Abstract
Accurate characterization of exposure–response relationship of clinical endpoints is important in drug development to identify optimal dose regimens. Endpoints with ≥ 10 ordered categories are typically analyzed as continuous. This manuscript aims to show circumstances where it is advantageous to analyze such data as ordered categorical. The results of continuous and categorical analyses are compared in a latent-variable based Indirect Response modeling framework for the longitudinal modeling of Mayo scores, ranging from 0 to 12, which is commonly used as a composite endpoint to measure the severity of ulcerative colitis (UC). Exposure response modeling of Mayo scores is complicated by the fact that studies typically include induction and maintenance phases with re-randomizations and other response-driven dose adjustments. The challenges are illustrated in this work by analyzing data collected from 3 phase II/III trials of golimumab in patients with moderate-to-severe UC. Visual predictive check was used for model evaluations. The ordered categorical approach is shown to be accurate and robust compared to the continuous approach. In addition, a disease progression model with an empirical bi-phasic rate of onset was found to be superior to the commonly used placebo model with one onset rate. An application of this modeling approach in guiding potential dose-adjustment was illustrated.
Similar content being viewed by others
References
Overgaard RV, Ingwersen SH, Tornoe CW (2015) Establishing good practices for exposure-response analysis of clinical endpoints in drug development. CPT 4(10):565–575. https://doi.org/10.1002/psp4.12015
Sharma A, Jusko WJ (1996) Characterization of four basic models of indirect pharmacodynamic responses. J Pharmacokinet Biopharm 24(6):611–635
Hu C (2014) Exposure-response modeling of clinical end points using latent variable indirect response models. CPT 3:e117. https://doi.org/10.1038/psp.2014.15
Hutmacher MM, Krishnaswami S, Kowalski KG (2008) Exposure-response modeling using latent variables for the efficacy of a JAK3 inhibitor administered to rheumatoid arthritis patients. J Pharmacokinet Pharmacodyn 35:139–157
Hu C, Xu Z, Mendelsohn A, Zhou H (2013) Latent variable indirect response modeling of categorical endpoints representing change from baseline. J Pharmacokinet Pharmacodyn 40(1):81–91
Hu C, Szapary PO, Mendelsohn AM, Zhou H (2014) Latent variable indirect response joint modeling of a continuous and a categorical clinical endpoint. J Pharmacokinet Pharmacodyn 41(4):335–349. https://doi.org/10.1007/s10928-014-9366-0
Hu C, Zhou H (2016) Improvement in latent variable indirect response joint modeling of a continuous and a categorical clinical endpoint in rheumatoid arthritis. J Pharmacokinet Pharmacodyn 43(1):45–54
Hu C, Randazzo B, Sharma A, Zhou H (2017) Improvement in latent variable indirect response modeling of multiple categorical clinical endpoints: application to modeling of guselkumab treatment effects in psoriatic patients. J Pharmacokinet Pharmacodyn 44(5):437–448. https://doi.org/10.1007/s10928-017-9531-3
Liu Q, Shepherd BE, Li C, Harrell FE Jr (2017) Modeling continuous response variables using ordinal regression. Stat Med 36(27):4316–4335. https://doi.org/10.1002/sim.7433
Rutgeerts P, Feagan BG, Marano CW, Padgett L, Strauss R, Johanns J, Adedokun OJ, Guzzo C, Zhang H, Colombel JF, Reinisch W, Gibson PR, Sandborn WJ, group P-Is (2015) Randomised clinical trial: a placebo-controlled study of intravenous golimumab induction therapy for ulcerative colitis. Aliment Pharmacol Ther 42(5):504–514. https://doi.org/10.1111/apt.13291
