This is a response to Nancy Cook's Readers' Reaction to "Measures to Summarize and Compare the Predictive Capacity of Markers."
这是对Nancy Cook的读者对“总结和比较标记预测能力的措施”的反应的回应。
{"title":"Rejoinder to Nancy Cook's Comment on \"Measures to Summarize and Compare the Predictive Capacity of Markers\"","authors":"M. Pepe","doi":"10.2202/1557-4679.1280","DOIUrl":"https://doi.org/10.2202/1557-4679.1280","url":null,"abstract":"This is a response to Nancy Cook's Readers' Reaction to \"Measures to Summarize and Compare the Predictive Capacity of Markers.\"","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2010-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68718007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dynamic treatment regimes are set rules for sequential decision making based on patient covariate history. Observational studies are well suited for the investigation of the effects of dynamic treatment regimes because of the variability in treatment decisions found in them. This variability exists because different physicians make different decisions in the face of similar patient histories. In this article we describe an approach to estimate the optimal dynamic treatment regime among a set of enforceable regimes. This set is comprised by regimes defined by simple rules based on a subset of past information. The regimes in the set are indexed by a Euclidean vector. The optimal regime is the one that maximizes the expected counterfactual utility over all regimes in the set. We discuss assumptions under which it is possible to identify the optimal regime from observational longitudinal data. Murphy et al. (2001) developed efficient augmented inverse probability weighted estimators of the expected utility of one fixed regime. Our methods are based on an extension of the marginal structural mean model of Robins (1998, 1999) which incorporate the estimation ideas of Murphy et al. (2001). Our models, which we call dynamic regime marginal structural mean models, are specially suitable for estimating the optimal treatment regime in a moderately small class of enforceable regimes of interest. We consider both parametric and semiparametric dynamic regime marginal structural models. We discuss locally efficient, double-robust estimation of the model parameters and of the index of the optimal treatment regime in the set. In a companion paper in this issue of the journal we provide proofs of the main results.
{"title":"Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content","authors":"Liliana Orellana, A. Rotnitzky, J. Robins","doi":"10.2202/1557-4679.1200","DOIUrl":"https://doi.org/10.2202/1557-4679.1200","url":null,"abstract":"Dynamic treatment regimes are set rules for sequential decision making based on patient covariate history. Observational studies are well suited for the investigation of the effects of dynamic treatment regimes because of the variability in treatment decisions found in them. This variability exists because different physicians make different decisions in the face of similar patient histories. In this article we describe an approach to estimate the optimal dynamic treatment regime among a set of enforceable regimes. This set is comprised by regimes defined by simple rules based on a subset of past information. The regimes in the set are indexed by a Euclidean vector. The optimal regime is the one that maximizes the expected counterfactual utility over all regimes in the set. We discuss assumptions under which it is possible to identify the optimal regime from observational longitudinal data. Murphy et al. (2001) developed efficient augmented inverse probability weighted estimators of the expected utility of one fixed regime. Our methods are based on an extension of the marginal structural mean model of Robins (1998, 1999) which incorporate the estimation ideas of Murphy et al. (2001). Our models, which we call dynamic regime marginal structural mean models, are specially suitable for estimating the optimal treatment regime in a moderately small class of enforceable regimes of interest. We consider both parametric and semiparametric dynamic regime marginal structural models. We discuss locally efficient, double-robust estimation of the model parameters and of the index of the optimal treatment regime in the set. In a companion paper in this issue of the journal we provide proofs of the main results.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2010-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1200","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is devoted to the asymptotic study of adaptive group sequential designs in the case of randomized clinical trials (RCTs) with binary treatment, binary outcome and no covariate. By adaptive design, we mean in this setting a RCT design that allows the investigator to dynamically modify its course through data-driven adjustment of the randomization probability based on data accrued so far, without negatively impacting on the statistical integrity of the trial. By adaptive group sequential design, we refer to the fact that group sequential testing methods can be equally well applied on top of adaptive designs. We obtain that, theoretically, the adaptive design converges almost surely to the targeted unknown randomization scheme. In the estimation framework, we obtain that our maximum likelihood estimator of the parameter of interest is a strongly consistent estimator, and it satisfies a central limit theorem. We can estimate its asymptotic variance, which is the same as that it would feature had we known in advance the targeted randomization scheme and independently sampled from it. Consequently, inference can be carried out as if we had resorted to independent and identically distributed (iid) sampling. In the testing framework, we obtain that the multidimensional t-statistic that we would use under iid sampling still converges to the same canonical distribution under adaptive sampling. Consequently, the same group sequential testing can be carried out as if we had resorted to iid sampling. Furthermore, a comprehensive simulation study that we undertake in a companion article validates the theory. A three-sentence take-home message is “Adaptive designs do learn the targeted optimal design and inference, and testing can be carried out under adaptive sampling as they would under the targeted optimal randomization probability iid sampling. In particular, adaptive designs achieve the same efficiency as the fixed oracle design. This is confirmed by a simulation study, at least for moderate or large sample sizes, across a large collection of targeted randomization probabilities.'”
