Skip to main content
Top
Published in: BMC Medical Research Methodology 1/2014

Open Access 01-12-2014 | Research article

Network meta-analysis of (individual patient) time to event data alongside (aggregate) count data

Authors: Pedro Saramago, Ling-Hsiang Chuang, Marta O Soares

Published in: BMC Medical Research Methodology | Issue 1/2014

Login to get access

Abstract

Background

Network meta-analysis methods extend the standard pair-wise framework to allow simultaneous comparison of multiple interventions in a single statistical model. Despite published work on network meta-analysis mainly focussing on the synthesis of aggregate data, methods have been developed that allow the use of individual patient-level data specifically when outcomes are dichotomous or continuous. This paper focuses on the synthesis of individual patient-level and summary time to event data, motivated by a real data example looking at the effectiveness of high compression treatments on the healing of venous leg ulcers.

Methods

This paper introduces a novel network meta-analysis modelling approach that allows individual patient-level (time to event with censoring) and summary-level data (event count for a given follow-up time) to be synthesised jointly by assuming an underlying, common, distribution of time to healing. Alternative model assumptions were tested within the motivating example. Model fit and adequacy measures were used to compare and select models.

Results

Due to the availability of individual patient-level data in our example we were able to use a Weibull distribution to describe time to healing; otherwise, we would have been limited to specifying a uniparametric distribution. Absolute effectiveness estimates were more sensitive than relative effectiveness estimates to a range of alternative specifications for the model.

