Biostatistics and Computer-based Analysis of Health Data using Stata, 2016
This chapter focuses on measures of association between two categorical variables (χ 2 or Fisher ... more This chapter focuses on measures of association between two categorical variables (χ 2 or Fisher test for a contingency table, and the calculation of the odds ratio (OR)) or between a numeric variable and a classification factor. In the latter case, we will consider the case of two independent (or not) samples, as well as parametric (Students t -test) and non-parametric (Wilcoxon test) models for two or more samples situations (analysis of variance (ANOVA) and Kruskal–Wallis ANOVA). The Bonferroni correction method for multiple comparisons of treatment and the linear trend test for the ANOVA will also be discussed. The case of two-factor ANOVA is presented succinctly, restricted to the major commands allowing for the construction of the ANOVA table and an interaction graph to be plotted.
Factors associated with psychological and behavioral functioning in people with type 2 diabetes l... more Factors associated with psychological and behavioral functioning in people with type 2 diabetes living in France
Le chapitre 1 de cette these porte sur la construction des distributions conditionnellement gauss... more Le chapitre 1 de cette these porte sur la construction des distributions conditionnellement gaussiennes. Dans le chapitre 2, nous presentons des resultats sur l'effet des erreurs de mesures sur les estimations et les tests dans les tables de contingence mixtes. Nous montrons qu'en presence de certaines independances conditionnelles particulieres, l'association entre variables est soit toujours diminuee, soit toujours augmentee. Neanmoins dans certains cas les tests d'independance restent de niveau correct. Leur puissance est, pour certains types de modeles, toujours diminuee. Nous caracterisons ensuite la classe des modeles graphiques invariants par erreurs de type Korn. Le chapitre 3 porte sur la correction des erreurs de mesure, si l'on dispose d'un deuxieme echantillon, ou l'on observe conjointement la variable mesuree correctement et sa version erronee. Une methode generale consiste a construire une table de contingence partiellement observee croisant...
Communications in Statistics - Theory and Methods, 2018
With ordinal response items, a Graded Response Model (GRM) is of cumulative logits type, while th... more With ordinal response items, a Graded Response Model (GRM) is of cumulative logits type, while the polytomous Rasch Model (PRM) is based on adjacent logits. In this work, we compare the two approaches. We show that the PRM is superior to the GRM, with interesting properties that we prove. Note S ν the sum of item responses of individual ν and Θ ν its latent parameter, we show i) S ν is a sufficient statistic for θ ν and ii) a property of "stochastic ordering" of the conditional distributions G θ/S. The second property, less known, is, to our knowledge, nowhere satisfactorily demonstrated. monotone likelihood ratio, stochastic ordering, adjacent logit, cumulative logit, odds ratio, Rasch model, .
The problem of estimating the relationship between two variables when their cross-classification ... more The problem of estimating the relationship between two variables when their cross-classification is not directly observed is usually resolved by modelling the incomplete data by loglinear models. Some models are invalid, in the sense that they are incompatible with the observations, and the maximum likelihood method fails to give solutions. This paper gives simple rules to exclude these invalid models and presents a discussion about the choice among valid models.