{"title":"Targeting the Optimal Design in Randomized Clinical Trials with Binary Outcomes and No Covariate: Theoretical Study","authors":"A. Chambaz, M. J. van der Laan","doi":"10.2202/1557-4679.1247","DOIUrl":"https://doi.org/10.2202/1557-4679.1247","url":null,"abstract":"This article is devoted to the asymptotic study of adaptive group sequential designs in the case of randomized clinical trials (RCTs) with binary treatment, binary outcome and no covariate. By adaptive design, we mean in this setting a RCT design that allows the investigator to dynamically modify its course through data-driven adjustment of the randomization probability based on data accrued so far, without negatively impacting on the statistical integrity of the trial. By adaptive group sequential design, we refer to the fact that group sequential testing methods can be equally well applied on top of adaptive designs. We obtain that, theoretically, the adaptive design converges almost surely to the targeted unknown randomization scheme. In the estimation framework, we obtain that our maximum likelihood estimator of the parameter of interest is a strongly consistent estimator, and it satisfies a central limit theorem. We can estimate its asymptotic variance, which is the same as that it would feature had we known in advance the targeted randomization scheme and independently sampled from it. Consequently, inference can be carried out as if we had resorted to independent and identically distributed (iid) sampling. In the testing framework, we obtain that the multidimensional t-statistic that we would use under iid sampling still converges to the same canonical distribution under adaptive sampling. Consequently, the same group sequential testing can be carried out as if we had resorted to iid sampling. Furthermore, a comprehensive simulation study that we undertake in a companion article validates the theory. A three-sentence take-home message is “Adaptive designs do learn the targeted optimal design and inference, and testing can be carried out under adaptive sampling as they would under the targeted optimal randomization probability iid sampling. In particular, adaptive designs achieve the same efficiency as the fixed oracle design. This is confirmed by a simulation study, at least for moderate or large sample sizes, across a large collection of targeted randomization probabilities.'”","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"7 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2010-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1247","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given causal graph assumptions, intervention-specific counterfactual distributions of the data can be defined by the so called G-computation formula, which is obtained by carrying out these interventions on the likelihood of the data factorized according to the causal graph. The obtained G-computation formula represents the counterfactual distribution the data would have had if this intervention would have been enforced on the system generating the data. A causal effect of interest can now be defined as some difference between these counterfactual distributions indexed by different interventions. For example, the interventions can represent static treatment regimens or individualized treatment rules that assign treatment in response to time-dependent covariates, and the causal effects could be defined in terms of features of the mean of the treatment-regimen specific counterfactual outcome of interest as a function of the corresponding treatment regimens. Such features could be defined nonparametrically in terms of so called (nonparametric) marginal structural models for static or individualized treatment rules, whose parameters can be thought of as (smooth) summary measures of differences between the treatment regimen specific counterfactual distributions.In this article, we develop a particular targeted maximum likelihood estimator of causal effects of multiple time point interventions. This involves the use of loss-based super-learning to obtain an initial estimate of the unknown factors of the G-computation formula, and subsequently, applying a target-parameter specific optimal fluctuation function (least favorable parametric submodel) to each estimated factor, estimating the fluctuation parameter(s) with maximum likelihood estimation, and iterating this updating step of the initial factor till convergence. This iterative targeted maximum likelihood updating step makes the resulting estimator of the causal effect double robust in the sense that it is consistent if either the initial estimator is consistent, or the estimator of the optimal fluctuation function is consistent. The optimal fluctuation function is correctly specified if the conditional distributions of the nodes in the causal graph one intervenes upon are correctly specified. The latter conditional distributions often comprise the so called treatment and censoring mechanism. Selection among different targeted maximum likelihood estimators (e.g., indexed by different initial estimators) can be based on loss-based cross-validation such as likelihood based cross-validation or cross-validation based on another appropriate loss function for the distribution of the data. Some specific loss functions are mentioned in this article.Subsequently, a variety of interesting observations about this targeted maximum likelihood estimation procedure are made. This article provides the basis for the subsequent companion Part II-article in which concrete demonstrations for the implementation of the
