Design-Based Inference in a Mixture Model for Ordinal Variables for a Two Stage Stratified Design

Based on a rich dataset of recoveries donated by a debt collection business, recovery rates for non-performing loans taken from a single European country are modelled using linear regression, linear regression with Lasso, beta regression and inflated beta regression. We also propose a two-stage model: beta mixture model combined with a logistic regression model. The proposed model allowed us to model the multimodal distribution we found for these recovery rates. All models were built using loan characteristics, default data and collections data prior to purchase by the debt collection business. The intended use of the models was to estimate future recovery rates for improved risk assessment, capital requirement calculations and bad debt management. They were compared using a range of quantitative performance measures under K-fold cross validation. Among all the models, we found that the proposed two-stage beta mixture model performs best.

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Pattern-mixture model in network meta-analysis of binary missing outcome data: one-stage or two-stage approach?

BMC Medical Research Methodology ◽

10.1186/s12874-020-01205-6 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Loukia M. Spineli ◽

Katerina Papadimitropoulou ◽

Chrysostomos Kalyvas

Keyword(s):

Mixture Model ◽

Simulation Study ◽

Meta Analysis ◽

Credible Interval ◽

Outcome Data ◽

Systematic Bias ◽

Two Stage ◽

Pattern Mixture Model ◽

One Stage ◽

The One

Abstract Background Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The performance of the one-stage and the two-stage approaches has been documented extensively in the literature. However, little is known about how these approaches behave in the presence of missing outcome data (MOD), which are ubiquitous in clinical trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis using Bayesian methods to handle MOD appropriately. Methods We used 29 published networks to empirically compare the two approaches concerning the relative treatment effects of several competing interventions and the between-trial variance (τ2), while considering the extent and level of balance of MOD in the included trials. We additionally conducted a simulation study to compare the competing approaches regarding the bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and τ2 in the presence of moderate and large MOD. Results The empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. For these networks, the empirical results revealed slightly higher τ2 estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and τ2 when compared with the two-stage approach for large MOD. Conclusions Due to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

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A two-stage speaker adaptation approach for subspace Gaussian mixture model based nonnative speech recognition

10.21437/interspeech.2012-483 ◽

2012 ◽

Author(s):

Bo Li ◽

Khe Chai Sim

Keyword(s):

Speech Recognition ◽

Gaussian Mixture Model ◽

Mixture Model ◽

Gaussian Mixture ◽

Two Stage ◽

Model Based

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A mixture model for ordinal variables measured on semantic differential scales

Econometrics and Statistics ◽

10.1016/j.ecosta.2021.07.002 ◽

2021 ◽

Author(s):

Marica Manisera ◽

Paola Zuccolotto

Keyword(s):

Mixture Model ◽

Semantic Differential ◽

Ordinal Variables

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Pattern-mixture model in network meta-analysis of binary missing outcome data: one-stage or two-stage approach?

10.21203/rs.3.rs-39035/v1 ◽

2020 ◽

Author(s):

Loukia Maria Spineli ◽

Katerina Papadimitropoulou ◽

Chrysostomos Kalyvas

Keyword(s):

Empirical Study ◽

Mixture Model ◽

Simulation Study ◽

Meta Analysis ◽

Outcome Data ◽

Systematic Bias ◽

Two Stage ◽

Pattern Mixture Model ◽

One Stage ◽

The One

Abstract Background Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The advantages of the one-stage over the two-stage approach have been documented extensively in the literature. Little is known how these approaches behave in the presence of missing outcome data (MOD) which are ubiquitous in trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis Bayesian framework to handle MOD appropriately. Methods We used 29 published networks to empirically compare the two approaches with respect to the relative treatment effects of several competing interventions and the between-trial variance ( {\tau }^{2} ). We categorised the networks according to the extent and balance of MOD in the included trials. To complement the empirical study, we conducted a simulation study to compare the competing approaches regarding bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and {\tau }^{2} in the presence of moderate and large MOD. Results The empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. Furthermore, in these networks, the empirical results revealed slightly higher {\tau }^{2} estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and {\tau }^{2} when compared with the two-stage approach for large MOD. Conclusions Due to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

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Pattern-mixture model in network meta-analysis of binary missing outcome data: one-stage or two-stage approach?