Acknowledgements. Preface. Presenting Authors. Introduction D.R. Cox. 1: Measurement, Scale Devel... more Acknowledgements. Preface. Presenting Authors. Introduction D.R. Cox. 1: Measurement, Scale Development, and Study Design. regulatory Aspects of Quality of Life C. Gnecco, P.A. Lachenbruch. Biases in the Retrospective Calculation of Reliability and Responsiveness from Longitudinal Studies G. Norma, et al. Application of the Multi-attribute Utility Theory to the Development of a Preference based Health-Related Quality of Life Instrument C. Le Gales. Strategy and Methodology for Choice of Items in Psychometric Measurement: Designing a Quality of Life Instrument for Hip and Knee Osteoarthritis F. Guillemin, et al. Conception, Development and Validation of Instruments for Quality of Life Assessment: An Overview A.J. Chwalow, A.B. Adesina. Methodological Issues in the Analysis of Quality of Life Data in Clinical Trials: Illustrations from the National Surgical Adjuvant Breast and Bowel Project (NSABP) Breast Cancer Prevention Trial S. Land, et al. Disease-Specific Versus Generic Measurement of Health-Related Quality of Life in Cross-Sectional and Longitudinal Studies: an Inpatient Investigation of the SF-36 and Four Disease-Specific Instruments S. Briancon, et al. 2: Analysis and Interpretation of Multiple Endpoints. Analyzing Longitudinal Health-Related Quality of Life Data: Missing Data and Imputation Methods D.A. Revicki. Comparison of Treatments with Multiple Outcomes P. Tubert-Bitter, et al. The Use of Soft Endpoints in Clinical Trials: The Search for Clinical Significance J. Wittes. 3: Item Response Theory and Rasch Models. Parametric and Nonparametric Item Response Theory Models in Health Related Quality of Life Measurement I.W. Molenaar. Questionnaire Reliability Under the Rasch Model A. Hamon, M. Mesbah. Item Response Theory (IRT): Applications in Quality of LifeMeasurement, Analysis and Interpretation D. Cella, et al. Graphical Rasch Models S. Kreiner, K.B. Christensen. 4: Joint Analysis of Quality of Life and Survival. Semi-Markov Models for Quality of Life Data with Censoring N. Heutte, C. Huber-Carol. A Model Relating Quality of Life of Latent Health Status and Survival M.-L. Ting Lee, G.A. Whitmore. Applying Survival Data Methodology to Analyze Longitudinal Quality of Life Data L. Awad, et al. Latent Class Models to Describe Changes Over Time: A Case Study H.C. van Houwelingen. 5: Quality-Adjusted Survival Analysis and Related Methods. Prevalence Analysis of Recurrent and Transient Health States in Quality of Life Studies A. Kramar, R. Lancar. Measures of Quality Adjusted Life and Quality of Life Deficiency: Statistical Perspectives P.K. Sen. Quality-Adjusted Survival Analysis in Cancer Clinical Trials B.F. Cole, K.L. Kilbridge. 6: Methods for Informatively Missing Longitudinal Quality-of-Life Data. Handling of Missing Data M. Chavance. Guidelines For Administration of Self-Reported Health-Related Quality of Questionnaires: How to Minimize Avoidable Missing Data? D. Dubois. Joint Analysis of Survival and Nonignorable Missing Longitudinal Quality-of-Life Data J.-F. Dupuy. Multiple Imputation for Non-Random Missing Data in Longitudinal Studies of Health-Related Quality of Life D.L. Fairclough. Strategies to Fit Pattern-Mixture Models G. Molenberghs, et al. Analysis of Longitudinal Quality of Life Data with Informative Dropout M.C. Wu, et al.
The relationship between a time-dependent covariate and survival times is usually evaluated via t... more The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A frequent problem, however, is the occurence of missing covariate data. A recent approach to estimation in the Cox model in this case jointly models survival and the longitudinal covariate. However, theoretical justification of this approach is still lacking. In this paper we prove existence and consistency of the maximum likelihood estimators in a joint model. The asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.
Dans cet article, on montre que la validité de structure est une étape essentielle dans la valida... more Dans cet article, on montre que la validité de structure est une étape essentielle dans la validation psychométrique des échelles de mesure subjectives, le modèle de crédit partial est utilisé pour étudier la validité de structure. On prend comme exemple, la validation psychométrique de l'échelle GOHAI (General Oral Health Assessment Index) pour la population française générale. Le modèle de crédit partial vérifie l'unidimensionnalité de l'échelle GOHAI. ABSTRACT. In this article, we show that structure validity is an essential step in the psychometric validation of subjective measurement scales, the partial credit model is used to study the structure validity. We take as an example, the psychometric validation of the GOHAI scale (General Oral Health Assessment Index) for the general French population. The partial credit model verifies the unidimensionality of the GOHAI scale. MOTS-CLÉS. Validation psychométrique, Validité de structure, Modèle de crédit partiel, Unidimensionnalité, GOHAI.
