Coping with multiple testing.
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Biomedical subjects
Publications and source records attributed to D O Dixon.
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Consider the following situation: Two clinical trials are underway, closely related in terms of the interventions being compared and the target populations. In preparing for a planned interim analysis, the statistician for trial 1 finds that the results support a recommendation to stop the trial early. Should the statistician ask the investigators for trial 2 to make interim results of their trial available to the data and safety monitoring board (DSMB) for trial 1? If so, in what form? Would the answers change if the trial 1 results showed a strong but not convincing trend? What is the obligation of the trial 2 investigators to respond to such a request? What role do the two DSMBs have, either in initiating a request or in agreeing to respond to it? In this article, we examine this situation in some detail, having faced it occasionally in our own experience with clinical trials and DSMBs. The chief argument in favor of sharing data is that data from trial 2 are obviously relevant to the question being addressed by trial 1 and therefore ought to be available to those who must interpret the results from that trial. On the other hand, there are several reasons for not sharing interim data. For example, sharing is incompatible with the independence of the trials; the time for synthesizing evidence from both trials is after the two teams of investigators have presented the full analysis and interpretation of their separate trials. For this and other conceptual and practical reasons we conclude that it is better, in most cases, for DSMBs to consider only information that has already been made public in some form.
The results of multicenter clinical trials may differ across participating clinical sites. We present a diagnostic approach for evaluating this diversity that emphasizes the relationship between the observed event rates and treatment effects. We use as an example a trial of sequential strategies of Pneumocystis prophylaxis in human immunodeficiency virus infection with 842 patients randomly allocated to start prophylaxis with trimethoprim/sulfamethoxazole, dapsone, or pentamidine. Prophylaxis failure rates varied significantly across the 30 clinical sites (0-30.3%, p = 0.002 by Fisher's exact test) with prominent variability in the pentamidine arm (0-63.6%). Starting with oral regimens was better than starting with pentamidine in sites with high rates of events, whereas the three strategies had more similar efficacy in other sites. Sites enrolling fewer patients had lower event rates and had more patients who withdrew prematurely or were lost to follow-up. In a hierarchical regression model adjusting for random measurement error in the observed event rates, starting with trimethoprim/sulfamethoxazole was predicted to be increasingly better than starting with aerosolized pentamidine as the risk of prophylaxis failure increased (p = 0.01), reducing the risk of failure by 47% when the failure rate of pentamidine was 30%, whereas the two regimens were predicted to be equivalent when the failure rate was 17%. Differences in event rates could reflect a combination of heterogeneity in diagnosis, administration of treatments, and disease risk in patients across sites. The evaluation of clinical site differences with a systematic approach focusing on event rates may give further insight in the interpretation of the results of multicenter trials beyond an average treatment effect.
This paper summarizes the proceedings of an NIAID-sponsored workshop on statistical issues for HIV surrogate endpoints. The workshop brought together statisticians and clinicians in an attempt to shed light on some unresolved issues in the use of HIV laboratory markers (such as HIV RNA and CD4+ cell counts) in the design and analysis of clinical studies and in patient management. Utilizing a debate format, the workshop explored a series of specific questions dealing with the relationship between markers and clinical endpoints, and the choice of endpoints and methods of analysis in clinical studies. This paper provides the position statements from the two debaters on each issue. Consensus conclusions, based on the presentations and discussion, are outlined. While not providing final answers, we hope that these discussions have helped clarify a number of issues, and will stimulate further consideration of some of the highlighted problems. These issues will be critical in the proper assessment and use of future therapies for HIV disease.
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PURPOSE: to estimate the alpha/beta ratio for damage to human lung after thoracic irradiation for Hodgkin's disease. PATIENTS AND METHODS: The criterion for lung injury was the presence of radiological changes in the vicinity of the mediastinum as assessed on regular follow-up chest X-ray examinations. Patients with supradiaphragmatic stage I-II Hodgkin's disease received mantle field irradiation as part of their treatment between 1964 and 1981 (E.O.R.T.C. protocols H1, H2, and H5). The total mediastinal doses fixed by the protocols were 35-40 Gy. The fractional doses were left to the decision of the physicians in charge: the most frequent regimens were 5 x 1.8, 5 x 2.0, 4 x 2.5 and 3 x 3.3 Gy per week. The data were fit to the linear-quadratic (L.Q.) model using time-to-injury as endpoint. RESULTS: 1048 (97%) of 1082 patients were evaluable. The mean follow-up duration was 8 years. One hundred and ninety-five cases of radiologically-visible lung damage were observed after a median interval of 6 months (range: 0-101). The 3-year actuarial probability of lung damage was 19% (95% confidence limits: 17, 21). Multivariate analysis (Cox model, stratified by protocol) showed an increased risk of damage with dose per fraction (relative risk, R.R. = 2.22 per Gy (1.75, 2.82)), the presence of systemic symptoms (R.R. = 1.53 (1.09, 2.15)), and total mediastinal dose (R.R. = 1.06 per Gy (1.01, 1.12)). Age, sex, histological type, number of involved nodal sites and radiotherapy duration did not significantly modify the risk of lung damage. The L.Q. model parameters were: alpha = 0.031 Gy-1 (0.003, 0.059), beta = 0.010 Gy-2 (0.007, 0.013), alpha/beta = 3.07 Gy (-0.23, 8.46). CONCLUSION: this low alpha/beta ratio is consistent with late effects values from animals and humans, and illustrates the influence of large fraction sizes on the occurrence of late pulmonary complications.
