A Skew-Normal Bayesian Semi-parametric Latent Trait Linear Mixed Effect Model

Weiwei He1, Janice Zgibor1, Jongphil Kim2
1College of Public Health, University of South Florida, Tampa, USA
2Department of Biostatistics and Bioinformatics, H. Lee Moffitt Cancer Center, Tampa, USA

Tóm tắt

Clinical trials have longitudinally collected the biomarkers that may be associated with the time-to-event endpoints via latent variables such as disease severity. These longitudinal data may consist of different types of measurements. The multilevel item response theory (MLIRT) model is widely used in several fields including public health and health sciences, for these longitudinal outcomes. However, the violation of the normality assumption may produce inaccurate inferences if skewness is significantly present for continuous outcomes. Furthermore, the trajectories of these biomarkers over time are often observed in a nonlinear manner. This implies that partial linear regression may be more appropriate in practice. Challenges remain in interpreting such complicated and long-term survival data due to data attributes, including a mix of longitudinal outcomes, measurement errors, and skewness. Ignoring these characteristics in the data could lead to biased conclusions. In this article, we relax the assumptions and extend the MLIRT model to accommodate mixed types of multivariate longitudinal data. This article presents a novel method for analyzing longitudinal clinical data from the ACCORD trial. The methods are evaluated through simulation studies.

