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A framework for longitudinal latent factor modelling of treatment response in clinical trials with applications to Psoriatic Arthritis and Rheumatoid Arthritis

Published: 01 June 2024 Publication History

Abstract

Objective:

Clinical trials involve the collection of a wealth of data, comprising multiple diverse measurements performed at baseline and follow-up visits over the course of a trial. The most common primary analysis is restricted to a single, potentially composite endpoint at one time point. While such an analytical focus promotes simple and replicable conclusions, it does not necessarily fully capture the multi-faceted effects of a drug in a complex disease setting. Therefore, to complement existing approaches, we set out here to design a longitudinal multivariate analytical framework that accepts as input an entire clinical trial database, comprising all measurements, patients, and time points across multiple trials.

Methods:

Our framework composes probabilistic principal component analysis with a longitudinal linear mixed effects model, thereby enabling clinical interpretation of multivariate results, while handling data missing at random, and incorporating covariates and covariance structure in a computationally efficient and principled way.

Results:

We illustrate our approach by applying it to four phase III clinical trials of secukinumab in Psoriatic Arthritis (PsA) and Rheumatoid Arthritis (RA). We identify three clinically plausible latent factors that collectively explain 74.5% of empirical variation in the longitudinal patient database. We estimate longitudinal trajectories of these factors, thereby enabling joint characterisation of disease progression and drug effect. We perform benchmarking experiments demonstrating our method’s competitive performance at estimating average treatment effects compared to existing statistical and machine learning methods, and showing that our modular approach leads to relatively computationally efficient model fitting.

Conclusion:

Our multivariate longitudinal framework has the potential to illuminate the properties of existing composite endpoint methods, and to enable the development of novel clinical endpoints that provide enhanced and complementary perspectives on treatment response.