Rutgeerts P, Sandborn WJ, Feagan BG, Reinisch W, Olson A, Johanns J, Travers S, Rachmilewitz D, Hanauer SB, Lichtenstein GR, de Villiers WJ, Present D, Sands BE, Colombel JF (2005) Infliximab for induction and maintenance therapy for ulcerative colitis. N Engl J Med 353(23):2462–2476. https://doi.org/10.1056/NEJMoa050516
Sandborn WJ, van Assche G, Reinisch W, Colombel JF, D’Haens G, Wolf DC, Kron M, Tighe MB, Lazar A, Thakkar RB (2012) Adalimumab induces and maintains clinical remission in patients with moderate-to-severe ulcerative colitis. Gastroenterology 142(2):257–265. https://doi.org/10.1053/j.gastro.2011.10.032
Braun J, Deodhar A, Inman RD, van der Heijde D, Mack M, Xu S, Hsu B (2012) Golimumab administered subcutaneously every 4 weeks in ankylosing spondylitis: 104-week results of the GO-RAISE study. Ann Rheum Dis 71(5):661–667. https://doi.org/10.1136/ard.2011.154799
Kavanaugh A, van der Heijde D, McInnes IB, Mease P, Krueger GG, Gladman DD, Gomez-Reino J, Papp K, Baratelle A, Xu W, Mudivarthy S, Mack M, Rahman MU, Xu Z, Zrubek J, Beutler A (2012) Golimumab in psoriatic arthritis: one-year clinical efficacy, radiographic, and safety results from a phase III, randomized, placebo-controlled trial. Arthritis Rheum 64(8):2504–2517. https://doi.org/10.1002/art.34436
Kay J, Matteson EL, Dasgupta B, Nash P, Durez P, Hall S, Hsia EC, Han J, Wagner C, Xu Z, Visvanathan S, Rahman MU (2008) Golimumab in patients with active rheumatoid arthritis despite treatment with methotrexate: a randomized, double-blind, placebo-controlled, dose-ranging study. Arthritis Rheum 58(4):964–975. https://doi.org/10.1002/art.23383
Keystone E, Genovese MC, Klareskog L, Hsia EC, Hall S, Miranda PC, Pazdur J, Bae SC, Palmer W, Xu S, Rahman MU (2010) Golimumab in patients with active rheumatoid arthritis despite methotrexate therapy: 52-week results of the GO-FORWARD study. Ann Rheum Dis 69(6):1129–1135. https://doi.org/10.1136/ard.2009.116319
Smolen JS, Kay J, Doyle MK, Landewe R, Matteson EL, Wollenhaupt J, Gaylis N, Murphy FT, Neal JS, Zhou Y, Visvanathan S, Hsia EC, Rahman MU (2009) Golimumab in patients with active rheumatoid arthritis after treatment with tumour necrosis factor alpha inhibitors (GO-AFTER study): a multicentre, randomised, double-blind, placebo-controlled, phase III trial. Lancet 374(9685):210–221. https://doi.org/10.1016/S0140-6736(09)60506-7
Gibson PR, Feagan BG, Sandborn WJ, Marano C, Strauss R, Johanns J, Padgett L, Collins J, Tarabar D, Hebzda Z, Rutgeerts P, Reinisch W (2016) Maintenance of efficacy and continuing safety of golimumab for active ulcerative colitis: PURSUIT-SC maintenance study extension through 1 year. Clin Transl Gastroenterol 7:e168. https://doi.org/10.1038/ctg.2016.24
Sandborn WJ, Feagan BG, Marano C, Zhang H, Strauss R, Johanns J, Adedokun OJ, Guzzo C, Colombel JF, Reinisch W, Gibson PR, Collins J, Jarnerot G, Hibi T, Rutgeerts P, Group P-SS (2014) Subcutaneous golimumab induces clinical response and remission in patients with moderate-to-severe ulcerative colitis. Gastroenterology 146(1):85–95. https://doi.org/10.1053/j.gastro.2013.05.048
Sandborn WJ, Feagan BG, Marano C, Zhang H, Strauss R, Johanns J, Adedokun OJ, Guzzo C, Colombel JF, Reinisch W, Gibson PR, Collins J, Jarnerot G, Rutgeerts P, Group PU-MS (2014) Subcutaneous golimumab maintains clinical response in patients with moderate-to-severe ulcerative colitis. Gastroenterology 146(1):96–109. https://doi.org/10.1053/j.gastro.2013.06.010