Conclusions

The synthesis of time to event data considering individual patient-level data provides modelling flexibility, and can be particularly important when absolute effectiveness estimates, and not just relative effect estimates, are of interest.
Appendix
Available only for authorised users
Literature
1.
go back to reference Bucher H, Guyatt G, Griffith L, Walter S: The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol. 1997, 50 (6): 683-691.CrossRefPubMed Bucher H, Guyatt G, Griffith L, Walter S: The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol. 1997, 50 (6): 683-691.CrossRefPubMed
2.
go back to reference Sutton A, Ades A, Cooper N, Abrams K: Use of indirect and mixed treatment comparisons for technology assessment. Pharmacoeconomics. 2008, 26 (9): 753-767.CrossRefPubMed Sutton A, Ades A, Cooper N, Abrams K: Use of indirect and mixed treatment comparisons for technology assessment. Pharmacoeconomics. 2008, 26 (9): 753-767.CrossRefPubMed
4.
go back to reference Saramago P, Manca A, Sutton AJ: Deriving input parameters for cost-effectiveness modelling: taxonomy of data types and approaches to their statistical synthesis. Value Health. 2012, 15 (5): 639-649.CrossRefPubMed Saramago P, Manca A, Sutton AJ: Deriving input parameters for cost-effectiveness modelling: taxonomy of data types and approaches to their statistical synthesis. Value Health. 2012, 15 (5): 639-649.CrossRefPubMed
5.
go back to reference Dias S, Sutton AJ, Ades AE, Welton NJ: Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making. 2013, 33 (5): 607-617.CrossRefPubMedPubMedCentral Dias S, Sutton AJ, Ades AE, Welton NJ: Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making. 2013, 33 (5): 607-617.CrossRefPubMedPubMedCentral
6.
go back to reference Saramago P, Sutton AJ, Cooper NJ, Manca A: Mixed treatment comparisons using aggregate- and individual-participant level data. Stat Med. 2012, 10; 31 (28): 3516-3536.CrossRef Saramago P, Sutton AJ, Cooper NJ, Manca A: Mixed treatment comparisons using aggregate- and individual-participant level data. Stat Med. 2012, 10; 31 (28): 3516-3536.CrossRef
7.
go back to reference Jansen J, Cope S: Network meta-analysis of individual and aggregate level data. Value Health. 2012, 15 (4): A159-CrossRef Jansen J, Cope S: Network meta-analysis of individual and aggregate level data. Value Health. 2012, 15 (4): A159-CrossRef
8.
go back to reference Donegan S, Williamson P, D’Alessandro U, Garner P, Smith C: Combining individual patient data and aggregate data in mixed treatment comparison meta-analysis: individual patient data may be beneficial if only for a subset of trials. Stat Med. 2013, 32 (6): 914-930.CrossRefPubMed Donegan S, Williamson P, D’Alessandro U, Garner P, Smith C: Combining individual patient data and aggregate data in mixed treatment comparison meta-analysis: individual patient data may be beneficial if only for a subset of trials. Stat Med. 2013, 32 (6): 914-930.CrossRefPubMed
9.
go back to reference Berlin J, Santanna J, Schmid C, Szczech L, Feldman H: Individual patient- versus group-level data meta-regressions for the investigation of treatment effect modifiers: ecological bias rears its ugly head. Stat Med. 2002, 21 (3): 371-387.CrossRefPubMed Berlin J, Santanna J, Schmid C, Szczech L, Feldman H: Individual patient- versus group-level data meta-regressions for the investigation of treatment effect modifiers: ecological bias rears its ugly head. Stat Med. 2002, 21 (3): 371-387.CrossRefPubMed
10.
go back to reference Riley R, Lambert P, Staessen J, Wang J, Gueyffier F, Thijs L, Boutitie F: Meta-analysis of continuous outcomes combining individual patient data and aggregate data. Stat Med. 2008, 27 (11): 1870-1893.CrossRefPubMed Riley R, Lambert P, Staessen J, Wang J, Gueyffier F, Thijs L, Boutitie F: Meta-analysis of continuous outcomes combining individual patient data and aggregate data. Stat Med. 2008, 27 (11): 1870-1893.CrossRefPubMed
11.
go back to reference Sutton AJ: Methods for Meta-Analysis in Medical Research. 2000, Chichester ; New York: J. Wiley Sutton AJ: Methods for Meta-Analysis in Medical Research. 2000, Chichester ; New York: J. Wiley
12.
go back to reference Welton NJ, Willis SR, Ades AE: Synthesis of survival and disease progression outcomes for health technology assessment of cancer therapies. Res Synth Method. 2010, 1: 239-257. doi: 10.1002/jrsm.21CrossRef Welton NJ, Willis SR, Ades AE: Synthesis of survival and disease progression outcomes for health technology assessment of cancer therapies. Res Synth Method. 2010, 1: 239-257. doi: 10.1002/jrsm.21CrossRef
13.
