
@article{Hothorn_2018,
  author = {Torsten Hothorn},
  title = {Most Likely Transformations: The \textbf{mlt} Package},
  journal = {Journal of Statistical Software},
  year = 2018,
  url = {https://cran.r-project.org/web/packages/mlt.docreg/vignettes/mlt.pdf},
  note = {Accepted for publication 2018-03-05}
}

@article{Seibold_Zeileis_Hothorn_2017,
  author = {Heidi Seibold and Achim Zeileis and Torsten Hothorn},
  title = {Individual Treatment Effect Prediction for {ALS} Patients},
  year = {2017},
  journal = {Statistical Methods in Medical Research},
  doi = {10.1177/0962280217693034},
}

@article{Seibold_Zeileis_Hothorn_2015,
  author = {Heidi Seibold and Achim Zeileis and Torsten Hothorn},
  title = {Model-Based Recursive Partitioning for Subgroup Analyses},
  journal = {International Journal of Biostatistics},
  year = 2016,
  doi = {10.1515/ijb-2015-0032},
  volume = 12,
  number = 1,
  pages = {45--63}
}


@techreport{Hothorn_Zeileis_2017,
  author = {Torsten Hothorn and Achim Zeileis},
  title = {Transformation Forests},
  year = {2017},
  institution = {arXiv 1701.02110},
  url = {https://arxiv.org/abs/1701.02110}
}


@article{Lohse_Rohrmann_Faeh_2017,
  author = {Tina Lohse and Sabine Rohrmann and David Faeh and Torsten Hothorn},
  title = {Continuous Outcome Logistic Regression for Analyzing 
           Body Mass Index Distributions},
  journal = {F1000Research},
  year = 2017, 
  volume = 6,
  pages = {1933},
  doi = {10.12688/f1000research.12934.1}
}


@Article{         Currie_Durban_Eilers_2006,
  author        = {I. D. Currie and M. Durban and P. H. C. Eilers},
  title         = {Generalized Linear Array Models With Applications to
                  Multidimensional Smoothing},
  year          = {2006},
  journal       = {Journal of the Royal Statistical Society B},
  volume        = {68},
  number        = {2}, 
  pages         = {259--280},
  doi           = {10.1111/j.1467-9868.2006.00543.x}
}

@book{vdGeer_2000,
  title = {Empirical Processes in M-Estimation},
  author = {Sarah van de Geer},
  year = 2000,
  publisher = {Cambridge University Press},
  address = {Cambridge, UK}
}

@book{vdVaart_1998,
  title = {Asymptotic Statistics},
  author = {Aart W. van der Vaart},
  year = 1998,
  publisher = {Cambridge University Press},
  address = {Cambridge, UK}
}

@book{Fraser_1968,
  title = {The Structure of Inference},
  author = {Donald A. S. Fraser},
  year = {1968},
  publisher = {John Wiley \& Sons},
  address = {New York, U.S.A.}
}

@article{Pitman_1939,
  title = {The Estimation of the Location and Scale Parameters
           of a Continuous Population of Any Given Form},
  author = {Edwin James George Pitman},
  journal = {Biometrika},
  volume = 30,
  number = {3/4},
  year = 1939,
  pages = {391--421}
}

@article{Fisher_1934,
  title = {Two New Properties of Mathematical Likelihood},
  author = {Ronald Aylmer Fisher},
  year = 1934,
  journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
  volume = 53,
  pages = {285--306}
}

@book{Lindsey_1996,
  title = {Parametric Statistical Inference},
  author = {Jim K. Lindsey},
  year = 1996,
  publisher = {Clarendon Press},
  address = {Oxford, UK}
}

@book{Tutz_2012,
  author = {Gerhard Tutz},
  year = 2012,
  title = {Regression for Categorical Data},
  publisher = {Cambridge University Press},
  address = {New York, U.S.A.},
}

@article{Hothorn_Kneib_Buehlmann_2014,
  author = {Torsten Hothorn and Thomas Kneib and Peter B{\"u}hlmann},
  title = {Conditional Transformation Models},
  journal = {Journal of the Royal Statistical Society B},
  year = {2014},
  volume = 76,
  number = 1,   
  doi = {10.1111/rssb.12017},
  pages = {3--27},
  code = {http://R-forge.R-project.org/projects/ctm},
  data = {http://R-forge.R-project.org/projects/ctm}
}

@Article{         Hayfield_Racine_2008,
  author        = {Tristen Hayfield and Jeffrey S. Racine},
  title         = {Nonparametric Econometrics: The np Package},
  journal       = {Journal of Statistical Software},
  volume        = {27},
  number        = {5},
  pages         = {1--32},
  day           = {29},
  month         = {7},
  year          = {2008},
  url           = {http://www.jstatsoft.org/v27/i05}
}

 
@Article{         Mayr_Fenske_Hofner_2012,  
  author        = {Andreas Mayr and Nora Fenske and Benjamin Hofner and
                  Thomas Kneib and Matthias Schmid},
  year          = 2012,
  title         = {{GAMLSS} for High-dimensional Data--{A} Flexible Approach
                  Based on Boosting},
  journal       = {Journal of the Royal Statistical Society: Series C
                  (Applied Statistics)},
  volume        = 61,
  number        = 3,
  pages         = {403--427},
  doi           = {10.1111/j.1467-9876.2011.01033.x}
}

@article{gbsg2:1994,
   author    = {M. Schumacher and G. Basert and H. Bojar and K. H\"ubner and
M. Olschewski and W. Sauerbrei and C. Schmoor and C. Beyerle and R. L. A.
Neumann and {Rauschecker, H. F., for the German Breast Cancer Study Group}},
   title     = {Randomized $2\times2$ Trial Evaluating Hormonal Treatment
and the Duration of Chemotherapy in Node-positive Breast Cancer Patients},
   journal   = {Journal of Clinical Oncology},
   year      = {1994},
   volume    = {12},
   pages     = {2086-2093}
}