Probability, Statistics and Modelling in Public Health
Early stopping of clinical trials either in case of beneficial or deleterious effect of treatment... more Early stopping of clinical trials either in case of beneficial or deleterious effect of treatment on quality of life (QoL) is an important issue. QoL is usually evaluated using self-assessment questionnaires and responses to the items are combined into scores assumed to be normally distributed (which is rarely the case). An alternative is to use item response theory (IRT) models such as the Rasch model for binary items which takes into account the categorical nature of the items. Sequential analysis and mixed Rasch models (MRM) were combined in the context of phaseII non-comparative trials. The statistical properties of the Sequential Probability Ratio Test (SPRT) and of the Triangular Test (TT) were compared using MRM and traditional average scores methods (ASM) by means of simulations. The type I error of the SPRT and TT was correctly maintained for both methods. While remaining a bit underpowered, MRM displayed higher power than the ASM for both sequential tests. Both methods allowed substantial reductions in average sample numbers as compared with fixed sample designs (about 60%). The use of IRT models in sequential analysis of QoL endpoints is promising and should provide a more powerful method to detect therapeutic effects than the traditional ASM.
In this final chapter, we will essentially introduce two new statistical procedures: PROC LIFETES... more In this final chapter, we will essentially introduce two new statistical procedures: PROC LIFETEST and PROC PHREG. These two procedures enable the analysis of survival data.
Survival studies usually collect on each participant, both duration until some terminal event and... more Survival studies usually collect on each participant, both duration until some terminal event and repeated measures of a time-dependent covariate. Such a covariate is referred to as an internal time-dependent covariate. Usually, some subjects drop out of the study before occurrence of the terminal event of interest. One may then wish to evaluate the relationship between time to dropout and the internal covariate. The Cox model is a standard framework for that purpose. Here, we address this problem in situations where the value of the covariate at dropout is unobserved. We suggest a joint model which combines a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. We consider maximum likelihood estimation in this model and show how estimation can be carried out via the EM-algorithm. We state that the suggested joint model may have applications in the context of longitudinal data with nonignorable dropout. Indeed, i...
Abstract: In many survival studies one is interested not only in the duration time to some termin... more Abstract: In many survival studies one is interested not only in the duration time to some terminal event, but also in repeated measurements made on a time-dependent covariate. In these studies, subjects often drop out of the study before the occurrence of the terminal event and the problem of interest then becomes modelling the relationship between the time to dropout and the internal covariate. Dupuy and Mesbah (2002) (DM) proposed a model that described this relationship when the value of the covariate at the dropout time is unobserved. This model combined a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. Parameters were estimated using the EM algorithm and shown to be consistent and asymptotically normal. In this paper, we propose a test statistic to test the validity of Dupuy and Mesbah’s model. Using the techniques developed by Lin (1991), we develop a class of estimators of the regression parameters u...
The International Quality of Life Assessment (IQOLA) Project is a 4 year project initiated in 199... more The International Quality of Life Assessment (IQOLA) Project is a 4 year project initiated in 1991 to translate and adapt the Medical Outcome Study Short Form 36 item Health Survey (SF-36) in at least 15 countries. This paper reports on the preliminary psychometric assessment of the SF-36 in French (version 1.1). The validation data come from two studies: a phase IV study of 121 patients with arthritis and a phase IV study of 159 patients with angina. In both cases, the patients were surveyed using the SF-36 and a disease specific module. The main objective of this analysis was to determine how well the scaling assumptions (summated rating or Likert type scaling construction) of the SF-36 were satisfied. Item convergent validity was supported as items-scale correlation range from 0.47-0.87. Item discriminant validity was supported as all items were more correlated with their hypothesised scales than with scales measuring other concepts. Our data support the assumption that the items...
