed populations. In this paper, I describe alternative K and 1 d.f. distribution-free procedures which allow for randomly missing observations. These include a large-sample analysis of means, the Wei and Lachin multivariate Wilcoxon test with estimates of the Mann-Whitney parameter, and a multivariate Hodges-Lehmann location shift estimator based on the multivariate U-statistic of Wei and Johnson. Each of these methods provides a distribution-free K-variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences. These tests include the K d.f. omnibus T2-like test, 1 d.f. tests of restricted hypotheses, such as the Wei-Lachin multivariate one-sided test of stochastic ordering, and the test of general association based on a minimum variance generalized least squares (GLS) estimate of the average group difference. I then describe covariate stratified-adjusted GLS estimates and tests of group differences. This approach also provides tests of homogeneity (interaction) for within-subjects and between-subjects effects. I illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients, stratified by sex. Such analyses provide an overall distribution-free summary estimate and test of the treatment effect obtained by combining the group differences over both time (repeated measures) and strata.

Chenodeoxycholic Acid↗
PubMed1992

Power and sample size evaluation for the McNemar test with application to matched case-control studies.

Various expressions have appeared for sample size calculation based on the power function of McNemar's test for paired or matched proportions, especially with reference to a matched case-control study. These differ principally with respect to the expression for the variance of the statistic under the alternative hypothesis. In addition to the conditional power function, I identify and compare four distinct unconditional expressions. I show that the unconditional calculation of Schlesselman for the matched case-control study can be expressed as a first-order unconditional calculation as described by Miettinen. Corrections to Schlesselman's unconditional expression presented by Fleiss and Levin and by Dupont, which use different models to describe exposure association among matched cases and controls, are also equivalent to a first-order unconditional calculation. I present a simplification of these corrections that directly provides the underlying table of cell probabilities, from which one can perform any of the alternative sample size calculations. Also, I compare the four unconditional sample size expressions relative to the exact power function. The conclusion is that Miettinen's first-order expression tends to underestimate sample size, while his second-order expression is usually fairly accurate, though possibly slightly anti-conservative. A multinomial-based expression presented by Connor, among others, is also fairly accurate and is usually slightly conservative. Finally, a local unconditional expression of Mitra, among others, tends to be excessively conservative.

Case-Control Studies↗
PubMed1992

A controlled trial of plasmapheresis therapy in severe lupus nephritis. The Lupus Nephritis Collaborative Study Group.

BACKGROUND: The prognosis of patients with systemic lupus erythematosus who have glomerulonephritis is poor, despite treatment with immunosuppressive therapy. Plasmapheresis therapy has been used, but there have been few controlled clinical observations of its efficacy. METHODS: We carried out a randomized, controlled trial comparing a standard-therapy regimen of prednisone and cyclophosphamide (standard therapy) with a regimen of standard therapy plus plasmapheresis in 86 patients with severe lupus nephritis in 14 medical centers. The patients underwent plasmapheresis three times weekly for four weeks. Drug therapy was standardized, with strict adherence to nine detailed medical-management protocols. RESULTS: Forty-six patients received standard therapy, and 40 patients received standard therapy plus plasmapheresis. The mean follow-up was 136 weeks. Six patients (13 percent) in the standard-therapy group and eight patients (20 percent) in the plasmapheresis group died. Renal failure developed in 8 patients (17 percent) in the standard-therapy group, as compared with 10 (25 percent) in the plasmapheresis group. Thirty patients (35 percent) reached stopping points--14 (30 percent) in the standard-therapy group and 16 (40 percent) in the plasmapheresis group. A similar number of patients in each group had a decrease in both the serum creatinine concentration and urinary protein excretion to approximately normal values. Patients treated with plasmapheresis had a significantly more rapid reduction of serum concentrations of antibodies against double-stranded DNA and cryoglobulins. CONCLUSIONS: Treatment with plasmapheresis plus a standard regimen of prednisone and cyclophosphamide therapy does not improve the clinical outcome in patients with systemic lupus erythematosus and severe nephritis, as compared with the standard regimen alone.

Adult↗
PubMed1992

Termination of a clinical trial with no treatment group difference: the Lupus Nephritis Collaborative Study.

The Lupus Nephritis Collaborative Study (LNCS) was a multicenter randomized clinical trial designed to assess the effects of standard drug therapy alone versus drug therapy plus plasmapheresis (plasma exchange) on the incidence of fatal or nonfatal renal failure associated with lupus nephritis. After 86 patients had been entered, with a mean of 97 weeks of follow-up, the trial was terminated partly due to lack of a beneficial effect of plasmapheresis. Although there are numerous methods for the statistical analysis of emerging results in a clinical trial, there have been relatively few descriptions of the application of these methods to the termination of a clinical trial when no favorable difference exists between groups. This report presents a review of the statistical methods employed for the pivotal interim analyses of the LNCS that were performed in order to help reach the decision to terminate the trial. These included the assessment of unconditional power post-hoc and the assessment of conditional power using an exact method appropriate for small sample sizes. Conditional power was used to assess the likelihood of detecting a significant treatment effect in the future given the data thus far observed and given reasonable hypotheses regarding the nature of the possible differences between the treatment groups. In addition, weighted-likelihood ratios (Bayes odds ratios) were computed to assess the likelihood of various alternative hypotheses given the present data. We show how such analyses can be useful in reaching a decision to terminate a trial that fails to show a treatment effect.

Combined Modality Therapy↗
PubMed1992

Group sequential distribution-free methods for the analysis of multivariate observations.

Many studies involve the collection of multivariate observations, such as repeated measures, on two groups of subjects who are recruited over time, i.e., with staggered entry of subjects. Various marginal distribution-free multivariate methods have been proposed for the analyses of such multivariate observations where some measures may be missing at random. Using the multivariate U statistic of Wei and Johnson (1985, Biometrika 72, 359-364), we describe the group sequential analysis of such a study where the multivariate observations are observed sequentially--both within and among subjects. We describe a multivariate generalization of the Hodges and Lehmann (1963, Annals of Mathematical Statistics 34, 598-611) estimator of a location shift that can be obtained via the multivariate U statistic with the Mann-Whitney-Wilcoxon kernel. We then describe large-sample group sequential interval estimators and tests based on an aggregate estimate of the location shift combined over all of the repeated measures. We also describe how the same steps could be employed to perform a group sequential analysis based on any one of the variety of marginal multivariate methods that have been proposed. These methods are applied to a real-life example.

Biometry↗
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↗