- Email: [email protected]
Recursive structural model: An approach to analyze data with treatment adherence problem in randomized clinical trials
625
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probability of an event of each specific type at each time among the cohort of patients who are at dsk, and they exactly partition the observed overall event probability so that the individual probabilities sum to the total. Clinical data on local recurrence at any time versus distant relapse following adjuvant therapies for breast cancer, and on central nervous system involvement versus bone marrow relapses in pediatric acute lymphoblastic leukemia will be presented. We recommend that cumulative incidence functions replace integrated cause-specific hazard functions for descdblng patterns of recurrence in cancer clinical tdals.
A18 ANALYSIS OF NONFATAL OUTCOMES IN CUNICAL TRIALS WHEN MORTALITY IS PRESENT Robert McMahon, Frank Herrall and P.K. Tandon Maryland Medical Research Institute Baltimore, Maryland In clinical trials designed to measure a nonfatal outcome, Y, after a fixed time, M, the presence of missing data due to mortality or other causes poses problems for analysis. If Y is known for all patients who survive to time M, a ranking of all patients randomized on outcome may be established by the rules: (1) patients who die before M rank below all patients surviving up to M; (2) patients who die before M are ranked by their survival time, T; (3) patients surviving to M are ranked according to Y. With this ranking, a modified Wilcoxon statistic may be used to test for differences between two treatments and to estimate the probability of a =better" outcome. If Y is missing at random (MAR) among some surviving patients, a rule is proposed to test for treatment differences based upon an unbiased estimate of the probability of a =better" outcome. A conservative rule for testing treatment differences which preserves Type I error rates is proposed when the MAR assumption may not apply. This rule modifies the Wilcoxon test by assigning missing observations their expected scores under the null hypothesis. An example from a placebo controlled trial of treatments for congestive heart failure will be presented to illustrate these methods. A19 POST-STRATIFICATION APPROACH TO MISSING DATA PROBLEMS IN CLINICAL TRIALS Young Jack Lee and Jonee Ellenberg National Institutes of Health Bethesda, Maryland Missing data problems occur in randomized clinical trials, even if carefully conducted, due to dropping out from the trial, missing return visits, failing to complete tests, etc. Missing data are rarely random. The probability of missingness often depends on baseline variables that affect the outcome variable. Excluding the missing data from the analysis will introduce bias in estimating the treatment effect. We propose a post-stratification approach to this problem. Namely, we form a number of strata of subjects based on baseline variables within which expected outcomes and missing probabilities are relatively homogeneous. We then compute the average value for each treatment within the stratum, and combine the overall average using the inverse of the probability of non-missing as the weight. We apply this method to a recently concluded clinical tdal. We also discuss properties of this method of accounting for the missing data in clinical trials.
A20
RECURSIVE STRUCTURAL MODEL: AN APPROACH TO ANALYZE DATA WITH TREATMENT ADHERENCE PROBLEM IN RANDOMIZED CLINICAL TRIALS Benny C. Fee and Joseph L, Pater National Cancer Institute of Canada Clinical Trials Group Queen's University Kingston, Ontario, Canada It is well known that treatment adherence is important in randomized clinical trials in order that the efficacy of the study treatment can he evaluated properly. However, difficulties arise in practice. Patients who failed to respond to the assigned treatment are sometimes given an option to receive other therapy for ethical reasons. In such situations, the major end-points of the study will be contaminated, and the true study treatment effect may be masked by the effect of the additional therapy. To address this problem, we have used a
626
Abs~aas
recursive model to separate the effect of other therapy from that of the study treatment. The model contains beth the effects of study and additional treatments as independent variables in one linear model, and the additional treatment is being treated as dependent vadable in another linear model. Maximum likelihood estimates of the parameters and their standard errors can be obtained from the model. It can also be shown that the effect of the study treatment without modelling the contamination may be biased in either positive or negative direction. A randomized double-blinded antiemetic tdal performed by NCIC-CTG will be used to illustrate this method of analysis. Chemotherapy naive cancer patients treated with moderately emetoganic chemotherapy were allocated to one of six intravenous doses of Batanopdde, the study antlemetic treatment. Patients were given prochlorparazine as additional antiemetic rescue medication. A major end-point in this tdal is severity of nausea measured by visual analogue scale at a number of time points. Data obtained after patients had taken prochlorparazine were contaminated. The proposed recursive model will be used to delineate the effect of the study antiemetic treatment and the effect of additional antiemetic treatment for a better assessment of the efficacy of the trial medication. A21
STATISTICAL CONTROVERSIES IN META-ANALYSIS: RXED EFFECTS OR RANDOM EFFECTS MODELS? S.G. Thompson and S.J. Pocock