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References

[1]
U S Department of Health and Human Services, Multiple endpoints in clinical trials guidance for industry, 2017, Available from: https://www.fda.gov/files/drugs/published/Multiple-Endpoints-in-Clinical-Trials-Guidance-for-Industry.pdf.
[2]
Pocock SJ., Geller NL., Tsiatis AA., The analysis of multiple endpoints in clinical trials, Biometrics 43 (3) (1987) 487–498. Available from: http://www.jstor.org/stable/2531989.
[3]
An X., Yang Q., Bentler PM., A latent factor linear mixed model for high-dimensional longitudinal data analysis, Stat. Med. 32 (24) (2013) 4229–4239.
[4]
Hedeker D., Gibbons RD., Longitudinal Data Analysis, John Wiley & Sons, 2006.
[5]
Diggle PJ., Heagerty P., Liang KY., Zeger SL., Analysis of Longitudinal Data, second ed., Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, 2002.
[6]
Singer JD., Willett JB., Willett JB., et al., Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence, Oxford University Press, 2003.
[7]
Fitzmaurice GM., Ravichandran C., A primer in longitudinal data analysis, Circulation 118 (19) (2008) 2005–2010.
[8]
Box G., Jenkins G., Reinsel G., Time Series Analysis, Forecasting and Control, Prentice Hall, Englewood Clifs. NJ, 1994.
[9]
Vandemeulebroecke M., Bornkamp B., Krahnke T., Mielke J., Monsch A., Quarg P., A longitudinal item response theory model to characterize cognition over time in elderly subjects, CPT: Pharm. Syst. Pharmacol. 6 (9) (2017) 635–641.
[10]
Rasch G., Probabilistic Models for Some Intelligence and Attainment Tests, ERIC, 1993.
[11]
Hays RD., Morales LS., Reise SP., Item response theory and health outcomes measurement in the 21st century, Med. Care 38 (9 Suppl) (2000) II28.
[12]
Embretson SE., Reise SP., Item Response Theory, Psychology Press, 2013.
[13]
Barbieri A., Peyhardi J., Conroy T., Gourgou S., Lavergne C., Mollevi C., Item response models for the longitudinal analysis of health-related quality of life in cancer clinical trials, BMC Med. Res. Methodol. 17 (1) (2017) 1–13.
[14]
Darrell Bock R., Lieberman M., Fitting a response model forn dichotomously scored items, Psychometrika 35 (2) (1970) 179–197.
[15]
Muthén B., Contributions to factor analysis of dichotomous variables, Psychometrika 43 (4) (1978) 551–560.
[16]
Moustaki I., Knott M., Generalized latent trait models, Psychometrika 65 (3) (2000) 391–411.
[17]
McArdle JJ., Epstein D., Latent growth curves within developmental structural equation models, Child Dev. (1987) 110–133.
[18]
Preacher KJ., Wichman AL., MacCallum RC., Briggs NE., Latent Growth Curve Modeling, Sage, 2008.
[19]
Duncan TE., Duncan SC., Strycker LA., An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Applications, Routledge, 2013.
[20]
Carvalho CM., Chang J., Lucas JE., Nevins JR., Wang Q., West M., High-dimensional sparse factor modeling: applications in gene expression genomics, J. Am. Stat. Assoc. 103 (484) (2008) 1438–1456.
[21]
Broët P., Richardson S., Radvanyi F., Bayesian hierarchical model for identifying changes in gene expression from microarray experiments, J. Comput. Biol. 9 (4) (2002) 671–683.
[22]
West M., Blanchette C., Dressman H., Huang E., Ishida S., Spang R., et al., Predicting the clinical status of human breast cancer by using gene expression profiles, Proc. Natl. Acad. Sci. 98 (20) (2001) 11462–11467.
[23]
Lee KE., Sha N., Dougherty ER., Vannucci M., Mallick BK., Gene selection: a Bayesian variable selection approach, Bioinformatics 19 (1) (2003) 90–97.
[24]
Bae K., Mallick BK., Gene selection using a two-level hierarchical Bayesian model, Bioinformatics 20 (18) (2004) 3423–3430.
[25]
Joo J., Williamson SA., Vazquez AI., Fernandez JR., Bray MS., Advanced dietary patterns analysis using sparse latent factor models in young adults, J. Nutr. 148 (12) (2018) 1984–1992.
[26]
Liu Q., Cheng B., Jin Y., Hu P., Bayesian tensor factorization-drive breast cancer subtyping by integrating multi-omics data, J. Biomed. Inform. 125 (2022).