go back to reference Smith C, Williamson P, Marson A: An overview of methods and empirical comparison of aggregate data and individual patient data results for investigating heterogeneity in meta-analysis of time-to-event outcomes. J Eval Clin Pract. 2005, 11 (5): 468-478.CrossRefPubMed Smith C, Williamson P, Marson A: An overview of methods and empirical comparison of aggregate data and individual patient data results for investigating heterogeneity in meta-analysis of time-to-event outcomes. J Eval Clin Pract. 2005, 11 (5): 468-478.CrossRefPubMed
14.
go back to reference Woods B, Hawkins N, Scott D: Network meta-analysis on the log-hazard scale, combining count and hazard ratio statistics accounting for multi-arm trials: a tutorial. BMC Med Res Methodol. 2010, 10: 54-CrossRefPubMedPubMedCentral Woods B, Hawkins N, Scott D: Network meta-analysis on the log-hazard scale, combining count and hazard ratio statistics accounting for multi-arm trials: a tutorial. BMC Med Res Methodol. 2010, 10: 54-CrossRefPubMedPubMedCentral
15.
go back to reference Soares MO, Dumville JC, Ades AE, Welton NJ: Treatment comparisons for decision making: facing the problems of sparse and few data. J R Stat Soc A Stat Soc. 2014, 177: 259-279. doi: 10.1111/rssa.12010CrossRef Soares MO, Dumville JC, Ades AE, Welton NJ: Treatment comparisons for decision making: facing the problems of sparse and few data. J R Stat Soc A Stat Soc. 2014, 177: 259-279. doi: 10.1111/rssa.12010CrossRef
16.
go back to reference Sutton A, Kendrick D, Coupland C: Meta-analysis of individual- and aggregate-level data. Stat Med. 2008, 27 (5): 651-669.CrossRefPubMed Sutton A, Kendrick D, Coupland C: Meta-analysis of individual- and aggregate-level data. Stat Med. 2008, 27 (5): 651-669.CrossRefPubMed
17.
go back to reference Ashby RL, Gabe R, Ali S, Saramago P, Chuang LH, Adderley U, Bland JM, Cullum NA, Dumville JC, Iglesias CP, Soares MO, Stubbs NC, Torgerson DJ: VenUS IV (venous leg ulcer study IV): a randomised controlled trial of compression hosiery versus compression bandaging in the treatment of venous leg ulcers. Health Technology Assessment (forthcoming). 2014 Ashby RL, Gabe R, Ali S, Saramago P, Chuang LH, Adderley U, Bland JM, Cullum NA, Dumville JC, Iglesias CP, Soares MO, Stubbs NC, Torgerson DJ: VenUS IV (venous leg ulcer study IV): a randomised controlled trial of compression hosiery versus compression bandaging in the treatment of venous leg ulcers. Health Technology Assessment (forthcoming). 2014
18.
go back to reference Duby T, Hoffman D, Cameron J, Doblhoffbrown D, Cherry G, Ryan T: A randomized trial in the treatment of venous Leg ulcers comparing short stretch bandages, 4 layer bandage system, and a long stretch paste bandage system. Wounds-a Compendium Clin Res Pract. 1993, 5 (6): 276-279. Duby T, Hoffman D, Cameron J, Doblhoffbrown D, Cherry G, Ryan T: A randomized trial in the treatment of venous Leg ulcers comparing short stretch bandages, 4 layer bandage system, and a long stretch paste bandage system. Wounds-a Compendium Clin Res Pract. 1993, 5 (6): 276-279.
19.
go back to reference Scriven J, Taylor L, Wood Rgn A, Bell P, Naylor A, London N: A prospective randomised trial of four-layer versus short stretch compression bandages for the treatment of venous leg ulcers. Ann R Coll Surg Engl. 1998, 80 (3): 215-220.PubMedPubMedCentral Scriven J, Taylor L, Wood Rgn A, Bell P, Naylor A, London N: A prospective randomised trial of four-layer versus short stretch compression bandages for the treatment of venous leg ulcers. Ann R Coll Surg Engl. 1998, 80 (3): 215-220.PubMedPubMedCentral
20.
go back to reference Partsch H, Damstra R, Tazelaar D, Schuller-Petrovic S, Velders A, De Rooij M, Tjon Lim Sang R, Quinlan D: Multicentre, randomised controlled trial of four-layer bandaging versus short-stretch bandaging in the treatment of venous leg ulcers. Vasa. 2001, 30 (2): 108-113.CrossRefPubMed Partsch H, Damstra R, Tazelaar D, Schuller-Petrovic S, Velders A, De Rooij M, Tjon Lim Sang R, Quinlan D: Multicentre, randomised controlled trial of four-layer bandaging versus short-stretch bandaging in the treatment of venous leg ulcers. Vasa. 2001, 30 (2): 108-113.CrossRefPubMed
21.
go back to reference Ukat A, Konig M, Vanscheidt W, Munter K: Short-stretch versus multilayer compression for venous leg ulcers: a comparison of healing rates. J Wound Care. 2003, 12 (4): 139-143.CrossRefPubMed Ukat A, Konig M, Vanscheidt W, Munter K: Short-stretch versus multilayer compression for venous leg ulcers: a comparison of healing rates. J Wound Care. 2003, 12 (4): 139-143.CrossRefPubMed
22.