@article{Hyndman_Yao_2002,
  author = {Rob J. Hyndman and Qiwei Yao},
  title = {Nonparametric Estimation and Symmetry Tests for Conditional Density Functions},
  year = {2002},
  journal = {Journal of Nonparametric Statistics},
  volume = {14},
  number = {3},
  DOI = {10.1080/10485250212374},
  pages = {259--278}
}

@article{Azzalini_Bowman_1990,
  author = {A. Azzalini and A. W. Bowman},
  title = {A Look at Some Data on the Old Faithful Geyser},
  year = {1990},
  journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
  volume = {39},
  number = {3},
  DOI = {10.2307/2347385},
  pages = {357--365}
}

@Article{Fredriks_Buuren_Burgmeijer_2000,
  author        = {A. M. Fredriks and S. van Buuren and R. J. F. Burgmeijer
                  and J. F. Meulmeester and R. J. Beuker and E. Brugman and
                  M. J. Roede and S. P. Verloove-Vanhorick and J. Wit},
  title         = {Continuing Positive Secular Growth Change in {The}
                  {Netherlands} 1955--1997},
  year          = {2000},
  journal       = {Pediatric Research},
  volume        = {47},
  number        = {3},
  pages         = {316--323}
}

@Article{         Stasinopoulos_Rigby_2007,
  author        = {D. Mikis Stasinopoulos and Robert A. Rigby},
  title         = {Generalized Additive Models for Location Scale and Shape
                  {(GAMLSS)} in {R}},
  year          = {2007},
  journal       = {Journal of Statistical Software},
  volume        = {23},
  number        = {7},
  pages         = {1--46},
  url           = {http://www.jstatsoft.org/v23/i07}
}

@Article{Mueller_Hothorn_2004,
   author    = {J{\"o}rg M{\"u}ller and Torsten Hothorn},
   title     = {Maximally Selected Two-Sample Statistics as a New Tool for
                the Identification and Assessment of Habitat Factors with
                an Application to Breeding Bird Communities in Oak Forests},
   year      = {2004}, 
   volume = 123,
   journal   = {European Journal of Forest Research},
   pages = {218--228},
   DOI = {10.1007/s10342-004-0035-5},
}

@book{Klein_Moeschberger_2003,
  author = {John P. Klein and Melvin K. Moeschberger},
  title = {Survival Analysis. Techniques for Censored and Truncated Data.},
  year = {2003},
  edition = {2nd},
  publisher = {Springer-Verlag},
  address = {New York, U.S.A.}
}

%VIP %LTM %spezi %splines %pen_lik
% NEW iterative optimisation algorithm: combination of Newton's method and an
% iterative multiplicative algorithm
@article{Maetal_2014,
  title = {On the Maximum Penalized Likelihood Approach for 
           Proportional Hazard Models with Right Censored Survival Data},
  journal = {Computational Statistics \& Data Analysis},
  volume = {74},
  pages = {142--156},
  year = {2014},
  doi = {10.1016/j.csda.2014.01.005},
  author = {J. Ma and S. Heritier and S. N. L\^{o}}
}



%VIP %LTM %flex_int_y %spezi %full_lik %splines
% note: right-censored log-likelihood is parametrised in terms of the hazard function
% => hazard function needs to be (numerically) integrated / computational disadvantage 
@article {CrowtherLambert_2014,
  author = {M. J. Crowther and P. C. Lambert},
  title = {A General Framework for Parametric Survival Analysis},
  journal = {Statistics in Medicine},
  volume = 33,
  number = 30,
  pages = {5280--5297},
  doi = {10.1002/sim.6300},
  year = {2014}
}


%VIP %flex_int %spezi %full_lik %splines
% Note: Parametrisations for conditional and unconditional log-hazard functions.
% PH models, PH models with time-varying effects, nonparametric PH models are included.
@article{Kooperbergetal_1995,
  title = {Hazard Regression},
  author = {Kooperberg, Charles and Stone, Charles J. and Truong, Young K.},
  journal = {Journal of the American Statistical Association},
  volume = {90},
  number = {429},
  pages = {78--94},
  year = {1995}
}

%optional %flex_int %spezi %full_lik %splines
% Note: Extension of Kooperberg et al. (1995) to interval-censored data and 
%       time-dependent covariates.
%       Modified Newton-Raphson algorithm because the log-likelihood is not 
%       necessarily concave for interval-censored data.
@article{KooperbergClarkson_1997,
  title = {Hazard Regression with Interval-Censored Data},
  author = {Kooperberg, Charles and Clarkson, Douglas B.},
  journal = {Biometrics},
  volume = {53},
  number = {4},
  pages = {1485--1494},
  year = {1997}
}


%LTM %spezi %full_lik %splines
% Note: Baseline-hazard function is approximated with quadratic splines.
@article{Etezadi-Amoli_Ciampi_1987,
  title = {Extended Hazard Regression for Censored Survival Data with 
           Covariates: A Spline Approximation for the Baseline Hazard Function},
  author = {Etezadi-Amoli, Jamshid and Ciampi, Antonio},
  journal = {Biometrics},
  volume = {43},
  number = {1},
  pages = {181--192},
  year = {1987}
}


%hazard_est %spezi %pen_lik %splines
% Note: Hazard function is parametrised in M-splines; I-splines are corresponding
%       splines for the cumulative hazard function; identical basis coefficients.
%       Approach can be extended to include covariate information.
%       Interval censored and interval truncated observations are considered.
@article{Jolyetal_1998,
  title = {A Penalized Likelihood Approach for Arbitrarily Censored 
           and Truncated Data: Application to Age-Specific Incidence of Dementia},
  author = {Joly, Pierre and Commenges, Daniel and Letenneur, Luc},
  journal = {Biometrics},
  volume = {54},
  number = {1},
  pages = {185--194},
  year = {1998}
}