[27]
Chu J., Sun Z., Dong W., Shi J., Huang Z., On learning disentangled representations for individual treatment effect estimation, J. Biomed. Inform. 124 (2021).
[28]
Bryk AS., Raudenbush SW., Application of hierarchical linear models to assessing change, Psychol. Bull. 101 (1) (1987) 147.
[29]
Rogosa DR., Willett JB., Understanding correlates of change by modeling individual differences in growth, Psychometrika 50 (2) (1985) 203–228.
[30]
Venables WN., Ripley BD., Random and mixed effects, in: Modern Applied Statistics with S, Springer, 2002, pp. 271–300.
[31]
Davidian M., Giltinan DM., Nonlinear models for repeated measurement data: an overview and update, J. Agric. Biol. Environ. Stat. 8 (4) (2003) 387–419.
[32]
Todem D., Kim K., Lesaffre E., Latent-variable models for longitudinal data with bivariate ordinal outcomes, Stat. Med. 26 (5) (2007) 1034–1054.
[33]
Laffont CM., Vandemeulebroecke M., Concordet D., Multivariate analysis of longitudinal ordinal data with mixed effects models, with application to clinical outcomes in osteoarthritis, J. Amer. Statist. Assoc. 109 (507) (2014) 955–966.
[34]
Bianconcini S., Bollen KA., The latent variable-autoregressive latent trajectory model: A general framework for longitudinal data analysis, Struct. Equation Model.: Multidiscip. J. 25 (5) (2018) 791–808.
[35]
Tipping ME., Bishop CM., Probabilistic principal component analysis, J. R. Stat. Soc. Ser. B Stat. Methodol. 61 (1999) 611–622. Available from: https://www.jstor.org/stable/2680726.
[36]
Pearson K., LIII. on lines and planes of closest fit to systems of points in space, Lond. Edinb. Dublin Philos. Mag. J. Sci. 2 (11) (1901) 559–572.
[37]
Sportisse A., Boyer C., Josses J., Estimation and imputation in probabilistic principal component analysis with missing not at random data, Adv. Neural Inf. Process. Syst. (2020) 33.
[38]
Peterson LE., Partitioning large-sample microarray-based gene expression profiles using principal components analysis, Comput. Methods Programs Biomed. 70 (2) (2003) 107–119.
[39]
Oba S., Ma Sato., Takemasa I., Monden M., Ki Matsubara., Ishii S., A Bayesian missing value estimation method for gene expression profile data, Bioinformatics 19 (16) (2003) 2088–2096.
[40]
Menaga D., Revathi S., Probabilistic principal component analysis (PPCA) based dimensionality reduction and deep learning for cancer classification, in: Intelligent Computing and Applications: Proceedings of ICICA 2019, Springer, 2021, pp. 353–368.
[41]
Alavi M., Visentin DC., Thapa DK., Hunt GE., Watson R., Cleary M., Exploratory factor analysis and principal component analysis in clinical studies: Which one should you use, J. Adv. Nurs. 76 (8) (2020) 1886–1889.
[42]
RdO Santos., Gorgulho BM., MAd Castro., Fisberg RM., Marchioni DM., Baltar VT., Principal component analysis and factor analysis: Differences and similarities in nutritional epidemiology application, Rev. Bras. Epidemiol. (2019) 22.
[43]
Bédard A., Garcia-Aymerich J., Sanchez M., Moual N.Le., Clavel-Chapelon F., Boutron-Ruault MC., et al., Confirmatory factor analysis compared with principal component analysis to derive dietary patterns: a longitudinal study in adult women, J. Nutr. 145 (7) (2015) 1559–1568.
[44]
Laird NM., Ware JH., Random-effects models for longitudinal data, Biometrics (1982) 963–974.
[45]
Lindstrom MJ., Bates DM., Nonlinear mixed effects models for repeated measures data, Biometrics (1990) 673–687.
[46]
Lindstrom MJ., Bates DM., Newton—Raphson and EM algorithms for linear mixed-effects models for repeated-measures data, J. Am. Stat. Assoc. 83 (404) (1988) 1014–1022.
[47]
Vonesh E., Chinchilli VM., Linear and Nonlinear Models for the Analysis of Repeated Measurements, CRC Press, 1996.
[48]
Searle SR., Casella G., McCulloch CE., Variance Components, John Wiley & Sons, 2009.
[49]
Pinheiro J., Bates D., Mixed-Effects Models in S and S-PLUS, Springer science & business media, 2006.
