Continuous(ly) missing outcome data in network meta-analysis: A one-stage pattern-mixture model approach

Appropriate handling of aggregate missing outcome data is necessary to minimise bias in the conclusions of systematic reviews. The two-stage pattern-mixture model has been already proposed to address aggregate missing continuous outcome data. While this approach is more proper compared with the exclusion of missing continuous outcome data and simple imputation methods, it does not offer flexible modelling of missing continuous outcome data to investigate their implications on the conclusions thoroughly. Therefore, we propose a one-stage pattern-mixture model approach under the Bayesian framework to address missing continuous outcome data in a network of interventions and gain knowledge about the missingness process in different trials and interventions. We extend the hierarchical network meta-analysis model for one aggregate continuous outcome to incorporate a missingness parameter that measures the departure from the missing at random assumption. We consider various effect size estimates for continuous data, and two informative missingness parameters, the informative missingness difference of means and the informative missingness ratio of means. We incorporate our prior belief about the missingness parameters while allowing for several possibilities of prior structures to account for the fact that the missingness process may differ in the network. The method is exemplified in two networks from published reviews comprising a different amount of missing continuous outcome data.

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A pattern-mixture model approach for handling missing continuous outcome data in longitudinal cluster randomized trials

Statistics in Medicine ◽

10.1002/sim.7418 ◽

2017 ◽

Vol 36 (26) ◽

pp. 4094-4105 ◽

Cited By ~ 4

Author(s):

Mallorie H. Fiero ◽

Chiu-Hsieh Hsu ◽

Melanie L. Bell

Keyword(s):

Mixture Model ◽

Randomized Trials ◽

Outcome Data ◽

Cluster Randomized Trials ◽

Continuous Outcome ◽

Pattern Mixture Model ◽

Mixture Model Approach ◽

Cluster Randomized ◽

Model Approach

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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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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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