{"title":"Targeted Maximum Likelihood Based Causal Inference: Part I","authors":"M. J. van der Laan","doi":"10.2202/1557-4679.1211","DOIUrl":"https://doi.org/10.2202/1557-4679.1211","url":null,"abstract":"Given causal graph assumptions, intervention-specific counterfactual distributions of the data can be defined by the so called G-computation formula, which is obtained by carrying out these interventions on the likelihood of the data factorized according to the causal graph. The obtained G-computation formula represents the counterfactual distribution the data would have had if this intervention would have been enforced on the system generating the data. A causal effect of interest can now be defined as some difference between these counterfactual distributions indexed by different interventions. For example, the interventions can represent static treatment regimens or individualized treatment rules that assign treatment in response to time-dependent covariates, and the causal effects could be defined in terms of features of the mean of the treatment-regimen specific counterfactual outcome of interest as a function of the corresponding treatment regimens. Such features could be defined nonparametrically in terms of so called (nonparametric) marginal structural models for static or individualized treatment rules, whose parameters can be thought of as (smooth) summary measures of differences between the treatment regimen specific counterfactual distributions.In this article, we develop a particular targeted maximum likelihood estimator of causal effects of multiple time point interventions. This involves the use of loss-based super-learning to obtain an initial estimate of the unknown factors of the G-computation formula, and subsequently, applying a target-parameter specific optimal fluctuation function (least favorable parametric submodel) to each estimated factor, estimating the fluctuation parameter(s) with maximum likelihood estimation, and iterating this updating step of the initial factor till convergence. This iterative targeted maximum likelihood updating step makes the resulting estimator of the causal effect double robust in the sense that it is consistent if either the initial estimator is consistent, or the estimator of the optimal fluctuation function is consistent. The optimal fluctuation function is correctly specified if the conditional distributions of the nodes in the causal graph one intervenes upon are correctly specified. The latter conditional distributions often comprise the so called treatment and censoring mechanism. Selection among different targeted maximum likelihood estimators (e.g., indexed by different initial estimators) can be based on loss-based cross-validation such as likelihood based cross-validation or cross-validation based on another appropriate loss function for the distribution of the data. Some specific loss functions are mentioned in this article.Subsequently, a variety of interesting observations about this targeted maximum likelihood estimation procedure are made. This article provides the basis for the subsequent companion Part II-article in which concrete demonstrations for the implementation of the ","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Parametric modeling of univariate cumulative incidence functions and logistic models have been studied extensively. However, to the best of our knowledge, there is no study using logistic models to characterize cumulative incidence functions. In this paper, we propose a novel parametric model which is an extension of a widely-used four-parameter logistic function for dose-response curves. The modified model can accommodate various shapes of cumulative incidence functions and be easily implemented using standard statistical software. The simulation studies demonstrate that the proposed model is as efficient as or more efficient than its nonparametric counterpart when it is correctly specified, and outperforms the existing Gompertz model when the underlying cumulative incidence function is sigmoidal. The practical utility of the modified three-parameter logistic model is illustrated using the data from the Cache County Study of dementia.