[50]
Pinheiro J., Bates D., DebRoy S., Sarkar D., R Core Team, Nlme: Linear and nonlinear mixed effects models, 2022.
[51]
Proust-Lima C., Philipps V., Liquet B., Estimation of extended mixed models using latent classes and latent processes: the R package lcmm, 2015, arXiv preprint arXiv:150300890.
[52]
Zeger SL., Karim MR., Generalized linear models with random effects; a Gibbs sampling approach, J. Am. Stat. Assoc. 86 (413) (1991) 79–86.
[53]
DM. Bates, DG. Watts, Nonlinear regression analysis and lts applications, 519.536, B3; 1988.
[54]
Dunson DB., Bayesian latent variable models for clustered mixed outcomes, J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 62 (2) (2000) 355–366.
[55]
TJ. Hastie, Generalized additive models, in: Statistical Models in S, Routledge, 2017, pp. 249–307.
[56]
Wood SN., Stable and efficient multiple smoothing parameter estimation for generalized additive models, J. Am. Stat. Assoc. 99 (467) (2004) 673–686.
[57]
Wood SN., Mgcv: GAMs and generalized ridge regression for R, R news 1 (2) (2001) 20–25.
[58]
Wood S., Generalized Additive Models : An Introduction with R, Chapman and Hall/CRC, 2017, Available from: https://www.taylorfrancis.com/books/generalized-additive-models-simon-wood/10.1201/9781315370279.
[59]
Marra G., Wood SN., Coverage properties of confidence intervals for generalized additive model components, Scand. J. Stat. 39 (1) (2012) 53–74.
[60]
Aston JA., Chiou JM., Evans JP., Linguistic pitch analysis using functional principal component mixed effect models, J. R. Stat. Soc.: Ser. C (Appl. Stat.) 59 (2) (2010) 297–317.
[61]
Pickles A., Croudace T., Latent mixture models for multivariate and longitudinal outcomes, Stat. Methods Med. Res. 19 (3) (2010) 271–289.
[62]
Liu LC., Hedeker D., A mixed-effects regression model for longitudinal multivariate ordinal data, Biometrics 62 (1) (2006) 261–268.
[63]
Fieuws S., Verbeke G., Pairwise fitting of mixed models for the joint modeling of multivariate longitudinal profiles, Biometrics 62 (2) (2006) 424–431.
[64]
McInnes IB., Schett G., The pathogenesis of rheumatoid arthritis, N. Engl. J. Med. 365 (23) (2011) 2205–2219. Available from: https://doi.org/10.1056/NEJMra1004965.
[65]
Tahir H., Deodhar A., Genovese M., Takeuchi T., Aelion J., Van den Bosch F., et al., Secukinumab in active rheumatoid arthritis after Anti-TNFalpha therapy: A randomized, double-blind placebo-controlled phase 3 study, Rheumatol. Ther. 4 (2) (2017) 475–488.
[66]
Smolen JS., Aletaha D., McInnes IB., Rheumatoid arthritis, Lancet (London, England) 388 (10055) (2016) 2023–2038.
[67]
Blair HA., Secukinumab: A review in psoriatic arthritis, Drugs (2021) 1–12.
[68]
Hackett S., Coates L., et al., Psoriatic arthritis: an up to date overview, Indian J. Rheumatol. 15 (5) (2020) 45.
[69]
Ogdie A., Coates LC., Gladman DD., Treatment guidelines in psoriatic arthritis, Rheumatology 59 (1) (2020) i37–i46.
[70]
Toussi A., Maverakis N., Le ST., Sarkar S., Raychaudhuri SK., Raychaudhuri SP., Updated therapies for the management of psoriatic arthritis, Clin. Immunol. (2020).
[71]
Garcia-Montoya L., Marzo-Ortega H., The role of secukinumab in the treatment of psoriatic arthritis and ankylosing spondylitis, Ther. Adv. Musculoskelet. Dis. 10 (9) (2018) 169–180. Available from: https://doi.org/10.1177/1759720X18787766.
[72]
Gottlieb AB., Mease PJ., Kirkham B., Nash P., Combe Balsa.B.A.C., Rech J., et al., Secukinumab efficacy in psoriatic arthritis: Machine learning and meta-analysis of four phase 3 trials, J. Clin. Rheumatol. (2020).
[73]
Felson DT., Anderson JJ., Boers M., et al., The American college of rheumatology preliminary core set of disease activity measures for rheumatoid arthritis clinical trials. The committee on outcome measures in rheumatoid arthritis clinical trials, Arthritis Rheum. 36 (6) (1993) 729–740.
[74]