Anticipating the availability of one or more candidate HIV vaccines for efficacy testing in the next few years, public health agencies are now planning for the conduct of large-scale efficacy trials. We expect these trials to be randomized, double-blind, placebo-controlled studies with prevention of infection as the primary goal. We discuss in detail factors that influence sample size. Factors most influential are the incidence rate of HIV infection in the study population and the minimum efficacy at which a vaccine is still considered acceptable. The smaller either of these factors is, the larger the sample size will be. The desire to complete trials quickly, the gradual accrual of benefit from vaccination, the inaccuracies of assays to detect infection, the need to counsel participants to avoid exposure to HIV, and loss to follow-up all tend to drive up sample size. To illustrate, 83 subjects per study arm suffice to detect 90% efficacy in a population with a 7% annual risk of infection. This assumes a 3-year study with accrual completed in 1 year, no loss to follow-up, and Types I and II error rates of 5 and 10%, respectively. In contrast, 4,254 subjects per arm are required to identify a 60% effective vaccine in a population with a 1% annual risk. The study is also shortened to 2 years, assumes a 5% annual loss to follow-up, and supposes that the full benefit of vaccination is achieved in 6 months. The most realistic assumptions indicate that trials are very likely to require several thousand participants. Limitations of the proposed designs are also discussed.
Subset analysis is the examination of treatment comparisons within groups of patients with restricted levels of patient characteristics. Such analyses are vulnerable to multiplicity effects. We examine the problem in the context of a proportional hazards model with terms for treatment, each of several dichotomous covariates representing the patient characteristics of interest, and treatment-by-covariate interaction effects. Parametrically, a subset-specific treatment effect is equal to the treatment effect term plus a linear combination of the interaction terms. We present Bayesian point and interval estimates under the assumption that the interaction terms are exchangeable and the prior distributions for the other regression parameters are locally uniform. This produces a shrinking of the estimated interaction effects towards zero, thereby discounting them and dealing in a natural way with multiplicity. We illustrate the method using results of a recent North Central Cancer Treatment Group/Mayo Clinic study in advanced colorectal cancer.
We consider the problem of simultaneously comparing several treatment means with a control mean and also with one another. Following an elementary decision-theoretic Bayesian approach requiring the choice of a type-I to type-II error-seriousness ratio k, a posteriori t tests are derived for testing both treatment versus control (TvC) and treatment versus treatment (TvT) differences. These k-ratio t tests are strictly comparisonwise in nature. That is, the test applied to any TvC or TvT difference d, depends in no way at all on whether the other differences are being tested. The test for d, however, does depend on the sizes of the other differences through tG, the standardized average of the observed TvC differences, and through FT, the observed between-treatments F ratio. From these adaptive dependences on tG and FT, the critical t values can be large or small, thus avoiding the intuitive objections of under- or over-conservatism in classical comparisonwise or experimentwise level testing rules.
Patients with relapsed low-grade follicular lymphomas (LGFL) frequently respond to subsequent therapy and can have long survival, but are rarely cured. Factors associated with complete remission (CR) rate, length of survival, and time to treatment failure (TTF) after relapse are not well known. We assessed such factors by multivariate analysis in a retrospective review of 95 patients with relapsed LGFL treated with investigational chemotherapy regimens at our institution. The CR rate after therapy was 22%; the likelihood of achieving CR was inversely associated with the number of previous treatment failures (P less than 0.001) and serum LDH level (P less than 0.05). Both the presence of constitutional symptoms and a history of more than two previous treatment failures were associated with shortened survival and TTF. Hemoglobin level was also significantly associated with survival. Prognostic models for survival and TTF were derived to define patient groups with different projected outcomes after therapy for relapsed disease. The results of this study can be used to select patients for new investigational treatments and to evaluate the outcome of such therapies.
As a means of assessing the importance of variation in treatment effect among patient subsets, we derived posterior distributions for subset-specific treatment effects. The effects are represented by combinations of terms for treatment and treatment-by-covariate interaction effects in familiar regression models. Exchange-ability among the interactions is a key assumption; thus, the results are of interest primarily in the context of examining a collection of subsets with no definite a priori distinction relative to treatment effect. Exchangeability leads to a shrinking of the posterior distributions of the interaction terms toward the natural origin of 0, offsetting the tendency of the estimated effects to disperse. The method is applied to parameter estimates from a proportional hazards regression analysis of survival data from a clinical trial, invoking the approximate multivariate normal distribution of the estimates. No subjective prior distributions are required. Vague priors are used for all of the regression coefficients except the treatment-by-covariate interactions, which are assumed to follow a normal distribution.
