A SAS Program Combining R Functionalities to Implement Pattern-Mixture Models

Pattern-mixture models have gained considerable interest in recent years. Patternmixture modeling allows the analysis of incomplete longitudinal outcomes under a variety of missingness mechanisms. In this manuscript, we describe a SAS program which combines R functionalities to fit pattern-mixture models, considering the cases that missingness mechanisms are at random and not at random. Patterns are defined based on missingness at every time point and parameter estimation is based on a full group-bytime interaction. The program implements a multiple imputation method under so-called identifying restrictions. The code is illustrated using data from a placebo-controlled clinical trial. This manuscript and the program are directed to SAS users with minimal knowledge of the R language

Lois bayésiennes a priori dans un plan binomial séquentiel

The reformulation by R. de Cristofaro of the Bayes theorem allows to integrate the information on the experimental design in the prior distribution. In accepting to transgress the Likelihood and Stopping Rules principles, a new framework allows to move on the issue of sequenciality in the Bayesian inference. Considering that the information on the design is contained in the Fisher information, a new family of priors is derived from a likelihood directly related to the sampling rule. The case of the study of a proportion in the sequential context of successive Binomial samplings leads to consider the Beta-J distribution. The study on several sequential designs allows to state that the "corrected Jeffreys prior" compensates the bias induced on the observed proportion. An application in the estimation shows the relationship between the parameters of the Beta-J and Beta distributions in the fixed sampling. The mean and mode of the posterior distributions show remarkable frequentist properties. As well, the corrected Jeffreys interval has an optimal covering rates as the correction compensates the effect of stopping rule on the limits. Last, a test procedure, whose the errors are interpreted in terms of both bayesian probabilities of hypotheses and frequentist risks, is designed with a rule for stopping and rejecting H0 based on a limit value of the Bayes factor. It is shown how the corrected Jeffreys prior compensates the ratio of evidences and guarantees the unicity of solutions, even when the null hypothesis is composite.La reformulation du théorème de Bayes par R. de Cristofaro permet d'intégrer l'information sur le plan expérimental dans la loi a priori. En acceptant de transgresser les principes de vraisemblance et de la règle d'arrêt, un nouveau cadre théorique permet d'aborder le problème de la séquentialité dans l'inférence bayésienne. En considérant que l'information sur le plan expérimental est contenue dans l'information de Fisher, on dérive une famille de lois a priori à partir d'une vraisemblance directement associée à l'échantillonnage. Le cas de l'évaluation d'une proportion dans le contexte d'échantillonnages Binomiaux successifs conduit à considérer la loi Bêta-J. L'étude sur plusieurs plans séquentiels permet d'établir que l'"a priori de Jeffreys corrigé" compense le biais induit sur la proportion observée. Une application dans l'estimation ponctuelle montre le lien entre le paramétrage des lois Bêta-J et Bêta dans l'échantillonnage fixe. La moyenne et le mode des lois a posteriori obtenues présentent des propriétés fréquentistes remarquables. De même, l'intervalle de Jeffreys corrigé montre un taux de recouvrement optimal car la correction vient compenser l'effet de la règle d'arrêt sur les bornes. Enfin, une procédure de test, dont les erreurs s'interprètent à la fois en terme de probabilité bayésienne de l'hypothèse et de risques fréquentistes, est construite avec une règle d'arrêt et de rejet de H0 fondée sur une valeur limite du facteur de Bayes. On montre comment l'a priori de Jeffreys corrigé compense le rapport des évidences et garantit l'unicité des solutions, y compris lorsque l'hypothèse nulle est composite