Hickey GL., Philipson P., Jorgensen A., Kolamunnage-Dona R., Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues, BMC Med. Res. Methodol. 16 (1) (2016).
[75]
Novartis Pharmaceuticals, A Phase III, RandOmized, Double-Blind, Placebo Controlled Multi-Center Study of Subcutaneous Secukinumab (150 Mg and 300 Mg) in Prefilled Syringe To Demonstrate Efficacy (Including Inhibition of Structural Damage), Safety, and Tolerability Up To 2 Years in Subjects with Active Psoriatic Arthritis (FUTURE 5), clinicaltrials.gov, 2020, Available from: https://clinicaltrials.gov/study/NCT02404350, Submitted: March 16 2015.
[76]
Novartis Pharmaceuticals, A Phase III RandOmized, Double-Blind, Placebo-Controlled Multicenter Study of Subcutaneous Secukinumab in Prefilled Syringes To Demonstrate the Efficacy At 24 Weeks and To Assess the Long Term Efficacy, Safety and Tolerability Up To 5 Years in Patients with Active Psoriatic Arthritis, clinicaltrials.gov, 2020, Available from: https://clinicaltrials.gov/study/NCT01752634 Submitted: October 23 2012.
[77]
McInnes IB., Mease PJ., Kivitz AJ., Nash P., Rahman P., Rech J., et al., Long-term efficacy and safety of secukinumab in patients with psoriatic arthritis: 5-year (end-of-study) results from the phase 3 FUTURE 2 study, Lancet Rheumatol. 2 (4) (2020) e227–e235. Available from: https://www.sciencedirect.com/science/article/pii/S2665991320300369.
[78]
Mease PJ., Landewé R., Rahman P., Tahir H., Singhal A., Boettcher E., et al., Secukinumab provides sustained improvement in signs and symptoms and low radiographic progression in patients with psoriatic arthritis: 2-year (end-of-study) results from the FUTURE 5 study, RMD Open 7 (2) (2021).
[79]
Novartis Pharmaceuticals, A RandOmized, Double-Blind, Placebo-Controlled Study of Secukinumab To Demonstrate the Efficacy At 24 Weeks and To Assess the Safety, Tolerability and Long Term Efficacy Up To 2 Years in Patients with Active Rheumatoid Arthritis Who Have an Inadequate Response To Anti-TNFalpha Agents (CAIN457F2302) and a Three Year Extension Study To Evaluate the Long Term Efficacy, Safety and Tolerability of Secukinumab in Patients with Active Rheumatoid Arthritis (CAIN457F2302E1), clinicaltrials.gov, 2017, Available from: https://clinicaltrials.gov/study/NCT01377012 Submitted: June 17 2011.
[80]
Novartis Pharmaceuticals, A RandOmized Double-Blind Placebo- and Active-Controlled Study of Secukinumab To Demonstrate the Efficacy At 24 Weeks and To Assess the Safety, Tolerability and Long Term Efficacy Up To 1 Year in Patients with Active Rheumatoid Arthritis Who Have an Inadequate Response To Anti-TNF-Alpha Agents (CAIN457F2309) and a Four Year Extension Study To Evaluate the Long Term Efficacy, Safety and Tolerability of Secukinumab in Patients with Active Rheumatoid Arthritis (CAIN457F2309E1), clinicaltrials.gov, 2016, Available from: https://clinicaltrials.gov/study/NCT01350804 Novartis Pharmaceuticals.
[81]
Blanco FJ., Möricke R., Dokoupilova E., Codding C., Neal J., Andersson M., et al., Secukinumab in active rheumatoid arthritis: A phase III randomized, double-blind, active comparator- and placebo-controlled study, Arthritis Rheumatol. (Hoboken, NJ) 69 (6) (2017) 1144–1153.
[82]
Mallon AM., Häring DA., Dahlke F., Aarden P., Afyouni S., Delbarre D., et al., Advancing data science in drug development through an innovative computational framework for data sharing and statistical analysis, BMC Med. Res. Methodol. 21 (1) (2021) 1–11.
[83]
C. Bishop, Pattern Recognition and Machine Learning | Christopher Bishop | Springer, first ed., Springer-Verlag New York, 2006, Available from:.
[84]
Zwick WR., Velicer WF., Comparison of five rules for determining the number of components to retain, Psychol. Bull. 99 (3) (1986) 432–442. Place: US Publisher: American Psychological Association.
[85]
Hayton JC., Allen DG., Scarpello V., Factor retention decisions in exploratory factor analysis: a tutorial on parallel analysis, Organ. Res. Methods 7 (2) (2004) 191–205. Available from: https://doi.org/10.1177/1094428104263675, Publisher: SAGE Publications Inc.