Biostatistics and Computer-based Analysis of Health Data using Stata, 2016
This chapter focuses on measures of association between two categorical variables (χ 2 or Fisher ... more This chapter focuses on measures of association between two categorical variables (χ 2 or Fisher test for a contingency table, and the calculation of the odds ratio (OR)) or between a numeric variable and a classification factor. In the latter case, we will consider the case of two independent (or not) samples, as well as parametric (Students t -test) and non-parametric (Wilcoxon test) models for two or more samples situations (analysis of variance (ANOVA) and Kruskal–Wallis ANOVA). The Bonferroni correction method for multiple comparisons of treatment and the linear trend test for the ANOVA will also be discussed. The case of two-factor ANOVA is presented succinctly, restricted to the major commands allowing for the construction of the ANOVA table and an interaction graph to be plotted.
Factors associated with psychological and behavioral functioning in people with type 2 diabetes l... more Factors associated with psychological and behavioral functioning in people with type 2 diabetes living in France
Le chapitre 1 de cette these porte sur la construction des distributions conditionnellement gauss... more Le chapitre 1 de cette these porte sur la construction des distributions conditionnellement gaussiennes. Dans le chapitre 2, nous presentons des resultats sur l'effet des erreurs de mesures sur les estimations et les tests dans les tables de contingence mixtes. Nous montrons qu'en presence de certaines independances conditionnelles particulieres, l'association entre variables est soit toujours diminuee, soit toujours augmentee. Neanmoins dans certains cas les tests d'independance restent de niveau correct. Leur puissance est, pour certains types de modeles, toujours diminuee. Nous caracterisons ensuite la classe des modeles graphiques invariants par erreurs de type Korn. Le chapitre 3 porte sur la correction des erreurs de mesure, si l'on dispose d'un deuxieme echantillon, ou l'on observe conjointement la variable mesuree correctement et sa version erronee. Une methode generale consiste a construire une table de contingence partiellement observee croisant...
Communications in Statistics - Theory and Methods, 2018
With ordinal response items, a Graded Response Model (GRM) is of cumulative logits type, while th... more With ordinal response items, a Graded Response Model (GRM) is of cumulative logits type, while the polytomous Rasch Model (PRM) is based on adjacent logits. In this work, we compare the two approaches. We show that the PRM is superior to the GRM, with interesting properties that we prove. Note S ν the sum of item responses of individual ν and Θ ν its latent parameter, we show i) S ν is a sufficient statistic for θ ν and ii) a property of "stochastic ordering" of the conditional distributions G θ/S. The second property, less known, is, to our knowledge, nowhere satisfactorily demonstrated. monotone likelihood ratio, stochastic ordering, adjacent logit, cumulative logit, odds ratio, Rasch model, .
The problem of estimating the relationship between two variables when their cross-classification ... more The problem of estimating the relationship between two variables when their cross-classification is not directly observed is usually resolved by modelling the incomplete data by loglinear models. Some models are invalid, in the sense that they are incompatible with the observations, and the maximum likelihood method fails to give solutions. This paper gives simple rules to exclude these invalid models and presents a discussion about the choice among valid models.
