Evolution of association between renal and liver functions while awaiting heart transplant: An application using a bivariate multiphase nonlinear mixed effects model
Restricted accessResearch articleFirst published online July, 2018
Evolution of association between renal and liver functions while awaiting heart transplant: An application using a bivariate multiphase nonlinear mixed effects model
In many longitudinal follow-up studies, we observe more than one longitudinal outcome. Impaired renal and liver functions are indicators of poor clinical outcomes for patients who are on mechanical circulatory support and awaiting heart transplant. Hence, monitoring organ functions while waiting for heart transplant is an integral part of patient management. Longitudinal measurements of bilirubin can be used as a marker for liver function and glomerular filtration rate for renal function. We derive an approximation to evolution of association between these two organ functions using a bivariate nonlinear mixed effects model for continuous longitudinal measurements, where the two submodels are linked by a common distribution of time-dependent latent variables and a common distribution of measurement errors.
MasonDPRajeswaranJMurthySCet al.Spirometry after transplantation: how much better are two lungs than one?Ann Thorac Surg2008; 85: 1193–1201.
2.
BeckettLATancrediDJWilsonRS. Multivariate longitudinal models for complex change processes. Stat Med2004; 23: 231–239.
3.
FieuwsSVerbekeG. Joint modeling of multivariate longitudinal profiles: pitfalls of the random-effect approach. Stat Med2004; 23: 3093–3104.
4.
FieuwsSVerbekeGMolenbergsG. Random-effects models for multivariate repeated measures. Stat Methods Med Res2007; 16: 387–397.
5.
O’BrianPC. Procedures for comparing samples with multiple endpoints. Biometrics1984; 40: 1079–1087.
6.
Proust-LimaCLetenneurLJacqmin-GaddaH. A nonlinear latent class model for joint analysis of multivariate longitudinal data and a binary outcome. Stat Med2007; 26: 2229–2245.
7.
FaesCAertsMMolenberghsGet al.A high-dimensional joint model for longitudinal outcomes of different nature. Stat Med2008; 27: 4408–4427.
8.
RochonJ. Analyzing bivariate repeated measures for discrete and continuous outcome variables. Biometrics1996; 52: 740–750.
9.
RoyJLinX. Latent variable models for longitudinal data with multiple continuous outcomes. Biometrics2000; 56: 1047–1054.
10.
VerbekeGFieuwsSMolenbergsGet al.The analysis of multivariate longitudinal data: a review. Stat Methods Med Res2014; 23: 42–59.
11.
TsiatisAADeGruttolaVWulfsohnMS. Modeling relationship of survival to longitudinal data measured with error. Applications to survival and CD4 counts in patients with AIDS. J Am Stat Assoc1995; 429: 27–37.
12.
ShahALairdNSchoenfieldD. A random effect model for multiple characteristics with possibly missing data. J Am Stat Assoc1997; 92: 775–779.
13.
RajeswaranJBlackstoneEH. A multiphase non-linear mixed effects model: an application to spirometry after lung transplantation. Stat Methods Med Sci2017; 26: 21–42.
14.
BlackstoneEHNaftelDCTurnerMEJr. The decomposition of time-varying hazard into phases, each incorporating a separate stream of concomitant information. J Am Stat Assoc1986; 81: 615–624.
15.
GelmanABoisFJiangLM. Physiology pharmacokinetic analysis using population modeling and informative prior distributions. J Am Stat Assoc1996; 91: 1400–1412.
16.
HazelrigJBTurnerME JrBlackstoneEH. Parametric survival analysis combining longitudinal and cross-sectional censored and interval-censored data with concomitant information. Biometrics1982; 39: 1–5.
17.
MarshallGCruz-MesiaRDBaronAEet al.Non-linear random effect model for multivariate responses with missing data. Stat Med2006; 25: 2817–2830.
18.
PantazisNTouloumiGWalkerASet al.Bivariate modeling of longitudinal measurements of two human immunodeficiency Type 1 disease progression markers in the presence of informative drop-outs. J R Stat Soc Ser A2005; 54: 405–423.
19.
ThiebautRJacqmin-GaddaHBabikerAet al.Joint Modeling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection. Stat Med2005; 24: 65–82.
20.
PinheiroJCBatesDM. Approximations to the log-likelihood function in a nonlinear mixed-effects model. J Comput Graph Stat1995; 4: 12–35.
21.
VoneshEF. A note on the use of Laplace’s approximation for nonlinear mixed-effects models. Biometrika1996; 83: 447–452.
ReinhartzOFarrarDJHershonJHet al.Importance of liver function as a predictor of survival in patients supported with Thoratec ventricular assist devices as a bridge to transplantation. J Thorac Cardiovasc Surg1998; 116: 633–640.
24.
HuntSAAbrahamWTChinMHet al.American College of Cardiology/American Heart Association 2005 guideline update for the diagnosis and management of chronic heart failure in the adult. Circulation2005; 112: 1824–1852.
25.
LeveyASBoschJPLewisJBet al.More accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Ann Intern Med1999; 130: 461–470.
26.
Akaike H. Information theory and an extension of the maximum likelihood principle. In: Petrov BN and Csáki F (eds) 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, USSR, 2–8 September 1971, Budapest: Akadémiai Kiadó, p. 267-281.
27.
VoneshEFChincillVMPuK. Goodness-of-fit in generalized nonlinear mixed-effects models. Biometrics1996; 52: 572–587.
28.
FieuwsSVerbekeG. Pairwise fitting of mixed models for the joint modeling of multivariate longitudinal profiles. Biometrics2006; 62: 424–431.
29.
JoeH. Accuracy of Laplace approximation for discrete response mixed models. Comput Data Anal2008; 52: 506–574.