%hazard_est %spezi %pen_lik %splines %optional
% Note: sqrt(lambda(y)) is parametrised; roughness penalty is considered.
%       General spline function that minimises the penalised log-likelihood
%       can be determined (similar principal as for natural cubic splines???)
@article{Senthil_1992,
  title = {Nonparametric Estimation of Hazard Function from Left 
           Truncated and Right Censored Data},
  author = {Selvan A. Senthil},
  journal = {Journal of Nonparametric Statistics},
  volume = {2},
  number = {1},
  pages = {29--35},
  year = {1992},
  doi = {10.1080/10485259208832540}
}


%hazard_est %spezi %pen_lik %splines %optional
% Note: estimation of an unconditional log-hazard function or log-density.
@article{Osullivan_1988,
  title = {Fast Computation of Fully Automated Log-Density and Log-Hazard Estimators},
  author = {Finbarr O'Sullivan},
  journal = {SIAM Journal on Scientific and Statistical Computing},
  volume = {9},
  number = {2},
  pages = {363--379},
  year = {1988}
}

%LTM %spezi %full_lik %splines 
% Note: baseline function has density with mild smoothness conditions; 
%       density is parametrised by a truncated series expantion with fixed degree of
%       truncation; adaptive choice of degree of truncation;
%       Given examples only include LTMs, but AFT-extensions to heteroscedastic errors
%       and time-dependent covariates are given in the appendix.
@article{ZhangDavidian_2008,
  author = {Zhang, Min and Davidian, Marie},
  title = {''Smooth'' Semiparametric Regression Analysis for 
           Arbitrarily Censored Time-to-Event Data},
  journal = {Biometrics},
  volume = {64},
  number = {2},
  doi = {10.1111/j.1541-0420.2007.00928.x},
  pages = {567--576},
  year = {2008}
}


%optional %LTM $spezi %full_lik %splines (= parametric transformation) %bayes
% Note: Transform both sides model is more restrictive than LTMs because both sides of
%       the model equation are transformed in terms of the same function g_lambda!
%       Extension of Box-Cox power family.
@article{Polpoetal_2014,
  title = {Transform Both Sides Model: A Parametric Approach},
  journal = {Computational Statistics \& Data Analysis},
  volume = {71},
  pages = {903--913},
  year = {2014},
  doi = {10.1016/j.csda.2013.07.023},
  author = {A. Polpo and C. P. {de Campos} and D. Sinha and S. Lipsitz and J. Lin}
}


%LTM %spezi %full_lik %splines (= parametric transformation) %bayes
% Note: LTM with parametric response transformation and fixed error distribution
%       F = Phi.
@article{BoxCox_1964,
  author = {G. E. P. Box and D. R. Cox}, 
  title = {An Analysis of Transformations},
  volume = {26}, 
  number = {2}, 
  pages = {211--252}, 
  year = {1964},  
  journal = {Journal of the Royal Statistical Society B},
}

%optional %LTM %spezi %full_lik %splines (= parametric transformation)
% Note: Generalisation of Box-Cox, e.g. to arbitrary but fixed error distribution F.
@article{BickelDoksum_1981,
  author = {P. J. Bickel and K. A. Doksum},
  title = {An Analysis of Transformations Revisited},
  journal = {Journal of the American Statistical Association},
  volume = {76},
  number = {374},
  pages = {296--311},
  year = {1981},
  doi = {10.1080/01621459.1981.10477649}
}

%optional
% Note: Reference for Exponential PH and Weibull PH model.
@article{Prentice_1973,
  author = {R. L. Prentice}, 
  title = {Exponential Survivals with Censoring and Explanatory Variables},
  volume = {60}, 
  number = {2}, 
  pages = {279--288}, 
  year = {1973}, 
  doi = {10.1093/biomet/60.2.279}, 
  journal = {Biometrika} 
}


%VIP %LTM %random %spezi %NPMLE %profile_lik or %full_lik
% Note: relationship of LTMs and frailty models;
%       time-dependent covariates are considered;
%       log-likelihood is formulated based on a counting process.
%       Model estimation: direct maximisation of full-lik or profile likelihood 
%       (both NPMLE).
@article {ChoiHuang_2012,
  author = {S. Choi and X. Huang},
  title = {A General Class of Semiparametric Transformation Frailty 
           Models for Nonproportional Hazards Survival Data},
  journal = {Biometrics},
  volume = {68},
  number = {4},
  doi = {10.1111/j.1541-0420.2012.01784.x},
  pages = {1126--1135},
  year = {2012}
}


%optional %LTM %profile_lik %spezi %NPMLE
% Note: log-likelihood based on counting processes is used;
%       time-dependent covariates are considered.
%       Estimation: weighted Breslow-type estimator for jump sizes of the cumulative
%       baseline function; profile score equation for regression coefficients.
%       Extension of Chen et al. (2002) (unweighted Breslow-type estimator)!
@article{Chen_2009,
  author = {Chen, Yi-Hau}, 
  title = {Weighted Breslow-type and Maximum Likelihood Estimation in 
           Semiparametric Transformation Models},
  year = {2009}, 
  volume = 96,
  number = 3,
  pages = {591--600},
  doi = {10.1093/biomet/asp032}, 
  journal = {Biometrika} 
}


%optional %spezi %NPMLE
% Note: proportional intensity model (for counting processes) with time-dependent
%       covariates;
%       nonparametric log-likelihood for counting processes;
%       LTM and PH model are included as special cases;
%       in contrast to Chen et al. (2002) the estimators are asympt. efficient;
%       quasi-Newton method for model estimation.
@article{ZengLin_2006,
  author = {D. Zeng and D. Y. Lin}, 
  title = {Efficient Estimation of Semiparametric Transformation 
           Models for Counting Processes},
  volume = {93}, 
  number = {3}, 
  pages = {627--640}, 
  year = {2006}, 
  doi = {10.1093/biomet/93.3.627}, 
  journal = {Biometrika} 
}