[86]
Horn JL., A Rationale and test for the number of factors in factor analysis, Psychometrika. 30 (1965) 179–185.
[87]
Glorfeld LW., An improvement on Horn’s parallel analysis methodology for selecting the correct number of factors to retain, Educ. Psychol. Meas. 55 (3) (1995) 377–393. Place: US Publisher: Sage Publications.
[88]
Dinno A., Exploring the sensitivity of horn’s parallel analysis to the distributional form of random data, Multivar. Behav. Res. 44 (3) (2009) 362–388. Publisher: Routledge _eprint: https://doi.org/10.1080/00273170902938969 Available from: https://doi.org/10.1080/00273170902938969.
[89]
Dinno A., Implementing Horn’s parallel analysis for principal component analysis and factor analysis, Stata J. 9 (2) (2009) 291–298. Publisher: SAGE Publications. Available from: https://doi.org/10.1177/1536867X0900900207.
[90]
Wood SN., Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models, J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 73 (1) (2011) 3–36.
[91]
Macdougall J., Analysis of dose–response studies—Emax model, in: Ting N. (Ed.), Dose Finding in Drug Development, in: Statistics for Biology and Health, Springer, New York, NY, 2006, pp. 127–145. Available from: https://doi.org/10.1007/0-387-33706-7_9.
[92]
JC. Pinheiro, D. Bates, Mixed-Effects Models in S and S-PLUS, Springer Science & Business Media, 2009, Google-Books-ID: y54QDUTmvDcC.
[93]
Fisher ZF., Kim Y., Fredrickson BL., Pipiras V., Penalized estimation and forecasting of multiple subject intensive longitudinal data, Psychometrika 87 (2) (2022) 1–29. Available from: https://doi.org/10.1007/s11336-021-09825-7.
[94]
Murphy KP., Probabilistic Machine Learning: An Introduction, MIT Press, 2022, Available from: probml.ai.
[95]
Cho K., Van Merriënboer B., Gulcehre C., Bahdanau D., Bougares F., Schwenk H., et al., Learning phrase representations using RNN encoder–decoder for statistical machine translation, 2014, arXiv preprint arXiv:14061078.
[96]
Hochreiter S., Schmidhuber J., Long short-term memory, Neural Comput. 9 (8) (1997) 1735–1780.
[97]
Kulldorff G., On the conditions for consistency and asymptotic efficiency of maximum likelihood estimates, Scand. Actuar. J. 1957 (3–4) (1957) 129–144. Publisher: Taylor & Francis _eprint: https://doi.org/10.1080/03461238.1957.10405966 Available from: https://doi.org/10.1080/03461238.1957.10405966.
[98]
Murphy KP., Machine Learning: A Probabilistic Perspective, in: Adaptive computation and machine learning series, MIT Press, Cambridge, MA, 2012.
[99]
Medvidovic N., Rosenblum DS., Redmiles DF., Robbins JE., Modeling software architectures in the Unified Modeling Language, ACM Trans. Softw. Eng. Methodol. 11 (1) (2002) 2–57. Available from: https://dl.acm.org/doi/10.1145/504087.504088.
[100]
Nicholson G., Blangiardo M., Briers M., Diggle PJ., Fjelde TE., Ge H., et al., Interoperability of statistical models in pandemic preparedness: principles and reality, Stat. Sci. 37 (2) (2022) 183–206.

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            Published In

            cover image Journal of Biomedical Informatics
            Journal of Biomedical Informatics  Volume 154, Issue C
            Jun 2024
            142 pages

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            Elsevier Science

            San Diego, CA, United States

            Publication History

            Published: 01 June 2024

            Author Tags

            1. Longitudinal latent factor analysis
            2. Linear mixed-effects model
            3. Multilevel linear models
            4. Probabilistic principal component analysis
            5. Dimensionality reduction
            6. Missing data
            7. Clinical trials
            8. Psoriatic Arthritis
            9. Rheumatoid Arthritis

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