{"title":"Modeling Cumulative Incidences of Dementia and Dementia-Free Death Using a Novel Three-Parameter Logistic Function","authors":"Y. Cheng","doi":"10.2202/1557-4679.1183","DOIUrl":"https://doi.org/10.2202/1557-4679.1183","url":null,"abstract":"Parametric modeling of univariate cumulative incidence functions and logistic models have been studied extensively. However, to the best of our knowledge, there is no study using logistic models to characterize cumulative incidence functions. In this paper, we propose a novel parametric model which is an extension of a widely-used four-parameter logistic function for dose-response curves. The modified model can accommodate various shapes of cumulative incidence functions and be easily implemented using standard statistical software. The simulation studies demonstrate that the proposed model is as efficient as or more efficient than its nonparametric counterpart when it is correctly specified, and outperforms the existing Gompertz model when the underlying cumulative incidence function is sigmoidal. The practical utility of the modified three-parameter logistic model is illustrated using the data from the Cache County Study of dementia.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2009-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1183","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Benedetti, M. Abrahamowicz, K. Leffondré, M. Goldberg, R. Tamblyn
In a variety of research settings, investigators may wish to detect and estimate a threshold in the association between continuous variables. A threshold model implies a non-linear relationship, with the slope changing at an unknown location. Generalized additive models (GAMs) (Hastie and Tibshirani, 1990) estimate the shape of the non-linear relationship directly from the data and, thus, may be useful in this endeavour.We propose a method based on GAMs to detect and estimate thresholds in the association between a continuous covariate and a continuous dependent variable. Using simulations, we compare it with the maximum likelihood estimation procedure proposed by Hudson (1966).We search for potential thresholds in a neighbourhood of points whose mean numerical second derivative (a measure of local curvature) of the estimated GAM curve was more than one standard deviation away from 0 across the entire range of the predictor values. A threshold association is declared if an F-test indicates that the threshold model fit significantly better than the linear model.For each method, type I error for testing the existence of a threshold against the null hypothesis of a linear association was estimated. We also investigated the impact of the position of the true threshold on power, and precision and bias of the estimated threshold.Finally, we illustrate the methods by considering whether a threshold exists in the association between systolic blood pressure (SBP) and body mass index (BMI) in two data sets.
{"title":"Using Generalized Additive Models to Detect and Estimate Threshold Associations","authors":"A. Benedetti, M. Abrahamowicz, K. Leffondré, M. Goldberg, R. Tamblyn","doi":"10.2202/1557-4679.1172","DOIUrl":"https://doi.org/10.2202/1557-4679.1172","url":null,"abstract":"In a variety of research settings, investigators may wish to detect and estimate a threshold in the association between continuous variables. A threshold model implies a non-linear relationship, with the slope changing at an unknown location. Generalized additive models (GAMs) (Hastie and Tibshirani, 1990) estimate the shape of the non-linear relationship directly from the data and, thus, may be useful in this endeavour.We propose a method based on GAMs to detect and estimate thresholds in the association between a continuous covariate and a continuous dependent variable. Using simulations, we compare it with the maximum likelihood estimation procedure proposed by Hudson (1966).We search for potential thresholds in a neighbourhood of points whose mean numerical second derivative (a measure of local curvature) of the estimated GAM curve was more than one standard deviation away from 0 across the entire range of the predictor values. A threshold association is declared if an F-test indicates that the threshold model fit significantly better than the linear model.For each method, type I error for testing the existence of a threshold against the null hypothesis of a linear association was estimated. We also investigated the impact of the position of the true threshold on power, and precision and bias of the estimated threshold.Finally, we illustrate the methods by considering whether a threshold exists in the association between systolic blood pressure (SBP) and body mass index (BMI) in two data sets.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2009-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1172","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider the problem of testing s null hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to multiple testing procedures that control the familywise error rate (FWE). The closure method of Marcus et al. (1976) reduces the problem of constructing such procedures to one of constructing single tests that control the usual probability of a Type 1 error. It was shown by Sonnemann (1982, 2008) that any coherent multiple testing procedure can be constructed using the closure method. Moreover, it was shown by Sonnemann and Finner (1988) that any incoherent multiple testing procedure can be replaced by a coherent multiple testing procedure which is at least as good. In this paper, we first show an analogous result for dissonant and consonant multiple testing procedures. We show further that, in many cases, the improvement of the consonant multiple testing procedure over the dissonant multiple testing procedure may in fact be strict in the sense that it has strictly greater probability of detecting a false null hypothesis while still maintaining control of the FWE. Finally, we show how consonance can be used in the construction of some optimal maximin multiple testing procedures. This last result is especially of interest because there are very few results on optimality in the multiple testing literature.