%VIP %flex_int %random %spezi %NPMLE
% Note: General class of transformation models for counting processes that is able to
%       handle time-dependent covariates, heteroscedasticity, multiple types of events,
%       random effects;
%       unified and general asymptotic theory is provided.
@article {ZengLin_2007,
  author = {D. Zeng and D. Y. Lin},
  title = {Maximum Likelihood Estimation in Semiparametric 
           Regression Models with Censored Data},
  journal = {Journal of the Royal Statistical Society B},
  volume = {69},
  number = {4},
  doi = {10.1111/j.1369-7412.2007.00606.x},
  pages = {507--564},
  year = {2007}
}


%optional %LTM %random %spezi %NPMLE
% Note: Aim: Prove large sample existence and consistency of the NPMLE.  
@article {SludVonta_2004,
  author = {E. V. Slud and F. Vonta},
  title = {Consistency of the {NPML} Estimator in the Right-Censored Transformation Model},
  journal = {Scandinavian Journal of Statistics},
  volume = {31},
  number = {1},
  doi = {10.1111/j.1467-9469.2004.00370.x},
  pages = {21--41},
  year = {2004}
}

%VIP %LTM_flex %spezi %NPMLE
% Note: Varying coefficients for covariates not for the response! 
%       Partial linear transformation model is included as a special case;
%       Varying coefficients are parametrised using B-splines;
%       Iterative procedure is suggested for model estimation because direct maximisation
%       of the log-likelihood is problematic because of the high number of parameters.
@article{ChenTong_2010,
  author = {K. Chen and X. Tong}, 
  title = {Varying Coefficient Transformation Models with Censored Data},
  volume = {97}, 
  number = {4}, 
  pages = {969--976}, 
  year = {2010}, 
  doi = {10.1093/biomet/asq032}, 
  journal = {Biometrika} 
}


%VIP %LTM (PO model) %spezi %NPMLE 
% Note: NPMLE approach for the PO model;
%       important reference for the PO model for survival data.
@article {Bennett_1983a,
  author = {Bennett, Steve},
  title = {Analysis of Survival Data by the Proportional Odds Model},
  journal = {Statistics in Medicine},
  volume = {2},
  number = {2},
  doi = {10.1002/sim.4780020223},
  pages = {273--277},
  year = {1983}
}


%LTM (PO model) %spezi %NPMLE
% Note: authors show that Bennett (1983)'s estimates are efficient;
%       large sample porperties of the estimators are established;
%       Newton-Raphson algorithm.
@article {Murphyetal_1997,
  author = {S. A. Murphy and A. J. Rossini and A. W. van der Vaart},
  title = {Maximum Likelihood Estimation in the Proportional Odds Model},
  journal = {Journal of the American Statistical Association},
  volume = {92},
  number = {439},
  doi = {10.1080/01621459.1997.10474051},
  pages = {968--976},
  year = {1997}
}

%optional %LTM (PO model) %spezi %NPMLE
% Note: identical approach to Murphy et al. (1997) but different estimation algorithm;
%       minorisation-maximisation algorithm;
%       Newton-Raphson might be problematic for large data sets where number of
%       parameters exceeds the number of uncensored observations. 
@article{HunterLange_2002,
  year={2002},
  journal={Annals of the Institute of Statistical Mathematics},
  volume={54},
  number={1},
  doi={10.1023/A:1016126007531},
  title={Computing Estimates in the Proportional Odds Model},
  author={D. R. Hunter and K. Lange},
  pages={155--168}
}


%flex_int_y (PO model with time-varying effects) %spezi %NPMLE %estequ
% Note: Extended PO model with time-varying coefficients or time-dependent covariates;
%       Estimation techniques:
%       1) Moment-based estimating equations (Chen et al. (2002))
%       2) NPMLE (Zeng and Lin (2006, 2007))
@article {Chenetal_2012,
  author = {Y. Q. Chen and N. Hu and S.-C. Cheng and P. Musoke and L. P. Zhao},
  title = {Estimating Regression Parameters in an Extended Proportional Odds Model},
  journal = {Journal of the American Statistical Association},
  volume = {107},
  number = {497},
  year = {2012},
  pages = {318--330},
  doi = {10.1080/01621459.2012.656021}
}

%optional %LTM %spezi %NPMLE
% Note: authors propose an efficient algorithm for calculating MLEs;
%       dimensionality of the parameter space is dramatically reduced.
@article{YinZeng_2006,
  title = {Efficient Algorithm for Computing Maximum Likelihood 
           Estimates in Linear Transformation Models},
  author = {G. Yin and D. Zeng},
  journal = {Journal of Computational and Graphical Statistics},
  volume = {15},
  number = {1},
  pages = {228--245},
  doi = {10.1198/106186006X100542},
  year = {2006}
}

%LTM (PO model) %random %spezi %NPMLE
% Note: right-censored log-likelihood is integrated over the random effects;
%       random effects follow a normal distribution.
@article {Zengetal_2005,
  author = {D. Zeng and D. Y. Lin and G. Yin},
  title = {Maximum Likelihood Estimation for the Proportional Odds Model with Random Effects},
  journal = {Journal of the American Statistical Association},
  volume = {100},
  number = {470},
  doi = {10.1198/016214504000001420},
  pages = {470--483},
  year = {2005}
}

%LTM_flex %random %spezi %NPMLE
% Note: NPMLE approach for linear transformation models with time-varying covariates
%       and random effects for clustered or correlated failure times.
@article{Zengetal_2008,
  author = {D. Zeng and D. Y. Lin and X. Lin},
  title = {Semiparametric Transformation Models with Random Effects 
           for Clustered Failure Time Data},
  journal = {Statistica Sinica},
  volume = {18},
  number = {1},
  pages = {355--377},
  year = {2008}
}