go back to reference Franks P, Moody M, Moffatt C, Martin R, Blewett R, Seymour E, Hildreth A, Hourican C, Collins J, Heron A: Randomized trial of cohesive short-stretch versus four-layer bandaging in the management of venous ulceration. Wound Repair Regen. 2004, 12 (2): 157-162.CrossRefPubMed Franks P, Moody M, Moffatt C, Martin R, Blewett R, Seymour E, Hildreth A, Hourican C, Collins J, Heron A: Randomized trial of cohesive short-stretch versus four-layer bandaging in the management of venous ulceration. Wound Repair Regen. 2004, 12 (2): 157-162.CrossRefPubMed
23.
go back to reference Junger M, Wollina U, Kohnen R, Rabe E: Efficacy and tolerability of an ulcer compression stocking for therapy of chronic venous ulcer compared with a below-knee compression bandage: results from a prospective, randomized, multicentre trial. Curr Med Res Opin. 2004, 20 (10): 1613-1623.CrossRefPubMed Junger M, Wollina U, Kohnen R, Rabe E: Efficacy and tolerability of an ulcer compression stocking for therapy of chronic venous ulcer compared with a below-knee compression bandage: results from a prospective, randomized, multicentre trial. Curr Med Res Opin. 2004, 20 (10): 1613-1623.CrossRefPubMed
24.
go back to reference Kralj B, Kosicek M: Randomised Comparative Trial of Single-Layer and Multi-Layer Bandages in the Treatment of Venous leg Ulcer. 1995, Harrogate, UK: 6th European Conference on Advances in Wound Management: 1995, 158-160. Kralj B, Kosicek M: Randomised Comparative Trial of Single-Layer and Multi-Layer Bandages in the Treatment of Venous leg Ulcer. 1995, Harrogate, UK: 6th European Conference on Advances in Wound Management: 1995, 158-160.
25.
go back to reference Polignano R, Bonadeo P, Gasbarro S, Allegra C: A randomised controlled study of four-layer compression versus Unna’s boot for venous ulcers. J Wound Care. 2004, 13 (1): 21-24.CrossRefPubMed Polignano R, Bonadeo P, Gasbarro S, Allegra C: A randomised controlled study of four-layer compression versus Unna’s boot for venous ulcers. J Wound Care. 2004, 13 (1): 21-24.CrossRefPubMed
26.
go back to reference Wilkinson E, Buttfield S, Cooper S, Young E: Trial of two bandaging systems for chronic venous leg ulcers. J Wound Care. 1997, 6 (7): 339-340.PubMed Wilkinson E, Buttfield S, Cooper S, Young E: Trial of two bandaging systems for chronic venous leg ulcers. J Wound Care. 1997, 6 (7): 339-340.PubMed
27.
go back to reference Colgan MP, Teevan M, McBride C, O’Sullivan L, Moore D, Shanik G: Cost Comparisons in the Management of Venous Ulceration. 1995, Harrogate, UK: 5th European Conference on Advances in Wound Management: 21–24 November 1995 Colgan MP, Teevan M, McBride C, O’Sullivan L, Moore D, Shanik G: Cost Comparisons in the Management of Venous Ulceration. 1995, Harrogate, UK: 5th European Conference on Advances in Wound Management: 21–24 November 1995
28.
go back to reference Blecken S, Villavicencio J, Kao T: Comparison of elastic versus nonelastic compression in bilateral venous ulcers: a randomized trial. J Vasc Surg. 2005, 42 (6): 1150-1155.CrossRefPubMed Blecken S, Villavicencio J, Kao T: Comparison of elastic versus nonelastic compression in bilateral venous ulcers: a randomized trial. J Vasc Surg. 2005, 42 (6): 1150-1155.CrossRefPubMed
29.
go back to reference Moffatt C, Edwards L, Collier M, Treadwell T, Miller M, Shafer L, Sibbald G, Brassard A, McIntosh A, Reyzelman A, Price P, Kraus SM, Walters SA, Harding K: A randomised controlled 8-week crossover clinical evaluation of the 3M coban 2 layer compression system versus profore to evaluate the product performance in patients with venous leg ulcers. Int Wound J. 2008, 5 (2): 267-279.CrossRefPubMed Moffatt C, Edwards L, Collier M, Treadwell T, Miller M, Shafer L, Sibbald G, Brassard A, McIntosh A, Reyzelman A, Price P, Kraus SM, Walters SA, Harding K: A randomised controlled 8-week crossover clinical evaluation of the 3M coban 2 layer compression system versus profore to evaluate the product performance in patients with venous leg ulcers. Int Wound J. 2008, 5 (2): 267-279.CrossRefPubMed
30.
go back to reference Szewczyk M, Jawie A, Cierzniakowska K, Cwajda-Bialasik J, Moscicka P: Comparison of the effectiveness of compression stockings and layer compression systems in venous ulceration treatment. Archives of Medical Science. 2010, 6 (5): 793-799.CrossRefPubMedPubMedCentral Szewczyk M, Jawie A, Cierzniakowska K, Cwajda-Bialasik J, Moscicka P: Comparison of the effectiveness of compression stockings and layer compression systems in venous ulceration treatment. Archives of Medical Science. 2010, 6 (5): 793-799.CrossRefPubMedPubMedCentral
31.