{"title":"Consonance and the Closure Method in Multiple Testing","authors":"Joseph P. Romano, A. Shaikh, Michael Wolf","doi":"10.2202/1557-4679.1300","DOIUrl":"https://doi.org/10.2202/1557-4679.1300","url":null,"abstract":"Consider the problem of testing s null hypotheses simultaneously. In order to deal with the multiplicity problem, the classical approach is to restrict attention to multiple testing procedures that control the familywise error rate (FWE). The closure method of Marcus et al. (1976) reduces the problem of constructing such procedures to one of constructing single tests that control the usual probability of a Type 1 error. It was shown by Sonnemann (1982, 2008) that any coherent multiple testing procedure can be constructed using the closure method. Moreover, it was shown by Sonnemann and Finner (1988) that any incoherent multiple testing procedure can be replaced by a coherent multiple testing procedure which is at least as good. In this paper, we first show an analogous result for dissonant and consonant multiple testing procedures. We show further that, in many cases, the improvement of the consonant multiple testing procedure over the dissonant multiple testing procedure may in fact be strict in the sense that it has strictly greater probability of detecting a false null hypothesis while still maintaining control of the FWE. Finally, we show how consonance can be used in the construction of some optimal maximin multiple testing procedures. This last result is especially of interest because there are very few results on optimality in the multiple testing literature.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"7 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2009-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1300","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68717898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Likelihood-based inference for epidemic models can be challenging, in part due to difficulties in evaluating the likelihood. The problem is particularly acute in models of large-scale outbreaks, and unobserved or partially observed data further complicates this process. Here we investigate the performance of Markov Chain Monte Carlo and Sequential Monte Carlo algorithms for parameter inference, where the routines are based on approximate likelihoods generated from model simulations. We compare our results to a gold-standard data-augmented MCMC for both complete and incomplete data. We illustrate our techniques using simulated epidemics as well as data from a recent outbreak of Ebola Haemorrhagic Fever in the Democratic Republic of Congo and discuss situations in which we think simulation-based inference may be preferable to likelihood-based inference.
{"title":"Inference in Epidemic Models without Likelihoods","authors":"T. McKinley, A. Cook, R. Deardon","doi":"10.2202/1557-4679.1171","DOIUrl":"https://doi.org/10.2202/1557-4679.1171","url":null,"abstract":"Likelihood-based inference for epidemic models can be challenging, in part due to difficulties in evaluating the likelihood. The problem is particularly acute in models of large-scale outbreaks, and unobserved or partially observed data further complicates this process. Here we investigate the performance of Markov Chain Monte Carlo and Sequential Monte Carlo algorithms for parameter inference, where the routines are based on approximate likelihoods generated from model simulations. We compare our results to a gold-standard data-augmented MCMC for both complete and incomplete data. We illustrate our techniques using simulated epidemics as well as data from a recent outbreak of Ebola Haemorrhagic Fever in the Democratic Republic of Congo and discuss situations in which we think simulation-based inference may be preferable to likelihood-based inference.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2009-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1171","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68716137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To select items from a uni-dimensional scale to create a reduced scale for disease screening, Liu and Jin (2007) developed a non-parametric method based on binary risk classification. When the measure for the risk of a disease is ordinal or quantitative, and possibly subject to random censoring, this method is inefficient because it requires dichotomizing the risk measure, which may cause information loss and sample size reduction. In this paper, we modify Harrell's C-index (1984) such that the concordance probability, used as a measure of the discrimination accuracy of a scale with integer valued scores, can be estimated consistently when data are subject to random censoring. By evaluating changes in discrimination accuracy with the addition or deletion of items, we can select risk-related items without specifying parametric models. The procedure first removes the least useful items from the full scale, then, applies forward stepwise selection to the remaining items to obtain a reduced scale whose discrimination accuracy matches or exceeds that of the full scale. A simulation study shows the procedure to have good finite sample performance. We illustrate the method using a data set of patients at risk of developing Alzheimer's disease, who were administered a 40-item test of olfactory function before their semi-annual follow-up assessment.