%LTM_flex %random (= frailty PH model) %spezi %NPMLE
% Note: NPMLE approach for semiparametric frailty Cox models;
%       frailty parameter is from a known one-parameter family of distributions with 
%       mean 1;
%       linear predictor with time-varying covariates.
@article{Kosoroketal_2004,
  title = {Robust Inference for Univariate Proportional Hazards Frailty Regression Models},
  author = {M. R. Kosorok and B. L. Lee and J. P. Fine},
  journal = {The Annals of Statistics},
  volume = {32},
  number = {4},
  pages = {1448--1491},
  doi = {10.1214/009053604000000535},
  year = {2004}
}


%VIP %LTM %random %spezi %NPMLE
% Note: NPMLE approach for the frailty PH model with arbitrarily truncated and 
%       censored response;
%       approach can be generalised to frailty LTMs by adapting link G.
@article{HuberCarolVonta_2004,
  year = {2004},
  journal = {Lifetime Data Analysis},
  volume = {10},
  number = {4},
  doi = {10.1007/s10985-004-4773-y},
  title = {Frailty Models for Arbitrarily Censored and Truncated Data},
  author = {C. Huber-Carol and I. Vonta},
  pages = {369--388}
}

%LTM_flex %spezi %NPMLE
% Note: LTM with nonparametric covariate effects (additive transformation model); 
%       nonparametric covariate effects are estimated using local linear regression.
@article{Zhaoetal_2007,
  author = {X. Zhao and X. Zhou and X. Wu},
  title = {Local Linear Regression in Proportional Hazards Model with Censored Data},
  journal = {Communications in Statistics--Theory and Methods},
  volume = {36},
  number = {15},
  pages = {2761--2776},
  year = {2007},
  doi = {10.1080/03610920701386828}
}


%VIP %LTM %random %pen_lik %mixedmod
% Note: log-hazard function is parametrised using a piecewise-linear spline;
%       penalised likelihood is maximised by a mixed model - based approach
%       => smooth estimate of the hazard function, where amount of smoothing is
%          estimated from the data;
%       integrated log-likelihood is approximated by a PQL approach; 
%       variance parameter of the spline coefficients / random effects is estimated
%       using REML.
@article{CaiBetensky_2003,
  author = {T. Cai and R. A. Betensky},
  title = {Hazard Regression for Interval-Censored Data with Penalized Spline},
  journal = {Biometrics},
  volume = {59},
  number = {3},
  doi = {10.1111/1541-0420.00067},
  pages = {570--579},
  year = {2003}
}



%LTM_flex (AFT model) %spezi %NPMLE %profile_lik
% Note: nonparametric ML method for AFT models with possibly time-dependent covariates;
%       regression parameters are estimated by maximising a kernel-smoothed profile
%       likelihood function;
%       cumulative hazard function has to be smoothed in AFT models because otherwise
%       there exists no maximum of the log-likelihood!
@article{ZengLin_2007a,
  author = {D. Zeng and D. Y. Lin}, 
  title = {Efficient Estimation for the Accelerated Failure Time Model},
  volume = {102}, 
  number = {480}, 
  pages = {1387--1396}, 
  year = {2007}, 
  doi = {10.1198/016214507000001085},
  journal = {Journal of the American Statistical Association} 
}

%VIP %LTM %not_spezi %estequ
% Note: dichotomous comparisons {I(Y_i > Y_j)} are used => h can be ignored because
%       rank configurations of Y_i > Y_j and h(Y_i) > h(Y_j) are identical;
%       estimating equation for beta which can be solved using Newton-Raphson algorithm;
%       right-censored observations: reweight estimating equation by the inverse
%       squared marginal Kaplan-Meier estimator (IPCW approach).
@article{Chengetal_1995,
  author = 	{S. C. Cheng and L. J. Wei and Z. Ying}, 
  title = 	{Analysis of Transformation Models with Censored Data},
  volume = 	{82}, 
  number = 	{4}, 
  pages = 	{835--845}, 
  year = 	{1995}, 
  doi = 	{10.1093/biomet/82.4.835}, 
  journal = 	{Biometrika} 
}

%VIP %LTM %spezi %estequ
% Note: authors define an additional estimating equation for the response transformation
%       h; this is necessary for the prediction of survival probabilities;
%       beta and h are estimated separately based on two estimating equations
%       => no simultaneous estimation of h and beta!
@article{Chengetal_1997,
  title = {Predicting Survival Probabilities with Semiparametric Transformation Models},
  author = {S. C. Cheng and L. J. Wei and Z. Ying},
  journal = {Journal of the American Statistical Association},
  volume = {92},
  number = {437},
  pages = {227--235},
  doi = {10.1080/01621459.1997.10473620},
  year = {1997}
}

%optional %LTM %spezi %estequ
% Note: Estimating equations of Cheng et al. (1995,1997) are simply modified because the 
%       estimators are asymptotically biased when the support of the censoring variable
%       is shorter than the support of the failure time;
%       root-finding equations are replaced by a least-squares criterion;
%       no simultaneous estimation of beta and h; 
%       => unique and consistent estimator
@article{Fineetal_1998,
  author = {J. P. Fine and Z. Ying and L. G. Wei},
  journal = {Biometrika}, 
  number = {4},
  pages = {980--986},
  title = {On the Linear Transformation Model for Censored Data},
  volume = {85},
  doi = {10.1093/biomet/85.4.980},
  year = {1998}
}

%optional %LTM_flex %spezi %estequ
% Note: linear transformation model is extended to parametric covariate transformations;
%       extension seems simple at first sight, but inference is challenging due to 
%       loss of identifiability under the hypotheses of no effects of transformed 
%       covariates.    
@article{FanFine_2013,
  author = {C. Fan and J. P. Fine},
  title = {Linear Transformation Model with Parametric Covariate Transformations},
  journal = {Journal of the American Statistical Association},
  volume = {108},
  number = {502},
  pages = {701--712},
  year = {2013},
  doi = {10.1080/01621459.2013.770707}
}