London School of Hygiene and Tropical Medicine London, England In meta-analyses (overviews) of clinical trials there is a need to clarify the statistical methods used, especially as regards their conceptual basis. The commonly used methods can be separated into those using a single fixed effect and heterogeneous (random) effects assumptions. However beth approaches suffer drawbacks, either from ignoring heterogeneity or from problems in quantifying heterogeneity between triais. It proves useful to compare these methods in terms of the relative weights given to each of the tdais in dedving the pooled estimate of treatment effect. A conceptual altamative is to consider a meta-analysis as a summary of different fixed effects. These distinctions are exemplified by meta-analyses of trials in preeclampsia, liver disease and cardiovascular disease. A22
RECENT DEVELOPMENTS IN STATISTICAL METHODS FOR EVALUATING UNIFORMITY OF TREATMENT EFFECTS Richard Simon
National Cancer Institute Bethasda, Maryland Subset analysis is a key feature of the report of many major multicanter clinical tdals. It is also a common source of misleading conclusions. Because of the expanse of clinical trials and the heterogeneity of patient populations, subset analysis is likely to remain an important part of the reporting of clinical trial results. It is therefore important that such analyses be conducted properly and reported appmpdetaly. Statistical tools for subset analyses will he reviewed with particular emphasis on recently developed methods. Recent extensions of the Gall-Simon test for qualitative treatment by subset interactions will be dascdbed. A method of Bayesian subset analysis developed by Dixon and Simon will be illustrated. Recommended publication guidelines for subset analyses will also be presented. A23
ESTIMATING SUBGROUP TREATMENT EFFECTS IN CLINICAL TRIALS Kent R. Bailey
Mayo Clinic Rochester, Minnesota In reporting the results of a clinical trial, there is an issue of whether or not to report subgroup results. Some would argue that these should generally not be presented since they are less reliable (more variable) than overall results. Others would argue that they should be presented, if they are a priori subgroups, since the information is unbiased (whatever that might mean), but should not be taken too seriously. Still another
Abs~a~s
probability of an event of each specific type at each time among the cohort of patients who are at dsk, and they exactly partition the observed overall event probability so that the individual probabilities sum to the total. Clinical data on local recurrence at any time versus distant relapse following adjuvant therapies for breast cancer, and on central nervous system involvement versus bone marrow relapses in pediatric acute lymphoblastic leukemia will be presented. We recommend that cumulative incidence functions replace integrated cause-specific hazard functions for descdblng patterns of recurrence in cancer clinical tdals.
A18 ANALYSIS OF NONFATAL OUTCOMES IN CUNICAL TRIALS WHEN MORTALITY IS PRESENT Robert McMahon, Frank Herrall and P.K. Tandon Maryland Medical Research Institute Baltimore, Maryland In clinical trials designed to measure a nonfatal outcome, Y, after a fixed time, M, the presence of missing data due to mortality or other causes poses problems for analysis. If Y is known for all patients who survive to time M, a ranking of all patients randomized on outcome may be established by the rules: (1) patients who die before M rank below all patients surviving up to M; (2) patients who die before M are ranked by their survival time, T; (3) patients surviving to M are ranked according to Y. With this ranking, a modified Wilcoxon statistic may be used to test for differences between two treatments and to estimate the probability of a =better" outcome. If Y is missing at random (MAR) among some surviving patients, a rule is proposed to test for treatment differences based upon an unbiased estimate of the probability of a =better" outcome. A conservative rule for testing treatment differences which preserves Type I error rates is proposed when the MAR assumption may not apply. This rule modifies the Wilcoxon test by assigning missing observations their expected scores under the null hypothesis. An example from a placebo controlled trial of treatments for congestive heart failure will be presented to illustrate these methods. A19 POST-STRATIFICATION APPROACH TO MISSING DATA PROBLEMS IN CLINICAL TRIALS Young Jack Lee and Jonee Ellenberg National Institutes of Health Bethesda, Maryland Missing data problems occur in randomized clinical trials, even if carefully conducted, due to dropping out from the trial, missing return visits, failing to complete tests, etc. Missing data are rarely random. The probability of missingness often depends on baseline variables that affect the outcome variable. Excluding the missing data from the analysis will introduce bias in estimating the treatment effect. We propose a post-stratification approach to this problem. Namely, we form a number of strata of subjects based on baseline variables within which expected outcomes and missing probabilities are relatively homogeneous. We then compute the average value for each treatment within the stratum, and combine the overall average using the inverse of the probability of non-missing as the weight. We apply this method to a recently concluded clinical tdal. We also discuss properties of this method of accounting for the missing data in clinical trials.