10.21203/rs.3.rs-39035/v2 ◽

2020 ◽

Author(s):

Loukia Maria Spineli ◽

Katerina Papadimitropoulou ◽

Chrysostomos Kalyvas

Keyword(s):

Mixture Model ◽

Simulation Study ◽

Meta Analysis ◽

Credible Interval ◽

Outcome Data ◽

Systematic Bias ◽

Two Stage ◽

Pattern Mixture Model ◽

One Stage ◽

The One

Abstract Background: Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The performance of the one-stage and the two-stage approaches has been documented extensively in the literature. However, little is known about how these approaches behave in the presence of missing outcome data (MOD), which are ubiquitous in trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis using Bayesian methods to handle MOD appropriately.Methods: We used 29 published networks to empirically compare the two approaches concerning the relative treatment effects of several competing interventions and the between-trial variance ( ), while considering the extent and level of balance of MOD in the included trials. We additionally conducted a simulation study to compare the competing approaches regarding the bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and in the presence of moderate and large MOD.Results: The empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. For these networks, the empirical results revealed slightly higher estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and when compared with the two-stage approach for large MOD.Conclusions: Due to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

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Pattern-mixture model in network meta-analysis of binary missing outcome data: one-stage or two-stage approach?

10.21203/rs.3.rs-39035/v3 ◽

2020 ◽

Author(s):

Loukia Maria Spineli ◽

Katerina Papadimitropoulou ◽

Chrysostomos Kalyvas

Keyword(s):

Mixture Model ◽

Simulation Study ◽

Meta Analysis ◽

Credible Interval ◽

Outcome Data ◽

Systematic Bias ◽

Two Stage ◽

Pattern Mixture Model ◽

One Stage ◽

The One

Abstract Background: Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The performance of the one-stage and the two-stage approaches has been documented extensively in the literature. However, little is known about how these approaches behave in the presence of missing outcome data (MOD), which are ubiquitous in clinical trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis using Bayesian methods to handle MOD appropriately.Methods: We used 29 published networks to empirically compare the two approaches concerning the relative treatment effects of several competing interventions and the between-trial variance ( ), while considering the extent and level of balance of MOD in the included trials. We additionally conducted a simulation study to compare the competing approaches regarding the bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and in the presence of moderate and large MOD.Results: The empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. For these networks, the empirical results revealed slightly higher estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and when compared with the two-stage approach for large MOD.Conclusions: Due to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

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Modelling Recovery Rates for Non-performing Loans

10.20944/preprints201902.0135.v1 ◽

2019 ◽

Author(s):

Anthony Bellotti ◽

Hui Ye

Keyword(s):

Linear Regression ◽

Mixture Model ◽

Debt Management ◽

Beta Regression ◽

Two Stage ◽

Data Set ◽

Recovery Rates ◽

Debt Collection ◽

Rich Data ◽

Beta Mixture Model

Based on a rich data set of recoveries donated by a debt collection business, recovery rates for non-performing loans taken from a single European country are modelled using linear regression, linear regression with Lasso, beta regression and inflated beta regression. We also propose a two-stage model: beta mixture model combined with a logistic regression model. The proposed model allows us to model the multimodal distribution we find for these recovery rates. All models are built using loan characteristics, default data and collections data prior to purchase by the debt collection business. The intended use of the models is to estimate future recovery rates for improved risk assessment, capital requirement calculations and bad debt management. They are compared using a range of quantitative performance measures under K-fold cross validation. Among all the models, we find that the proposed two-stage beta mixture model performs best.

Download Full-text