%optional %LTM_flex %spezi %estequ
% Note: LTMs are extended to correlated observations;
%       introduction of subject- and cluster-specific time-dependent covariates:
%       h(T_ik) = - beta^T %*% Z_ik(t) + eps;
%       estimating equations for beta and h (GEE with indpendence working assumption);
%       approach is more similar to NPMLE than to alternative estimating equations.
@article{Caietal_2000,
  author = {T. Cai and L. J. Wei and M. Wilcox},
  journal = {Biometrika},
  number = {4},
  pages = {867--878},
  title = {Semiparametric Regression Analysis for Clustered Failure Time Data},
  volume = {87},
  doi = {10.1093/biomet/87.4.867},
  year = {2000}
}

%VIP %LTM %random %spezi %estequ
% Note: Linear transformation model with random effects; 
%       frailty Cox model is included as a special case;
%       distribution of the random effects is specified up to a parameter;
%       h and beta are not estimated simultaneously but using separate estimating
%       equations.
@article{Caietal_2002,
  author = {T. Cai and S. C. Cheng and L. J. Wei},
  title = {Semiparametric Mixed-Effects Models for Clustered Failure Time Data},
  journal = {Journal of the American Statistical Association},
  volume = {97},
  number = {458},
  pages = {514--522},
  year = {2002},
  doi = {10.1198/016214502760047041}
}


%optional %LTM %not_spezi %estequ
% Note: LTMs for interval-censored observations;
%       rank-based estimating equation for the regression coefficients is provided
%       => baseline-free approach; 
%       approach is restricted to discrete covariates!
%% no DOI (checked)
@article{Zhangetal_2005,
  title = {Regression Analysis of Interval-Censored Failure Time Data 
           with Linear Transformation Models},
  author = {Z. Zhang and L. Sun and X. Zhao and J. Sun},
  journal = {The Canadian Journal of Statistics},
  volume = {33},
  number = {1},
  pages = {61--70},
  year = {2005}
}

%optional %LTM %spezi %estequ
% Note: approach of Zhang et al. (2005) is extended to survival probability prediction
%       by defining a separate estimating equation for h;
%       beta and h are not estimated simultaneously in the presence of interval
%       censoring;
%       tools for model checking and model selection are additionally considered.
@article{Zhang_2009,
  author = {Z. Zhang}, 
  title = {Linear Transformation Models for Interval-Censored Data: 
           Prediction of Survival Probability and Model Checking},
  volume = {9}, 
  number = {4}, 
  pages = {321--343}, 
  year = {2009}, 
  doi = {10.1177/1471082X0900900404},  
  journal = {Statistical Modelling} 
}


%LTM %random %not_spezi %estequ
% Note: consideration of a panel data version of the LTM with random effects in 
%       ECONOMETRICS!
%       estimating equation only for the regression coefficients beta
%       => baseline-free approach
@article{Lee_2008,
  author = {S. Lee},
  title = {Estimating Panel Data Duration Models with Censored Data},
  journal = {Econometric Theory},
  volume = {24},
  number = {05},
  year = {2008},
  pages = {1254--1276},
  doi = {10.1017/S0266466608080493}
}


%VIP %LTM %spezi %estequ
% Note: most estimating equations (e.g. Cheng et al. (1995)) assume independence of 
%       the censoring time C and the covariates X because the marginal Kaplan-Meier
%       estimator of the censoring distribution is used in the IPCWs;
%       assumption is relaxed here + e.g. Cox model does not make this assumption
%       => Cox partial likelihood estimator results as a special case;
%       maringale-based estimating equations for beta and h => beta and h are 
%       estimated iteratively;
%       h is assumed to be a nondecreasing step function with jumps at the failure 
%       times. 
@article{Chenetal_2002,
  author = {K. Chen and Z. Jin and Z. Ying}, 
  title = {Semiparametric Analysis of Transformation Models with Censored Data},
  volume = {89}, 
  number = {3}, 
  pages = {659--668}, 
  year = {2002}, 
  doi = {10.1093/biomet/89.3.659}, 
  journal = {Biometrika} 
}


%LTM_flex %spezi %estequ
% Note: non-linear covariate effects are incorporated into the LTM
%       => partially linear transformation model;
%       global and kernel-weighted local estimating equations based on martingale theory
%       => extension of Chen et al. (2002)'s EEs to non-linear covariate effects.
%       Global EEs for beta and h (step function) similar to Chen et al. (2002);
%       Local kernel-weighted EE for nonlinear covariate effects given beta and h.
@article{LuZhang_2010,
  author = {W. Lu and H. H. Zhang},
  title = {On Estimation of Partially Linear Transformation Models},
  journal = {Journal of the American Statistical Association},
  volume = {105},
  number = {490},
  pages = {683--691},
  year = {2010},
  doi = {10.1198/jasa.2010.tm09302}
}

%VIP %flex_int_y %spezi %estequ
% Note: LTMs are extended to time-varying structure for the transformation function
%       => time-varying structure in the data is allowed, baseline function may 
%          depend on the covariates;
%       stratified LTM is included as a special case;
%       martingale estimating equations are defined for model estimation.
@article{Scheike_2006,
  year = {2006},
  journal = {Lifetime Data Analysis},
  volume = {12},
  number = {4},
  doi = {10.1007/s10985-006-9021-1},
  title = {A Flexible Semiparametric Transformation Model for Survival Data},
  author = {T. H. Scheike},
  pages = {461--480}
}



%LTM %not_spezi %partial_lik
k@article{Cox_1972,
  author = {D. R. Cox},
  title = {Regression Models and Life-Tables},
  journal = {Journal of the Royal Statistical Society B},
  volume = {34},
  number = {2},
  pages = {187--220},
  year = {1972}
}