Lois bayésiennes a priori dans un plan binomial séquentiel

The reformulation by R. de Cristofaro of the Bayes theorem allows to integrate the information on the experimental design in the prior distribution. In accepting to transgress the Likelihood and Stopping Rules principles, a new framework allows to move on the issue of sequenciality in the Bayesian inference. Considering that the information on the design is contained in the Fisher information, a new family of priors is derived from a likelihood directly related to the sampling rule. The case of the study of a proportion in the sequential context of successive Binomial samplings leads to consider the Beta-J distribution. The study on several sequential designs allows to state that the "corrected Jeffreys prior" compensates the bias induced on the observed proportion. An application in the estimation shows the relationship between the parameters of the Beta-J and Beta distributions in the fixed sampling. The mean and mode of the posterior distributions show remarkable frequentist properties. As well, the corrected Jeffreys interval has an optimal covering rates as the correction compensates the effect of stopping rule on the limits. Last, a test procedure, whose the errors are interpreted in terms of both bayesian probabilities of hypotheses and frequentist risks, is designed with a rule for stopping and rejecting H0 based on a limit value of the Bayes factor. It is shown how the corrected Jeffreys prior compensates the ratio of evidences and guarantees the unicity of solutions, even when the null hypothesis is composite.La reformulation du théorème de Bayes par R. de Cristofaro permet d'intégrer l'information sur le plan expérimental dans la loi a priori. En acceptant de transgresser les principes de vraisemblance et de la règle d'arrêt, un nouveau cadre théorique permet d'aborder le problème de la séquentialité dans l'inférence bayésienne. En considérant que l'information sur le plan expérimental est contenue dans l'information de Fisher, on dérive une famille de lois a priori à partir d'une vraisemblance directement associée à l'échantillonnage. Le cas de l'évaluation d'une proportion dans le contexte d'échantillonnages Binomiaux successifs conduit à considérer la loi Bêta-J. L'étude sur plusieurs plans séquentiels permet d'établir que l'"a priori de Jeffreys corrigé" compense le biais induit sur la proportion observée. Une application dans l'estimation ponctuelle montre le lien entre le paramétrage des lois Bêta-J et Bêta dans l'échantillonnage fixe. La moyenne et le mode des lois a posteriori obtenues présentent des propriétés fréquentistes remarquables. De même, l'intervalle de Jeffreys corrigé montre un taux de recouvrement optimal car la correction vient compenser l'effet de la règle d'arrêt sur les bornes. Enfin, une procédure de test, dont les erreurs s'interprètent à la fois en terme de probabilité bayésienne de l'hypothèse et de risques fréquentistes, est construite avec une règle d'arrêt et de rejet de H0 fondée sur une valeur limite du facteur de Bayes. On montre comment l'a priori de Jeffreys corrigé compense le rapport des évidences et garantit l'unicité des solutions, y compris lorsque l'hypothèse nulle est composite

Lois bayésiennes a priori dans un plan binomial séquentiel

En acceptant de transgresser le principe de vraisemblance, un nouveau cadre théorique permet d'aborder le problème de la séquentialité dans l'interférence bayésienne. En considérant que l'information sur le plan expérimental est contenue dans l'information de Fisher, on dérive une famille de lois a priori à partir d'une vraisemblance directement associée à l'échantillonnage. Le cas de l'évaluation d'une proportion avec des échantillonnages Binomiaux successifs conduit à considérer la loi Bêta-J. On établit que l'a priori de Jeffreys corrigé compense le biais induit sur la proportion observée. Une application dans l'estimation ponctuelle montre le lien entre le paramétrage des lois Bêta-J et Bêta dans l'échantillonnage fixe. La moyenne et le mode des lois a posteriori obtenues présentent des propriétés fréquentistes remarquables. L'intervalle de Jeffreys corrigé montre un taux de recouvrement optimal car la correction vient compenser l'effet de la règle d'arrêt sur les bornes. Une procédure de test est construite avec une règle d'arrêt et de rejet de H0 fondée sur une valeur du facteur de Bayes. L'a priori de Jeffreys corrigé compense le rapport des évidences et garantit l'unicité des solutions.In accepting to relax the Likelihood principle, a new framework allows to move on the issue of sequenciality in the bayesian inference. Considering that the information on the design is contained in the Fisher information, a new family of priors is derived from a likelihood directly related to the sampling rule. The case of the study of a proportion using successive Binomial samplings leads to consider the Beta-J distribution. The study on several sequential designs allows to state that the corrected Jeffreys prior compensates the bias induced on the observed proportion. An application in the estimation shows the relationship between the parameters of the Beta-J and Beta distributions in the fixed sampling. The mean and mode of the posterior distributions show remarkable frequentist properties. As well, the corrected Jeffreys interval has an optimal covering rates as the correction compensates the effect of stopping rule on the limits. Last, a test procedure is designed with a rule for stopping and rejecting H0 based on a limit value of the Bayes factor. The corrected Jeffreys prior compensates the ratio of evidences and garanties the unicity of solutions.ROUEN-BU Sciences (764512102) / SudocROUEN-BU Sciences Madrillet (765752101) / SudocROUEN-Bib.maths (764512206) / SudocSudocFranceF