A20
RECURSIVE STRUCTURAL MODEL: AN APPROACH TO ANALYZE DATA WITH TREATMENT ADHERENCE PROBLEM IN RANDOMIZED CLINICAL TRIALS Benny C. Fee and Joseph L, Pater National Cancer Institute of Canada Clinical Trials Group Queen's University Kingston, Ontario, Canada It is well known that treatment adherence is important in randomized clinical trials in order that the efficacy of the study treatment can he evaluated properly. However, difficulties arise in practice. Patients who failed to respond to the assigned treatment are sometimes given an option to receive other therapy for ethical reasons. In such situations, the major end-points of the study will be contaminated, and the true study treatment effect may be masked by the effect of the additional therapy. To address this problem, we have used a
626
Abs~aas
recursive model to separate the effect of other therapy from that of the study treatment. The model contains beth the effects of study and additional treatments as independent variables in one linear model, and the additional treatment is being treated as dependent vadable in another linear model. Maximum likelihood estimates of the parameters and their standard errors can be obtained from the model. It can also be shown that the effect of the study treatment without modelling the contamination may be biased in either positive or negative direction. A randomized double-blinded antiemetic tdal performed by NCIC-CTG will be used to illustrate this method of analysis. Chemotherapy naive cancer patients treated with moderately emetoganic chemotherapy were allocated to one of six intravenous doses of Batanopdde, the study antlemetic treatment. Patients were given prochlorparazine as additional antiemetic rescue medication. A major end-point in this tdal is severity of nausea measured by visual analogue scale at a number of time points. Data obtained after patients had taken prochlorparazine were contaminated. The proposed recursive model will be used to delineate the effect of the study antiemetic treatment and the effect of additional antiemetic treatment for a better assessment of the efficacy of the trial medication. A21
STATISTICAL CONTROVERSIES IN META-ANALYSIS: RXED EFFECTS OR RANDOM EFFECTS MODELS? S.G. Thompson and S.J. Pocock
London School of Hygiene and Tropical Medicine London, England In meta-analyses (overviews) of clinical trials there is a need to clarify the statistical methods used, especially as regards their conceptual basis. The commonly used methods can be separated into those using a single fixed effect and heterogeneous (random) effects assumptions. However beth approaches suffer drawbacks, either from ignoring heterogeneity or from problems in quantifying heterogeneity between triais. It proves useful to compare these methods in terms of the relative weights given to each of the tdais in dedving the pooled estimate of treatment effect. A conceptual altamative is to consider a meta-analysis as a summary of different fixed effects. These distinctions are exemplified by meta-analyses of trials in preeclampsia, liver disease and cardiovascular disease. A22
RECENT DEVELOPMENTS IN STATISTICAL METHODS FOR EVALUATING UNIFORMITY OF TREATMENT EFFECTS Richard Simon
National Cancer Institute Bethasda, Maryland Subset analysis is a key feature of the report of many major multicanter clinical tdals. It is also a common source of misleading conclusions. Because of the expanse of clinical trials and the heterogeneity of patient populations, subset analysis is likely to remain an important part of the reporting of clinical trial results. It is therefore important that such analyses be conducted properly and reported appmpdetaly. Statistical tools for subset analyses will he reviewed with particular emphasis on recently developed methods. Recent extensions of the Gall-Simon test for qualitative treatment by subset interactions will be dascdbed. A method of Bayesian subset analysis developed by Dixon and Simon will be illustrated. Recommended publication guidelines for subset analyses will also be presented. A23
ESTIMATING SUBGROUP TREATMENT EFFECTS IN CLINICAL TRIALS Kent R. Bailey
Mayo Clinic Rochester, Minnesota In reporting the results of a clinical trial, there is an issue of whether or not to report subgroup results. Some would argue that these should generally not be presented since they are less reliable (more variable) than overall results. Others would argue that they should be presented, if they are a priori subgroups, since the information is unbiased (whatever that might mean), but should not be taken too seriously. Still another