%LTM %not_spezi %partial_lik
@article{Cox_1975,
  author = {D. R. Cox},
  title = {Partial Likelihood},
  journal = {Biometrika},
  volume = {62},
  number = {2},
  pages = {269--276},
  year = {1975}
}

%VIP %flex_int_y %not_spezi %partial_lik
% Note: Cox model with time-dependent coefficients;
%       estimation via local partial likelihood techniques;
%       local linear fitting techniques known from scatterplot smoothing are used;
%       coefficients are estimated locally based on the partial likelihood in a 
%       window around each time point;
%       approach can be used to check the validity of the PH assumption.
@article {CaiSun_2003,
  author = {Z. Cai and Y. Sun},
  title = {Local Linear Estimation for Time-Dependent 
           Coefficients in {C}ox's Regression Models},
  journal = {Scandinavian Journal of Statistics},
  volume = {30},
  number = {1},
  doi = {10.1111/1467-9469.00320},
  pages = {93--111},
  year = {2003}
}


%LTM_flex %not_spezi %partial_lik
@article{SlepperHarrington_1990,
  author = {Sleeper, Lynn A. and Harrington, David P.},
  title = {Regression Splines in the {C}ox Model with Application 
           to Covariate Effects in Liver Disease},
  journal = {Journal of the American Statistical Association},
  volume = {85},
  number = {412},
  pages = {941--949},
  year = {1990},
  doi = {10.1080/01621459.1990.10474965}
}


%flex_int %not_spezi %marg_lik
% Note: baseline-free approach for a general class of semiparametric transformation
%       models under interval censoring;
%       model estimation via maximising the marginal log-likelihood;
%       marginal log-likelihood has no closed analytic form => three-stage MCMC
%       stochastic approximation algorithm;
%       frailty models and heteroscedastic hazard/rank regression models are included
%       as special cases.
@article{Guetal_2005,
  year = {2005},
  journal = {Lifetime Data Analysis},
  volume = {11},
  number = {4},
  doi = {10.1007/s10985-005-5235-x},
  title = {A Baseline-free Procedure for Transformation Models Under Interval Censorship},
  author={M. Gu and L. Sun and G. Zuo},
  pages = {473--488}
}

%LTM (= PO model) %not_spezi %marg_lik
% Note: survival times are replaced by their ranks => marginal likelihood is maximised
%       w.r.t. the regression coefficients.
@article {Pettitt_1984,
  author = {A. N. Pettitt},
  title = {Proportional Odds Models for Survival Data and Estimates Using Ranks},
  journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
  volume = {33},
  number = 2,
  pages = {169--175},
  year = {1984}
}


%LTM (= PO model) %not_spezi %marg_lik
% Note: baseline-free approach because only rank order information among patients is
%       used; rank order preserves information about the regression parameters;
%       marginal likelihood is approximated using a Monte Carlo method.
@article{LamLeung_2001,
  year = {2001},
  journal = {Lifetime Data Analysis},
  volume = {7},
  number = {1}, 
  doi = {10.1023/A:1009673026121},
  title = {Marginal Likelihood Estimation for Proportional Odds Models 
           with Right Censored Data},
  author = {K. F. Lam and T. L. Leung},
  pages = {39--54}
}


%LTM (= PO model) %random %not_spezi %marg_lik
% Note: Semiparametric random effects PO model for multivariate survival times with 
%       various types of dependence structures;
%       cluster data and repeated measurements are covered;
%       assumption of multivariate normal effects;
%       regression and variance parameters are estimated by maximising the 
%       marginal rank likelihood;
%       marginal likelihood is approximated by a Monte Carlo method.
@article{Lametal_2002,
  author = {K. F. Lam and Y. W. Lee and T. L. Leung},
  title = {Modeling Multivariate Survival Data by a Semiparametric 
           Random Effects Proportional Odds Model},
  journal = {Biometrics},
  volume = {58},
  number = {2},
  doi = {10.1111/j.0006-341X.2002.00316.x},
  pages = {316--323},
  year = {2002}
}


%LTM_flex %not_spezi %marg_lik
% Note: special case of Gu et al. (2005);
%       varying coefficient component is included in linear transformation models;
%       coefficient functions are parametrised using B-splines;
%       estimation is based on maximising the marginal rank log-likelihood;
%       three-stage MCMC stochastic approximation algorithm.
@article{Lietal_2012,
  author = {J. Li and M. Gu and T. Hu},
  title = {General Partially Linear Varying-Coefficient 
           Transformation Models for Ranking Data},
  journal = {Journal of Applied Statistics},
  volume = {39},
  number = {7},
  pages = {1475--1488},
  year = {2012},
  doi = {10.1080/02664763.2012.658357}
}

%VIP %LTM %spezi %bayes
% Note: Bayesian semiparametric transformation model;
%       PH, PH and AFT are included as special cases;
%       can be generalised to multivariate survival data using frailty models;
%       Priors: 
%       beta: multivariate normal
%       h: mixture of incomplete beta functions
%       F: Polya tree prior;
%       MCMC algorithm for model estimation.
@article{MallickWalker_2003,
  title = {A {B}ayesian Semiparametric Transformation Model Incorporating Frailties},
  journal = {Journal of Statistical Planning and Inference},
  volume = {112},
  number = {1--2},
  pages = {159--174},
  year = {2003},
  doi = {10.1016/S0378-3758(02)00330-0},
  author = {B. K. Mallick and S. Walker}
}


%LTM (= PO model) %spezi %bayes
% Note: Bayesian semiparametric PO model;
%       prior for the baseline survival function: mixture of finite Polya trees.
@article{HansonYang_2007,
  author = {T. Hanson and M. Yang},
  title = {Bayesian Semiparametric Proportional Odds Models},
  journal = {Biometrics},
  volume = {63},
  number = {1},
  doi = {10.1111/j.1541-0420.2006.00671.x},
  pages = {88--95},
  year = {2007}
}