Acknowledgements. Preface. Presenting Authors. Introduction D.R. Cox. 1: Measurement, Scale Devel... more Acknowledgements. Preface. Presenting Authors. Introduction D.R. Cox. 1: Measurement, Scale Development, and Study Design. regulatory Aspects of Quality of Life C. Gnecco, P.A. Lachenbruch. Biases in the Retrospective Calculation of Reliability and Responsiveness from Longitudinal Studies G. Norma, et al. Application of the Multi-attribute Utility Theory to the Development of a Preference based Health-Related Quality of Life Instrument C. Le Gales. Strategy and Methodology for Choice of Items in Psychometric Measurement: Designing a Quality of Life Instrument for Hip and Knee Osteoarthritis F. Guillemin, et al. Conception, Development and Validation of Instruments for Quality of Life Assessment: An Overview A.J. Chwalow, A.B. Adesina. Methodological Issues in the Analysis of Quality of Life Data in Clinical Trials: Illustrations from the National Surgical Adjuvant Breast and Bowel Project (NSABP) Breast Cancer Prevention Trial S. Land, et al. Disease-Specific Versus Generic Measurement of Health-Related Quality of Life in Cross-Sectional and Longitudinal Studies: an Inpatient Investigation of the SF-36 and Four Disease-Specific Instruments S. Briancon, et al. 2: Analysis and Interpretation of Multiple Endpoints. Analyzing Longitudinal Health-Related Quality of Life Data: Missing Data and Imputation Methods D.A. Revicki. Comparison of Treatments with Multiple Outcomes P. Tubert-Bitter, et al. The Use of Soft Endpoints in Clinical Trials: The Search for Clinical Significance J. Wittes. 3: Item Response Theory and Rasch Models. Parametric and Nonparametric Item Response Theory Models in Health Related Quality of Life Measurement I.W. Molenaar. Questionnaire Reliability Under the Rasch Model A. Hamon, M. Mesbah. Item Response Theory (IRT): Applications in Quality of LifeMeasurement, Analysis and Interpretation D. Cella, et al. Graphical Rasch Models S. Kreiner, K.B. Christensen. 4: Joint Analysis of Quality of Life and Survival. Semi-Markov Models for Quality of Life Data with Censoring N. Heutte, C. Huber-Carol. A Model Relating Quality of Life of Latent Health Status and Survival M.-L. Ting Lee, G.A. Whitmore. Applying Survival Data Methodology to Analyze Longitudinal Quality of Life Data L. Awad, et al. Latent Class Models to Describe Changes Over Time: A Case Study H.C. van Houwelingen. 5: Quality-Adjusted Survival Analysis and Related Methods. Prevalence Analysis of Recurrent and Transient Health States in Quality of Life Studies A. Kramar, R. Lancar. Measures of Quality Adjusted Life and Quality of Life Deficiency: Statistical Perspectives P.K. Sen. Quality-Adjusted Survival Analysis in Cancer Clinical Trials B.F. Cole, K.L. Kilbridge. 6: Methods for Informatively Missing Longitudinal Quality-of-Life Data. Handling of Missing Data M. Chavance. Guidelines For Administration of Self-Reported Health-Related Quality of Questionnaires: How to Minimize Avoidable Missing Data? D. Dubois. Joint Analysis of Survival and Nonignorable Missing Longitudinal Quality-of-Life Data J.-F. Dupuy. Multiple Imputation for Non-Random Missing Data in Longitudinal Studies of Health-Related Quality of Life D.L. Fairclough. Strategies to Fit Pattern-Mixture Models G. Molenberghs, et al. Analysis of Longitudinal Quality of Life Data with Informative Dropout M.C. Wu, et al.
The relationship between a time-dependent covariate and survival times is usually evaluated via t... more The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A frequent problem, however, is the occurence of missing covariate data. A recent approach to estimation in the Cox model in this case jointly models survival and the longitudinal covariate. However, theoretical justification of this approach is still lacking. In this paper we prove existence and consistency of the maximum likelihood estimators in a joint model. The asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.
Dans cet article, on montre que la validité de structure est une étape essentielle dans la valida... more Dans cet article, on montre que la validité de structure est une étape essentielle dans la validation psychométrique des échelles de mesure subjectives, le modèle de crédit partial est utilisé pour étudier la validité de structure. On prend comme exemple, la validation psychométrique de l'échelle GOHAI (General Oral Health Assessment Index) pour la population française générale. Le modèle de crédit partial vérifie l'unidimensionnalité de l'échelle GOHAI. ABSTRACT. In this article, we show that structure validity is an essential step in the psychometric validation of subjective measurement scales, the partial credit model is used to study the structure validity. We take as an example, the psychometric validation of the GOHAI scale (General Oral Health Assessment Index) for the general French population. The partial credit model verifies the unidimensionality of the GOHAI scale. MOTS-CLÉS. Validation psychométrique, Validité de structure, Modèle de crédit partiel, Unidimensionnalité, GOHAI.