Feagan BG, Sandborn WJ, Gasink C, Jacobstein D, Lang Y, Friedman JR, Blank MA, Johanns J, Gao LL, Miao Y, Adedokun OJ, Sands BE, Hanauer SB, Vermeire S, Targan S, Ghosh S, de Villiers WJ, Colombel JF, Tulassay Z, Seidler U, Salzberg BA, Desreumaux P, Lee SD, Loftus EV Jr, Dieleman LA, Katz S, Rutgeerts P, Group U-I-US (2016) Ustekinumab as induction and maintenance therapy for Crohn’s disease. N Engl J Med 375(20):1946–1960. https://doi.org/10.1056/nejmoa1602773
Sandborn WJ, Gasink C, Gao LL, Blank MA, Johanns J, Guzzo C, Sands BE, Hanauer SB, Targan S, Rutgeerts P, Ghosh S, de Villiers WJ, Panaccione R, Greenberg G, Schreiber S, Lichtiger S, Feagan BG, Group CS (2012) Ustekinumab induction and maintenance therapy in refractory Crohn’s disease. N Engl J Med 367(16):1519–1528. https://doi.org/10.1056/nejmoa1203572
Xu Z, Vu T, Lee H, Hu C, Ling J, Yan H, Baker D, Beutler A, Pendley C, Wagner C, Davis HM, Zhou H (2009) Population pharmacokinetics of golimumab, an anti-tumor necrosis factor-alpha human monoclonal antibody, in patients with psoriatic arthritis. J Clin Pharmacol 49(9):1056–1070. https://doi.org/10.1177/0091270009339192
Woo S, Pawaskar D, Jusko WJ (2009) Methods of utilizing baseline values for indirect response models. J Pharmacokinet Pharmacodyn 36:381–405
Hutmacher MM, French JL (2011) Extending the latent variable model for extra correlated longitudinal dichotomous responses. J Pharmacokinet Pharmacodyn 38:833–859
Hu C, Xu Y, Zhuang Y, Hsu B, Sharma A, Xu Z, Zhang L, Zhou H (2018) Joint longitudinal model development: application to exposure-response modeling of ACR and DAS scores in rheumatoid arthritis patients treated with sirukumab. J Pharmacokinet Pharmacodyn 45(5):679–691. https://doi.org/10.1007/s10928-018-9598-5
Zhang L, Beal SL, Sheiner LB (2003) Simultaneous vs sequential analysis for population PK/PD data I: best-case performance. J Pharmacokinet Pharmacodyn 30(6):387–404
Hutmacher MM (2016) Evaluation of estimation, prediction and inference for autocorrelated latent variable modeling of binary data-a simulation study. J Pharmacokinet Pharmacodyn 43(3):275–289. https://doi.org/10.1007/s10928-016-9471-3
Karlsson MO, Holford NHG (2008) A tutorial on visual predictive checks. www.page-meeting.org/?abstract=1434
Hu C, Adedokun OJ, Chen Y, Szapary PO, Gasink C, Sharma A, Zhou H (2017) Challenges in longitudinal exposure-response modeling of data from complex study designs: a case study of modeling CDAI score for ustekinumab in patients with Crohn’s disease. J Pharmacokinet Pharmacodyn 44(5):425–436. https://doi.org/10.1007/s10928-017-9529-x
Hutmacher MM, French JL, Krishnaswami S, Menon S (2011) Estimating transformations for repeated measures modeling of continuous bounded outcome data. Stat Med 30(9):935–949. https://doi.org/10.1002/sim.4155
Lesaffre E, Rizopoulos D, Tsonaka R (2007) The logistic transform for bounded outcome scores. Biostatistics 8(1):72–85
Hu C, Yeilding N, Davis HM, Zhou H (2011) Bounded outcome score modeling: application to treating psoriasis with ustekinumab. J Pharmacokinet Pharmacodyn 38(4):497–517
Ursino M, Gasparini M (2018) A new parsimonious model for ordinal longitudinal data with application to subjective evaluations of a gastrointestinal disease. Stat Methods Med Res 27(5):1376–1393. https://doi.org/10.1177/0962280216661370
Wellhagen GJK (2018) A bounded integer model for rating and composite scale data. PAGE 27 (2018) Abstr 8743 [www.page-meeting.org/?abstract=8743]
Iannario MP, Piccolo D (2016) A comprehensive framework of regression models for ordinal data. METRON 74(2):233–252. https://doi.org/10.1007/s40300-016-0091-x
Pilla Reddy V, Kozielska M, de Greef R, Vermeulen A, Proost JH (2013) Modelling and simulation of placebo effect: application to drug development in schizophrenia. J Pharmacokinet Pharmacodyn 40(3):377–388. https://doi.org/10.1007/s10928-012-9296-7