%flex_int %spezi %bayes
% Note: Bayesian analysis of a class of generalised odds-rate hazards (GORH) models;
%       non-PH, PH, PO, AFT are included as special cases.
@article{Banerjeeetal_2007, 
  year = {2007},
  journal = {Lifetime Data Analysis},
  volume = {13},
  number = {2},
  doi = {10.1007/s10985-007-9035-3},
  title = {Bayesian Analysis of Generalized Odds-Rate Hazards Models for Survival Data},
  author = {T. Banerjee and M.-H Chen and D. K. Dey and S. Kim},
  pages = {241--260}
}


%further_extension %LTM %spezi %estequ
% Note: authors suggest a Box-Cox transformation of the survivor function;
%       model class is related to frailty models.
@article {ZuckerYang_2006,
  author = {D. M. Zucker and S. Yang},
  title = {Inference for a Family of Survival Models Encompassing 
           the Proportional Hazards and Proportional Odds Models},
  journal = {Statistics in Medicine},
  volume = {25},
  number = {6},
  doi = {10.1002/sim.2255},
  pages = {995--1014},
  year = {2006}
}

%further_extension %LTM %spezi %profile_lik
% Note: response transformation h is parametric, but F and covariate effects are 
%       nonparametric;
%       constraints: h, F and covariate effects are smooth; h and F monotone increasing.
@article{lintonetal_2008,
  author = {O. Linton and S. Sperlich and I. {van Keilegom}},
  doi = {10.1214/009053607000000848},
  journal = {The Annals of Statistics},
  number = {2},
  pages = {686--718},
  title = {Estimation of a Semiparametric Transformation Model},
  volume = {36},
  year = {2008}
}


%further_extension %LTM %spezi %marg_lik
% Note: h and F are unspecified; 
%       smoothed partial rank estimator is suggested;
@article{Songetal_2007,
  author = 	{X. Song and S. Ma and J. Huang and X.-H. Zhou}, 
  title = 	{A Semiparametric Approach for the Nonparametric 
                 Transformation Survival Model with Multiple Covariates},
  volume = 	{8}, 
  number = 	{2}, 
  pages = 	{197--211}, 
  year = 	{2007}, 
  doi = 	{10.1093/biostatistics/kxl001}, 
  journal = 	{Biostatistics} 
}


%VIP %furhter_extension
% Note: Transformation models in econometrics;
%       - h and F are parametric => maximum likelihood methods;
%       - h is parametric, F is nonparmetric => F is estimated based on the empirical 
%         distribution of the residuals; beta with the generalised method of moments
%       - h and F are nonparametric => estimation techniques for single index models
@book{Horowitz_2009,
  author = {J. L. Horowitz},
  title = {Semiparametric and Nonparametric Methods in Econometrics},
  publisher = {Springer-Verlag},
  year = {2009},
  address = {New York, U.S.A.}
}


% Semiparametric AFT models (i.e. F is nonparametric):
@article{Jinetal_2003,
  author = {Z. Jin and D. Y. Lin and L. J. Wei and Z. Ying}, 
  title = {Rank--based Inference for the Accelerated Failure Time Model},
  volume = {90}, 
  number = {2}, 
  pages = {341--353}, 
  year = {2003}, 
  doi = {10.1093/biomet/90.2.341}, 
  journal = {Biometrika} 
}

@Manual{R,
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@article{Horowitz_1996,
  author = {Joel L. Horowitz},
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@article{Jones_Pewsey_2009,
  author = {M. C. Jones and A. Pewsey},
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  volume = {96},
  number = {4},
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@article{Chang_Hsiung_Wu_2005,
  author = {I. Chang and Chao A. Hsiung and Yuh-Jenn Wu and Che-Chi Yany},
  title = {Bayesian Survival Analysis Using {Bernstein} Polynomials},
  year = {2005},
  journal = {Scandinavian Journal of Statistics},
  volume = {32},
  number = {3},
  pages = {447--466},
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@article{Curtis_Ghosh_2011,
  author = {S. McKay Curtis and Sujit K. Ghosh},
  title = {A Variable Selection Approach to Monotonic Regression 
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  year = {2011},
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  number = {5},
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@article{Farouki_2012,
  author = {Rida T. Farouki},
  title = {The {Bernstein} Polynomial Basis: A Centennial Retrospective},
  year = {2012},
  journal = {Computer Aided Geometric Design},
  volume = {29},
  number = {6},
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  pages = {379--419}
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@article{Sun_Sundaram_Zhao_2009,
  author = {Yanqing Sun and Rajeshwari Sundaram and Yichuan Zhao},
  title = {Empirical Likelihood Inference for the {Cox} Model with Time-dependent
           Coefficients via Local Partial Likelihood},
  year = {2009},
  journal = {Scandinavian Journal of Statistics},
  volume = {36},
  number = {3},
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@Article{Hothorn_Bretz_Westfall_2008,
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  year = 2008,
  title = {Simultaneous Inference in General Parametric Models},
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  volume = 50,
  number = 3,
  pages = {346--363},
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@article{Royston_Parmar_2002,
  author = {Patrick Royston and Mahesh K. B. Parmar},
  title = {Flexible Parametric Proportional-hazards and Proportional-odds 
           Models for Censored Survival Data, with Application to Prognostic 
           Modelling and Estimation of Treatment Effects},
  year = {2002},
  journal = {Statistics in Medicine},
  volume = {21},
  number = {15},
  DOI = {10.1002/sim.1203},
  pages = {2175--2197}
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@Book{            Koenker_2005,
  title         = {Quantile Regression},
  publisher     = {Cambridge University Press},
  year          = {2005},
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  language      = {english},
  address       = {New York, U.S.A.}
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@Article{         Rigby_Stasinopoulos_2005,
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### constant effects of time-varying covariates
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