Từ khóa


Tài liệu tham khảo

Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB (2015) Fundamentals of clinical trials. Springer, New York Pocock SJ (1997) Clinical trials with multiple outcomes: a statistical perspective on their design, analysis, and interpretation. Control Clin Trials 18:530–545 Mayo-Wilson E et al (2017) Multiple outcomes and analyses in clinical trials create challenges for interpretation and research synthesis. J Clin Epidemiol 86:39–50 Lu X, Huang Y (2014) Bayesian analysis of nonlinear mixed-effects mixture models for longitudinal data with heterogeneity and skewness. Stat Med 33:2830–2849 Lu T (2018) Mixed-effects location and scale tobit joint models for heterogeneous longitudinal data with skewness, detection limits, and measurement errors. Stat Methods Med Res 27:3525–3543 Fox JP, Glas CAW (2001) Bayesian estimation of a multilevel IRT model using gibbs sampling. Psychometrika 66:271–288 Glas CA, Geerlings H, van de Laar MA, Taal E (2009) Analysis of longitudinal randomized clinical trials using item response models. Contemp Clin Trials 30:158–170 Luo S (2014) A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time. Stat Med 33:580–594 Fox JP (2010) Bayesian item response modeling: theory and applications. Springer, New York Fox JP (2007) Multilevel IRT modeling in practice with the package mlirt. J Stat Softw 20:1–16 Diez Roux AV (2000) Multilevel analysis in public health research. Annu Rev Public Health 21:171–192 Diez Roux AV (2002) A glossary for multilevel analysis. J Epidemiol Commun Health 56:588–594 Subramanian S, Jones K, Duncan C (2003) Multilevel methods for public health research. Neighborhoods and Health. Oxford University Press, New York Burton LJ (2015) Underrepresentation of women in sport leadership: A review of research. Sport Manag Rev 18:155–165 Bock RD, Aitkin M (1981) Marginal maximum likelihood estimation of item parameters: application of an EM algorithm. Psychometrika 46:443–459 Fama EF (1973) A note on the market model and the two-parameter model. J Financ 28:1181–1185 Adams RJ, Wilson M, Wang WC (1997) The multidimensional random coefficients multinomial logit model. Appl Psychol Meas 21:1–23 Muraki E, Carlson JE (1995) Full-information factor analysis for polytomous item responses. Appl Psychol Meas 19:73–90 Gruttola VD, Tu XM (1994) Modelling progression of CD4-lymphocyte count and its relationship to survival time. Biometrics 50:1003–1014 Tsiatis A, DeGruttola V, Wulfsohn M (1995) Modeling the relationship of survival to longitudinal data measured with error applications to survival and CD4 counts in patients with AIDS. J Am Stat Assoc 90:27–37 Pawitan Y, Self S (1993) Modeling disease marker processes in AIDS. J Am Stat Assoc 88:719–726 Taylor J, Cumberland W, Sy J (1994) A stochastic model for analysis of longitudinal aids data. J Am Stat Assoc 89:727–736 Dennis JM et al (2018) Evaluating associations between the benefits and risks of drug therapy in type 2 diabetes: a joint modeling approach. Clin Epidemiol 10:1869–1877 Huang Y, Yan C, Xing D, Zhang N, Chen H (2015) Jointly modeling event time and skewed-longitudinal data with missing response and mismeasured covariate for AIDS studies. J Biopharm Stat 25:670–694 Zhang H, Huang Y, Wang W, Chen H, Langland-Orban B (2019) Bayesian quantile regression-based partially linear mixed-effects joint models for longitudinal data with multiple features. Stat Methods Med Res 28:569–588 Verbeke G, Lesaffre E (1996) A linear mixed-effects model with heterogeneity in the random-effects population. J Am Stat Assoc 91:217–221 Huang Y, Dagne G (2011) A Bayesian approach to joint mixed-effects models with a skew-normal distribution and measurement errors in covariates. Biometrics 67:260–269 Chen G, Luo S (2018) Bayesian hierarchical joint modeling using skew-normal/independent distributions. Commun Stat Simul Comput 47:1420–1438 Ho HJ, Lin TI (2010) Robust linear mixed models using the skew t distribution with application to schizophrenia data. Biom J 52:449–469 Chen J, Huang Y (2015) A Bayesian mixture of semiparametric mixed-effects joint models for skewed-longitudinal and time-to-event data. Stat Med 34:2820–2843 Crow EL, Shimizu K (1988) Lognormal distributions: theory and applications. Marcel Dekker, New York and Basel, p 1 Sahu SK, Dey DK, Branco MD (2003) A new class of multivariate skew distributions with applications to Bayesian regression models. Can J Stat 31:129–150 ACCORD Study Group (2007) Action to control cardiovascular risk in diabetes (ACCORD) trial: design and methods. Am J Cardiol 99:21–33 Kannel WB, McGee DL (1979) Diabetes and cardiovascular disease: the Framingham study. JAMA 241:2035–2038 Stamler J, Vaccaro O, Neaton JD, Wentworth D (1993) Diabetes, other risk factors, and 12-yr cardiovascular mortality for men screened in the multiple risk factor intervention trial. Diabetes Care 16:434–444 Sowers JR, Epstein M, Frohlich ED (2001) Diabetes, hypertension, and cardiovascular disease: an update. Hypertension 37:1053–1059 Eberly, L. E., Cohen, J. D., Prineas, R., Yang, L., Multiple Risk Factor Intervention Trial Research Group (2003) Impact of incident diabetes and incident nonfatal cardiovascular disease on 18-year mortality: the multiple risk factor intervention trial experience. Diabetes care 26(3):848–854 Lonardo A, Nascimbeni F, Mantovani A, Targher G (2018) Hypertension, diabetes, atherosclerosis and nash: Cause or consequence? J Hepatol 68:335–352 DeFronzo RA, Ferrannini E (1991) Insulin resistance: a multifaceted syndrome responsible for NIDDM, obesity, hypertension, dyslipidemia, and atherosclerotic cardiovascular disease. Diabetes Care 14:173–194 Taskinen MR (2002) Diabetic dyslipidemia. Atheroscler Suppl 3:47–51 Kostis JB (2007) The importance of managing hypertension and dyslipidemia to decrease cardiovascular disease. Cardiovasc Drugs Ther 21:297–309 Johnson ML, Pietz K, Battleman DS, Beyth RJ (2004) Prevalence of comorbid hypertension and dyslipidemia and associated cardiovascular disease. Am J Manag Care 10:926–932 Goff DC Jr et al (2007) Prevention of cardiovascular disease in persons with type 2 diabetes mellitus: current knowledge and rationale for the action to control cardiovascular risk in diabetes (ACCORD) trial. Am J Cardiol 99:4i–20i Adler AI et al (2000) Association of systolic blood pressure with macrovascular and microvascular complications of type 2 diabetes (UKPDS 36): prospective observational study. BMJ 321:412–419 Action to Control Cardiovascular Risk in Diabetes Study Group (2008) Effects of intensive glucose lowering in type 2 diabetes. N Engl J Med 358:2545–2559 ACCORD Study (2010) Effects of combination lipid therapy in type 2 diabetes mellitus. N Engl J Med 362:1563–1574 ACCORD Study Group (2010) Effects of intensive blood-pressure control in type 2 diabetes mellitus. N Engl J Med 362:1575–1585 Rosenzweig S (1936) Some implicit common factors in diverse methods of psychotherapy. Am J Orthopsychiatry 6:412–415 Samejima F (1968) Estimation of latent ability using a response pattern of graded scores. ETS Res Bull Ser 1–169 van der Linden WJ, Hambleton RK (2013) Handbook of modern item response theory. Springer Science and Business Media, New York Wu L (2002) A joint model for nonlinear mixed-effects models with censoring and covariates measured with error, with application to AIDS studies. J Am Stat Assoc 97:955–964 Liu W, Wu L (2007) Simultaneous inference for semiparametric nonlinear mixed-effects models with covariate measurement errors and missing responses. Biometrics 63:342–350 Sakamoto Y, Ishiguro M, Kitagawa G. Akaike Information Criterion Statistics (KTK Scientific Publishers ; D. Reidel ; Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, Tokyo, 1986) Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464 Davidian M, Giltinan DM (2017) Nonlinear models for repeated measurement data. CRC Press, New York Jeon M, Rijmen F (2016) A modular approach for item response theory modeling with the R package flirt. Behav Res Methods 48:742–755 Reckase MD (2009) Multidimensional item response theory. Springer, New York Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models: a modern perspective, 2nd edn. Chapman and Hall/CRC, New York Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Am Stat 49:327–335 Team SD (2019) Stan Modeling Language Users Guide and Reference Manual 2.28 edn https://mc-stan.org Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc Ser B (Stat Methodol) 64:583–639 Watanabe S (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 11:3571–3594 Vehtari A, Gelman A, Gabry J (2017) Practical Bayesian model evaluation using leave-one-out cross-validation and waic. Stat Comput 27:1413–1432 McElreath R (2020) Statistical rethinking: a Bayesian course with examples in R and Stan, 1st edn. Chapman and Hall/CRC, New York R. C. Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna Komsta L, Novomestky F (2015) Moments, cumulants, skewness, kurtosis and related tests. R package version 0.14