Some things Bayesian Conditional Transformation Models (BCTMs) can do (as shown in our paper)
BCTMs are able to flexibly estimate the whole conditional distribution of the responses, i.e. a respone distribution does not have to be specified beforehand. The covariates impact (possibly) the whole conditional response distribution in form of linear, nonlinear, random or spatial effects on the scale of the transformation function. BCTMs perform posterior estimation on basis of the NUTS Sampler with mutlivariate Gaussian priors for the basis coefficients and with gamma priors for the smoothing variances.
Proportional Hazards with Spatial Frailties
Based on a dataset on acute myeloid leukemia survival ([1]).
- analyzing impact of prognostic factors age, sex, white blood cell count and Townsend score(indicating less affluent residential areas for higher values),
- investigating spatial patterns for 24 administrative regions in North West England; . * reference is the minimum extreme value distribution resulting in a proportional hazards model
Modelling Conditional Distribution of Cholesterol Levels for Heart Patients
Based on a Framingham Heart Study ([2]).
Semiparametric (Non-)Proportional Odds with Censoring
Based on a Veteran’s Administration lung cancer trial dataset ([3]).
- analyzing odds of survival dependent on Karnofsky Performance Score and different lung cancer types
- partial right-censoring
[1] Henderson, R., Shimakura, S. and Gorst, D. (2002). Modeling spatial variation in leukemia survival data. Biometrics 57(3): 795-802
[2] Zhang, D. and Davidian, M. (2001). Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrika 60(2): 279-288.
[3] Prentice, R. L. (1973). Exponential survivals with censoring and explanatory variables. Journal of the American Statistical Association 97(460): 965-972.