Probability, Statistics and Modelling in Public Health
Early stopping of clinical trials either in case of beneficial or deleterious effect of treatment... more Early stopping of clinical trials either in case of beneficial or deleterious effect of treatment on quality of life (QoL) is an important issue. QoL is usually evaluated using self-assessment questionnaires and responses to the items are combined into scores assumed to be normally distributed (which is rarely the case). An alternative is to use item response theory (IRT) models such as the Rasch model for binary items which takes into account the categorical nature of the items. Sequential analysis and mixed Rasch models (MRM) were combined in the context of phaseII non-comparative trials. The statistical properties of the Sequential Probability Ratio Test (SPRT) and of the Triangular Test (TT) were compared using MRM and traditional average scores methods (ASM) by means of simulations. The type I error of the SPRT and TT was correctly maintained for both methods. While remaining a bit underpowered, MRM displayed higher power than the ASM for both sequential tests. Both methods allowed substantial reductions in average sample numbers as compared with fixed sample designs (about 60%). The use of IRT models in sequential analysis of QoL endpoints is promising and should provide a more powerful method to detect therapeutic effects than the traditional ASM.
In this final chapter, we will essentially introduce two new statistical procedures: PROC LIFETES... more In this final chapter, we will essentially introduce two new statistical procedures: PROC LIFETEST and PROC PHREG. These two procedures enable the analysis of survival data.
Survival studies usually collect on each participant, both duration until some terminal event and... more Survival studies usually collect on each participant, both duration until some terminal event and repeated measures of a time-dependent covariate. Such a covariate is referred to as an internal time-dependent covariate. Usually, some subjects drop out of the study before occurrence of the terminal event of interest. One may then wish to evaluate the relationship between time to dropout and the internal covariate. The Cox model is a standard framework for that purpose. Here, we address this problem in situations where the value of the covariate at dropout is unobserved. We suggest a joint model which combines a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. We consider maximum likelihood estimation in this model and show how estimation can be carried out via the EM-algorithm. We state that the suggested joint model may have applications in the context of longitudinal data with nonignorable dropout. Indeed, i...
Abstract: In many survival studies one is interested not only in the duration time to some termin... more Abstract: In many survival studies one is interested not only in the duration time to some terminal event, but also in repeated measurements made on a time-dependent covariate. In these studies, subjects often drop out of the study before the occurrence of the terminal event and the problem of interest then becomes modelling the relationship between the time to dropout and the internal covariate. Dupuy and Mesbah (2002) (DM) proposed a model that described this relationship when the value of the covariate at the dropout time is unobserved. This model combined a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. Parameters were estimated using the EM algorithm and shown to be consistent and asymptotically normal. In this paper, we propose a test statistic to test the validity of Dupuy and Mesbah’s model. Using the techniques developed by Lin (1991), we develop a class of estimators of the regression parameters u...
The International Quality of Life Assessment (IQOLA) Project is a 4 year project initiated in 199... more The International Quality of Life Assessment (IQOLA) Project is a 4 year project initiated in 1991 to translate and adapt the Medical Outcome Study Short Form 36 item Health Survey (SF-36) in at least 15 countries. This paper reports on the preliminary psychometric assessment of the SF-36 in French (version 1.1). The validation data come from two studies: a phase IV study of 121 patients with arthritis and a phase IV study of 159 patients with angina. In both cases, the patients were surveyed using the SF-36 and a disease specific module. The main objective of this analysis was to determine how well the scaling assumptions (summated rating or Likert type scaling construction) of the SF-36 were satisfied. Item convergent validity was supported as items-scale correlation range from 0.47-0.87. Item discriminant validity was supported as all items were more correlated with their hypothesised scales than with scales measuring other concepts. Our data support the assumption that the items...
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