An objective Bayesian approach to multistage hypothesis testing

International audienceA new Bayesian approach to multistage hypothesis testing is considered. Prior is derived using Jeffreys' criterion on likelihood associated with the design information. We show that the prior for sequential Bernoulli design asymptotically converges toward the Jeffreys prior in Pascal sampling model. A general rule is given for determining the design-corrected version of default priors when Jeffreys' criterion results in improper distribution. Based on the principle of design impartiality, the Bayes factor as posterior-based evidential measure can be generalized to multistage testing, so that the decision boundaries reflect equal evidence for hypotheses over stages. Effect of prior correction on design parameters and on Bayesian inference upon test termination is studied. The approach is applied to a three-stage binomial design. Last, the use of the prior as the default objective choice in multistage hypothesis testing is discussed

On Bayesian estimators in multistage binomial designs

International audienceA new class of Bayesian estimators for a proportion in multistage binomial designs is considered. Priors belong to the beta-J distribution family, which is derived from the Fisher information associatedwith the design. The transposition of the beta parameters of theHaldane and the uniformpriors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs. We show that the estimator of the posterior mean based on the corrected Haldane prior and the estimator of the posterior mode based on the corrected uniform prior have good frequentist properties. An easy-to-use approximation of the estimator of the posteriormode is provided. The newBayesian estimators are compared to Whitehead's and the uniformly minimum variance estimators through several multistage designs. Last, the bias of the estimator of the posterior mode is derived for a particular case

A SAS

Pattern-mixture models have gained considerable interest in recent years. Patternmixture modeling allows the analysis of incomplete longitudinal outcomes under a variety of missingness mechanisms. In this manuscript, we describe a SAS program which combines R functionalities to fit pattern-mixture models, considering the cases that missingness mechanisms are at random and not at random. Patterns are defined based on missingness at every time point and parameter estimation is based on a full group-bytime interaction. The program implements a multiple imputation method under so-called identifying restrictions. The code is illustrated using data from a placebo-controlled clinical trial. This manuscript and the program are directed to SAS users with minimal knowledge of the R language

Bayesian sample size determination in non-sequential clinical trials: statistical aspects and some regulatory considerations?

International audienceThe most common Bayesian methods for sample size determination (SSD) are reviewed in the non-sequential context of a confirmatory phase III trial in drug development. After recalling the regulatory viewpoint on SSD, we discuss the relevance of the various priors applied to the planning of clinical trials. We then investigate whether these Bayesian methods could compete with the usual frequentist approach to SSD and be considered as acceptable from a regulatory viewpoint

New late‐emphasis and combination tests based on infimum and supremum logrank statistics with application in oncology trials

International audienceImmunotherapy cancer clinical trials routinely feature an initial period during which the treatment is given without evident therapeutic benefit, which may be followed by a period during which an effective therapy reduces the hazard for event occurrence. The nature of this treatment effect is incompatible with the proportional hazards assumption, which has prompted much work on the development of alternative effect measures of frameworks for testing. We consider tests based on individual and combination of early- and late-emphasis infimum and supremum logrank statistics, describe how they can be implemented, and evaluate their performance in simulation studies. Through this work and illustrative applications we conclude that this class of test statistics offers a new and powerful framework for assessing treatment effects in cancer clinical trials involving immunotherapies