**INTERNATIONAL SEMINAR ON MULTI-STATE MODELS**

**Vigo, March 26 2014**

*Salón de Grados** de la **Facultad de Ciencias Económicas y
Empresariales*

Universidad de Vigo

Campus Universitario Lagoas-Marcosende, 36310
Vigo – Spain

**Local
Organizer:**

*Jacobo de Uña Álvarez
Grupo de Investigación *

Universidad de Vigo

**PROGRAM:**

10:30 –
11:15 “The Jackknife estimate of variance for transition probabilities in the
non-Markov illness-death model”, **Leyla Azarang** (University of Vigo, Spain)

Abstract:
Non-parametric estimators of transition probabilities for non-Markov
illness-death model were introduced by Meira-Machado
et al. (2006). In this seminar, to compute confidence intervals for these
estimators, the problem of consistently estimating the limit variance will be
explored. To estimate the variance, the limit variances and covariance for some
special bivariate Kaplan-Meier integrals with covariates, where the
marginal distribution of the total survival time of the process weights the
data and the sojourn time in the initial state plays the role of covariate, are
approximated using the Jackknife method. Through some simulation study, the new
asymptotic result will be discussed.

11:15 –
11:45 Coffee-break

11:45 – 12:30
“A review of the estimation of transition probabilities in non-Markov models
and related quantities”, **Luís**** Filipe Meira-Machado** (University of Minho, Portugal) http://w3.math.uminho.pt/~lmachado/

Abstract:
One important goal in multi-state modeling is the estimation of transition
probabilities. In longitudinal medical studies these quantities are
particularly of interest since they allow for long-term predictions of the
process. In recent years significant contributions have been made regarding
this topic. First, new estimators have been introduced for non-Markov
processes; Second, recent methods were proposed that deal with the problem of
dependent censoring and account for the influence of covariates. Other
important targets include the state occupation probabilities (which can be seen
as a particular case of the transition probabilities), the cumulative incidence
function and the waiting time distributions. In this talk new estimators for
(some of) these quantities will be introduced. Simulations demonstrate that the
new estimators may outperform the later estimators. An illustration through
real data analysis is included.

12:30 –
13:15 "Robust estimates of state occupancy and transition probabilities
for Non-Markov multi-state models", **Andrew
Titman** (University of Lancaster, UK) http://www.maths.lancs.ac.uk/~titman/

Abstract:
The seminar will consider approaches for consistently estimating the marginal
state occupancy probabilities and transition probabilities in multi-state
models, considering both continuously observed and interval censored data. In
each case, the objective is to obtain estimates that remain consistent for
non-Markov models. For continuously observed data up to right-censoring
an extension of the work of Meira-Machado et al
(2006) and Allignol et al (2013), to allow estimation
of marginal transition probabilities for general non-Markov models will be
presented. The proposed estimator involves the cumulative incidence functions
of a constructed competing risks process.

In the latter part of the talk, a computationally simple method for obtaining
non-parametric estimates of the state occupation probabilities for progressive
multi-state models under interval censoring will be presented. The method
involves estimating time-to-absorption using standard survival techniques and
using methods for current status data to estimate the conditional probabilities
of occupancy in non-absorbing states. The basic estimator is valid under the
assumption that the observation times are completely independent of the
multi-state process. An estimator valid under general non-informative
observation can be constructed through the use of inverse intensity weighting.
Some discussion of the difficulties of estimating transition probabilities, as
opposed to occupation probabilities, in the interval-censored case will be also
be given.

**REGISTRATION/INSCRIPCIÓN:**

There is no
registration fee. However, due to organizational issues, sending an e-mail to maria.tallon@uvigo.es with subject: **Registration
MSM2014** before Wednesday March 19 at 14:00 is mandatory. Please indicate
full name and affiliation (students at the Galician interuniversity Statistics Master
Program or at the Galician interuniversity Statistics
and OR Doctorate Program are particularly welcome).

La inscripción es gratuita. Por motivos de organización, es
necesario para inscribirse enviar *antes del miércoles 19 de marzo a las
14:00 horas* un e-mail a maria.tallon@uvigo.es con
tema: **Inscripción MSM2014 **indicando nombre completo y
afiliación (los estudiantes del Máster
interuniversitario en Técnicas Estadísticas y del Programa
de Doctorado interuniversitario en Estadística e Investigación Operativa
son especialmente bienvenidos).