Hu C, Zhou H, Sharma A (2017) Landmark and longitudinal exposure-response analyses in drug development. J Pharmacokinet Pharmacodyn 44(5):503–507. https://doi.org/10.1007/s10928-017-9534-0
Hu C, Sale M (2003) A joint model for nonlinear longitudinal data with informative dropout. J Pharmacokinet Pharmacodyn 30(1):83–103
Funding
This research was funded by Janssen Research and Development, LLC.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Figure S1
: Visual predictive check of responder/non-responder status calculated from only Mayo scores at the end of the induction phase for the initial continuous analysis model with flexible placebo effect model. The 5th, 50th and 95th percentiles of observed proportion of responders are overlaid with the 90% prediction intervals (PI) of their model predictions at planned observation times by treatment. PBO, placebo; SC, subcutaneous; IV, intravenous. Supplementary material 1 (EPS 6 kb)
Figure S2
: Visual predictive check of responder/non-responder status calculated from only Mayo scores in the maintenance phase for the continuous analysis model with flexible placebo effect model. The 5th, 50th and 95th percentiles of observed proportion of responders are overlaid with the 90% prediction intervals (PI) of their model predictions at planned observation times by treatment. PBO, placebo; ACT, active (golimumab) treatment; PBO→PBO, Induction PBO responders receiving placebo in maintenance; PBO→100, Induction PBO responders receiving 100 mg golimumab in maintenance; ACT→PBO, Induction active treatment responders receiving placebo in maintenance; NonResp→100; Induction non-responders receiving 100 mg golimumab in maintenance; SC 50 mg, Induction active treatment responders receiving 50 mg golimumab in maintenance; SC 100 mg, Induction active treatment responders receiving 100 mg golimumab in maintenance. Supplementary material 2 (EPS 15 kb)
Figure S3
: Visual predictive check of responder/non-responder status calculated from only Mayo scores at the end of the induction phase for the categorical analysis model. The 5th, 50th and 95th percentiles of observed proportion of responders are overlaid with the 90% prediction intervals (PI) of their model predictions at planned observation times by treatment. PBO, placebo; SC, subcutaneous; IV, intravenous. Supplementary material 3 (EPS 6 kb)
Figure S4
: Visual predictive check of Mayo score in the maintenance phase for the categorical analysis model. The 5th, 50th and 95th percentiles of observed proportion of responders are overlaid with the 90% prediction intervals (PI) of their model predictions at planned observation times by treatment. PBO, placebo; ACT, active (golimumab) treatment; PBO→PBO, Induction PBO responders receiving placebo in maintenance; PBO→100, Induction PBO responders receiving 100 mg golimumab in maintenance; ACT→PBO, Induction active treatment responders receiving placebo in maintenance; NonResp→100; Induction non-responders receiving 100 mg golimumab in maintenance; SC 50 mg, Induction active treatment responders receiving 50 mg golimumab in maintenance; SC 100 mg, Induction active treatment responders receiving 100 mg golimumab in maintenance.Supplementary material 4 (EPS 15 kb)
Rights and permissions
About this article
Cite this article
Hu, C., Adedokun, O.J., Zhang, L. et al. Modeling near-continuous clinical endpoint as categorical: application to longitudinal exposure–response modeling of Mayo scores for golimumab in patients with ulcerative colitis. J Pharmacokinet Pharmacodyn 45, 803–816 (2018). https://doi.org/10.1007/s10928-018-9610-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10928-018-9610-0