NEMISA
NEW MODELS IN SURVIVAL ANALYSIS
The purpose of the research project
NEMISA (New Models in Survival
Analysis) is to be able to find a better model
for the survival function in survival analysis
both in the case of extreme values and when
there are missing values. Developed models
will be applied to problems in Health
Sciences as well as Engineering.
Let T denote a lifetime random
variable and X = (1,
x1, … xq)
explanatory/covariates. Various models
exist in the literature on describing data on T
and X. One of the simplest models is
assuming T ~ EXP (  ) where  = exp
(X  ),
 = ( 0
1
…  q)'. The
estimation of the parameters 
in this
model is well known and inferences on 
well documented. Even the case where no
distributional assumptions on T are made
has been studied extensively. The only
assumption is that the hazard function,
known as the proportional Cox hazard rate,
is given by  =  0 exp (X  ) where  0
is a baseline hazard rate. In this research
project models are developed where an
assumption is made on the distribution of T
such as the exponential, Weibull, gamma,
generalized
extreme
value,
Burr,
generalized Pareto and others. Special
interest is for the case where the data
contains extreme values. The work by
Thatcher gives a good summary of
applicable distributions where the maximum
age of human beings are predicted. The
estimation of the parameters in these models
where covariates are introduced and
censoring occurs, becomes extremely
problematic. NEMISA aproaches the
inferences in these models from a Bayesian
point of view. The estimation of the
parameters will be done using MCMC
algorithms. The results will be illustrated on
simulated data and real data.
Another type of model used in
lifetime data analyses is the ALM, when the
effect of environment (covariates) is
modelled via the scale transformation of the
baseline distribution functions. NEMISA
plans to compare ALM with PH in Bayesian
and non-Bayesian framework and to
consider the mentioned above distribution
functions as the baseline distribution
functions, specifically for modelling
extreme events.
This research is relevant in South
Africa with its high occurrence of some of
the big killer diseases, such as AIDS, TB
and Malaria. The expected lifetimes of HIV
positive patients under certain treatments
can be estimated more accurately with the
methods to be developed in this project. The
costs involved in treating these patients can
become a serious threat to governmental
funds and the demand for this kind of
research becomes therefore increasingly
important. The estimation of the probability
of any extremal event can be done with the
techniques from survival analysis. The
results of this research will not only be
important in the field of public health but
also in civil engineering and climatology.
More accurate assessments of the risk of
extreme hydrological events by estimating
appropriate multivariate statistical models
on observations are urgently desired in
complicated policy making decisions.
NEMISA will involve more in
detail:

Perform a comparative study of
conventional models in lifetime data
analyses,

Develop the Bayesian approach in
modelling environment via the
accelerated life model (ALM) and to
South African project leader: Prof. D.J. de Waal
Univ. of the Free State
P.O.Box 339
Bloemfontein 9300
Dutch project leader:Dr. P.H.A.J.M. van Gelder P.O.Box 5048
Delft University of Technology 2600 GA Delft - NL
Delft University of Technology
University of Fort Hare
compare it with the one based on the
proportional hazards (PH) model,

Model survival data with extreme
values,

Estimate the survival function under
such a model with the introduction of
explanatory variates or covariates,

Estimate missing data under the above
conditions,

Apply the results to simulated data and
real data.
In all cases use of the Bayesian approach in
the estimation process will be made. The
reason is that the MCMC algorithms allow
the introduction of a large number of
parameters in the model and make the
estimation of the parameters possible. It also
provides predictive distributions for future
observations which are valuable for model
checking and prediction of future
observations
This collaborative research project
must strengthen the linkages between UVS,
UFH and TU Delft. The fact that the other
members of the departments involved in this
research project will become aware of the
possibilities of such research collaboration
and how it is managed will be an additional
spin-off of this project. Other previously
disadvantaged academics will thus be
encouraged and motivated to do further
research of their own. In this way NEMISA
tries to fulfill the general objectives of
SANPAD:

Stimulating and promoting high
quality,
multidisciplinary,
collaborative, policy-oriented research

Facilitating the building of research
capacity in South Africa

Developing an institutional research
culture and a culture of interinstitutional research collaboration.
phone +27 51 4012311
fax +27 51 4442024
phone +31 15 2786544
fax +31 15 2785124
SANPAD
wwdw@wwg3.uovs.ac.za
email: p.vangelder@ct.tudelft.nl
www: http://surf.to/vangelder
University of the Free State
SANPAD - Workshop on
New Models in Survival Analysis
18-19 April 2002
TU Delft, Civil Engineering Building (Room 2.62 - 2.64)
Programme
Thursday 18 April
10.00 Opening by Dr. PHAJM van Gelder
10.05 An overview of SANPAD by N. van der Lans MSc.
10.15 The mixed linear model applied to heavy tail distributions by Prof. DJ de Waal
10.45 The use of modelling in survival analysis by Prof. J Tyler
11.15 Coffee
11.30 Life quality models by Dr. PHAJM van Gelder
12.00 Lunch
12.45 Modelling failure rates by mixtures by Prof. MS Finkelstein
13.15 Student presentation by Lucky Mukatlhe MSc
13.45 Departure to AIDS department of Amsterdam Medical Centre (AMC)
15.00 Welcome by Mrs. C.M.Roozeman
15.15 Movie on the AMC
15.30 Presentation by Dr. F.W.N.M.Wit (clinical epidemiologist)
16.15 Tour through the AMC
18.00 Dinner for invited workshop participants in Amsterdam
Friday 19 April
9.00 Coffee
9.10 Survival models by Prof. RM Cooke
9.40 AIDS survival models by Dr. R Geskus
10.10 Copula by Dr. D. Kurowicka
10.40 Bayesian Estimate and Inference for Entropy and Information Index of Fit by Prof. T. Mazzucchi
11.10 Coffee
11.30 Review of ZEDB data base processing methodology by C. Bunea MSc
12.00 Lunch
13.00 A critical review and some new proposals in extreme quantile and tail estimation by Prof. J Beirlant
13.30 The use of lifetime distributions in bridge replacement modelling by Prof. JM van Noortwijk
14.00 Coffee
14.30 General discussion
15.00 Closure
15.30 Team members discussion: evaluation of the workshop and research planning for 2002 and further.
18.00 Team members dinner in Delft
Annual report available on:
http://www.hydraulicengineering.tudelft.nl/public/gelder/sanpad011.zip