{"title":"A Non-Parametric Approach to Scale Reduction for Uni-Dimensional Screening Scales","authors":"Xinhua Liu, Zhezhen Jin","doi":"10.2202/1557-4679.1094","DOIUrl":"https://doi.org/10.2202/1557-4679.1094","url":null,"abstract":"To select items from a uni-dimensional scale to create a reduced scale for disease screening, Liu and Jin (2007) developed a non-parametric method based on binary risk classification. When the measure for the risk of a disease is ordinal or quantitative, and possibly subject to random censoring, this method is inefficient because it requires dichotomizing the risk measure, which may cause information loss and sample size reduction. In this paper, we modify Harrell's C-index (1984) such that the concordance probability, used as a measure of the discrimination accuracy of a scale with integer valued scores, can be estimated consistently when data are subject to random censoring. By evaluating changes in discrimination accuracy with the addition or deletion of items, we can select risk-related items without specifying parametric models. The procedure first removes the least useful items from the full scale, then, applies forward stepwise selection to the remaining items to obtain a reduced scale whose discrimination accuracy matches or exceeds that of the full scale. A simulation study shows the procedure to have good finite sample performance. We illustrate the method using a data set of patients at risk of developing Alzheimer's disease, who were administered a 40-item test of olfactory function before their semi-annual follow-up assessment.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"23 1","pages":"1-22"},"PeriodicalIF":1.2,"publicationDate":"2009-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1094","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68715807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Introduction. When faced with a medical classification, clinicians often rank-order the likelihood of potential diagnoses, treatment choices, or prognoses as a way to focus on likely occurrences without dropping rarer ones from consideration. To know how well clinicians agree on such rankings might help extend the realm of clinical judgment farther into the purview of evidence-based medicine. If rankings by different clinicians agree better than chance, the order of assignments and their relative likelihoods may justifiably contribute to medical decisions. If the agreement is no better than chance, the ranking should not influence the medical decision.Background. Available rank-order methods measure agreement over a set of decision choices by two rankers or by a set of rankers over two choices (rank correlation methods), or an overall agreement over a set of choices by a set of rankers (Kendall's W), but will not measure agreement about a single decision choice across a set of rankers. Rating methods (e.g. kappa) assign multiple subjects to nominal categories rather than ranking possible choices about a single subject and will not measure agreement about a single decision choice across a set of rankers.Method. In this article, we pose an agreement coefficient A for measuring agreement among a set of clinicians about a single decision choice and compare several potential forms of A. A takes on the value 0 when agreement is random and 1 when agreement is perfect. It is shown that A = 1 - observed disagreement/maximum disagreement. A particular form of A is recommended and tables of 5% and 10% significant values of A are generated for common numbers of ranks and rankers.Examples. In the selection of potential treatment assignments by a Tumor Board to a patient with a neck mass, there is no significant agreement about any treatment. Another example involves ranking decisions about a proposed medical research protocol by an Institutional Review Board (IRB). The decision to pass a protocol with minor revisions shows agreement at the 5% significance level, adequate for a consistent decision.
{"title":"Measuring Agreement about Ranked Decision Choices for a Single Subject","authors":"R. Riffenburgh, P. Johnstone","doi":"10.2202/1557-4679.1113","DOIUrl":"https://doi.org/10.2202/1557-4679.1113","url":null,"abstract":"Introduction. When faced with a medical classification, clinicians often rank-order the likelihood of potential diagnoses, treatment choices, or prognoses as a way to focus on likely occurrences without dropping rarer ones from consideration. To know how well clinicians agree on such rankings might help extend the realm of clinical judgment farther into the purview of evidence-based medicine. If rankings by different clinicians agree better than chance, the order of assignments and their relative likelihoods may justifiably contribute to medical decisions. If the agreement is no better than chance, the ranking should not influence the medical decision.Background. Available rank-order methods measure agreement over a set of decision choices by two rankers or by a set of rankers over two choices (rank correlation methods), or an overall agreement over a set of choices by a set of rankers (Kendall's W), but will not measure agreement about a single decision choice across a set of rankers. Rating methods (e.g. kappa) assign multiple subjects to nominal categories rather than ranking possible choices about a single subject and will not measure agreement about a single decision choice across a set of rankers.Method. In this article, we pose an agreement coefficient A for measuring agreement among a set of clinicians about a single decision choice and compare several potential forms of A. A takes on the value 0 when agreement is random and 1 when agreement is perfect. It is shown that A = 1 - observed disagreement/maximum disagreement. A particular form of A is recommended and tables of 5% and 10% significant values of A are generated for common numbers of ranks and rankers.Examples. In the selection of potential treatment assignments by a Tumor Board to a patient with a neck mass, there is no significant agreement about any treatment. Another example involves ranking decisions about a proposed medical research protocol by an Institutional Review Board (IRB). The decision to pass a protocol with minor revisions shows agreement at the 5% significance level, adequate for a consistent decision.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"47 47 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1113","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68715496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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