Multiple myeloma remains a universally fatal malignancy with a median survival time not exceeding 3 years. A clinical trial was undertaken to determine feasibility and efficacy of marrow-ablative chemoradiotherapy supported by unpurged autologous bone marrow (ABMT) and to define prognostic variables. Total body irradiation and either melphalan or thiotepa were administered to 55 patients (median age 53 years; range 20 to 66 years). The group of 21 patients with resistance to standard melphalan-prednisone and to continuous infusions of vincristine and Adriamycin with high dose dexamethasone (VAD) included 7 with primary unresponsive disease and 14 with resistant relapse; among the 34 patients achieving remission with the VAD regimen, 14 were in first and 20 in a subsequent remission. Marked cytoreduction by greater than or equal to 75% was observed among all 21 patients with refractory myeloma, whereas further cytoreduction of this magnitude was noted in only 56% of the 34 patients already in remission after VAD. Five of the 6 early deaths among all 55 patients occurred in the 14 patients with resistant relapse, none of whom achieved complete remission and who, as a group, had median durations of relapse-free and overall survival of only 8 and 7 months, respectively. Among the 41 remaining patients, there was only one early death, and 27% achieved complete remission including a 36% incidence among the 14 patients treated in first remission; their projected 4-year survival rate was 82% regardless of their disease status (first or later remission or primary resistance). When information about sensitivity to prior therapy is unavailable, the presence before ABMT of both high beta-2-microglobulin levels (greater than 3 mg/L) and non-IgG isotype helped identify 9 among the 55 patients with a very poor prognosis: all 8 responders relapsed within 9 months, and 8 patients died within 15 months. By contrast, a 4-year projected survival rate of over 70% for the other patients (about 80% of this series) justifies further investigation of this novel treatment approach in comparison with standard dose regimens. Our results indicate that marrow-ablative therapy cannot be recommended for myeloma patients with resistant relapse or those with a combination of risk factors (advanced tumor burden, absence of IgG isotype). The apparent lack of an adverse effect of even marked plasmacytosis in autografts (up to 30%) emphasizes the need for better cytoreduction rather than bone marrow purging.
High-dose melphalan has induced remissions in about 40% of patients with refractory myeloma, but the mortality has been high, at about 20%, due to complications of prolonged granulocytopenia. In an attempt to stimulate earlier granulocyte recovery, recombinant human granulocyte-macrophage colony-stimulating factor (GM-CSF) was administered subcutaneously to 23 patients with refractory myeloma who had been treated with melphalan at a high dose of 100 mg/m2. Thirty-nine percent of patients achieved marked tumor cytoreduction by at least 75%, 2 died within 2 months from infectious complications during severe neutropenia; and median durations of relapse-free and overall survival were 7 and 10+ months, respectively. The nine patients presenting with both advanced age over 50 years and a long history of prior therapy of over 1 year required significantly longer median times of 31 days for granulocytes and of 63 days for platelets to reach safe levels of at least 500/microL and 50,000/microL, respectively, than the 14 remaining patients who had none or only one of these adverse features (21 and 26 days, respectively). In a historic control of 43 patients treated previously with high-dose melphalan but without GM-CSF, hematologic recovery to the aforementioned levels of granulocytes and platelets proceeded over almost 5 weeks, regardless of age and prior treatment exposure. Thus GM-CSF seems to hasten marrow recovery, especially in patients with adequate normal marrow stem-cell reserve as defined by younger age or less prior therapy. While not shortening the duration of neutropenia, GM-CSF dose increments (from 0.25 to 0.5 to 0.75 mg/m2) increased the incidence of severe toxicity from 0% to almost 40%, especially among older patients. These results support the usefulness of low-dose GM-CSF (0.25 mg/m2) in stimulating marrow recovery in selected patients with adequate marrow reserve treated with high-dose melphalan for refractory multiple myeloma.
In the bronchial epithelium, smoking initiates a multistep process that first appears histologically as premalignant squamous metaplasia/dysplasia, a biological predecessor of squamous-cell lung cancer. Reflecting chromosomal damage from a carcinogenic insult, micronuclei may reveal earlier events in the carcinogenic sequence. We prospectively evaluated and correlated micronucleus count, histology (index of metaplasia) and smoking exposure in 35 consecutive subjects (9 active smokers, 10 previous smokers and 16 never-smokers) undergoing diagnostic bronchoscopy. Samples for micronuclei and histological evaluation were taken from the main carinal mucosa in each subject for site-specific comparisons. The median and mean micronucleus counts per 1,000 cells were significantly higher in active smokers than in non-smokers (subjects who had never smoked and previous smokers): median counts were 3.7 vs. 1.4, p = 0.03; mean counts were 4.7 vs. 1.9, p = 0.01. There was no significant difference, however, in micronucleus counts between subjects who had never smoked and previous smokers. Bronchial metaplasia and smoking history were not associated. Our findings suggest that micronuclei are a readily quantitated, early intermediate-endpoint marker for detecting tobacco-initiated tracheobronchial carcinogenesis.
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The identification of prognostic factors is an important area of cancer research. This article contains an introduction to the uses of prognostic factors, statistical methods for their identification, and a summary of the literature concerning the evolution of serum beta 2 microglobulin as a prognostic factor in multiple myeloma.
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