go back to reference Wong I, Andriessen A, Charles H, Thompson D, Lee D, So W, Abel M: Randomized controlled trial comparing treatment outcome of two compression bandaging systems and standard care without compression in patients with venous leg ulcers. J Eur Acad Dermatol Venereol. 2012, 26 (1): 102-110.CrossRefPubMed Wong I, Andriessen A, Charles H, Thompson D, Lee D, So W, Abel M: Randomized controlled trial comparing treatment outcome of two compression bandaging systems and standard care without compression in patients with venous leg ulcers. J Eur Acad Dermatol Venereol. 2012, 26 (1): 102-110.CrossRefPubMed
32.
go back to reference Iglesias C, Nelson E, Cullum N, Torgerson D: VenUS I: a randomised controlled trial of two types of bandage for treating venous leg ulcers. Health Technol Assess. 2004, 8 (29): iii, 1-iii, 105.CrossRef Iglesias C, Nelson E, Cullum N, Torgerson D: VenUS I: a randomised controlled trial of two types of bandage for treating venous leg ulcers. Health Technol Assess. 2004, 8 (29): iii, 1-iii, 105.CrossRef
33.
go back to reference Collett D: Modelling Survival Data in Medical Research. 2003, Boca Raton, Fla: Chapman & Hall/CRC, 2 Collett D: Modelling Survival Data in Medical Research. 2003, Boca Raton, Fla: Chapman & Hall/CRC, 2
34.
go back to reference Cooper N, Sutton A, Morris D, Ades A, Welton N: Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med. 2009, 28 (14): 1861-1881.CrossRefPubMed Cooper N, Sutton A, Morris D, Ades A, Welton N: Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med. 2009, 28 (14): 1861-1881.CrossRefPubMed
35.
go back to reference Lunn DJ, Thomas A, Best N, Spiegelhalter D: WinBUGS - a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing. 2000, 10 (4): 325-337.CrossRef Lunn DJ, Thomas A, Best N, Spiegelhalter D: WinBUGS - a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing. 2000, 10 (4): 325-337.CrossRef
36.
go back to reference Spiegelhalter DJ, Best NG, Carlin BR, van der Linde A: Bayesian measures of model complexity and fit. J R Stat Soc B Stat Soc. 2002, 64: 583-616.CrossRef Spiegelhalter DJ, Best NG, Carlin BR, van der Linde A: Bayesian measures of model complexity and fit. J R Stat Soc B Stat Soc. 2002, 64: 583-616.CrossRef
37.
go back to reference Ades A, Sculpher M, Sutton A, Abrams K, Cooper N, Welton N, Lu G: Bayesian methods for evidence synthesis in cost-effectiveness analysis. Pharmacoeconomics. 2006, 24 (1): 1-19.CrossRefPubMed Ades A, Sculpher M, Sutton A, Abrams K, Cooper N, Welton N, Lu G: Bayesian methods for evidence synthesis in cost-effectiveness analysis. Pharmacoeconomics. 2006, 24 (1): 1-19.CrossRefPubMed
38.
go back to reference StataCorp A: Stata Statistical Software: Release 12. 2011, College Station, TX: StataCorp LP StataCorp A: Stata Statistical Software: Release 12. 2011, College Station, TX: StataCorp LP
39.
go back to reference Akaike H: Information Theory and the Maximum Likelihood Principle. 1973, 2nd International Symposium in Information Theory: 1973, 267-281. Akaike H: Information Theory and the Maximum Likelihood Principle. 1973, 2nd International Symposium in Information Theory: 1973, 267-281.
40.
go back to reference O’Meara S, Tierney J, Cullum N, Bland J, Franks P, Mole T, Scriven M: Four layer bandage compared with short stretch bandage for venous leg ulcers: systematic review and meta-analysis of randomised controlled trials with data from individual patients. BMJ (Clinical research ed). 2009, 338 (7702): 1054-1057. O’Meara S, Tierney J, Cullum N, Bland J, Franks P, Mole T, Scriven M: Four layer bandage compared with short stretch bandage for venous leg ulcers: systematic review and meta-analysis of randomised controlled trials with data from individual patients. BMJ (Clinical research ed). 2009, 338 (7702): 1054-1057.
41.
go back to reference Guyot P, Ades AE, Ouwens MJ, Welton NJ: Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol. 2012, 12: 9-CrossRefPubMedPubMedCentral Guyot P, Ades AE, Ouwens MJ, Welton NJ: Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol. 2012, 12: 9-CrossRefPubMedPubMedCentral
42.
go back to reference Espinoza M: Heterogeneity in cost-effectiveness analysis: methods to explore the value of subgroups and individualised care in a collectively funded health system. 2012, University of York Espinoza M: Heterogeneity in cost-effectiveness analysis: methods to explore the value of subgroups and individualised care in a collectively funded health system. 2012, University of York
Metadata
Title
Network meta-analysis of (individual patient) time to event data alongside (aggregate) count data
Authors
Pedro Saramago
Ling-Hsiang Chuang
Marta O Soares
Publication date
01-12-2014
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2014
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-14-105

Other articles of this Issue 1/2014

BMC Medical Research Methodology 1/2014 Go to the issue