Download University of Warwick, Department of Sociology, 2012/13 SO 201

University of Warwick, Department of Sociology, 2012/13
SO 201: SSAASS (Surveys and Statistics) (Richard Lampard)
Survival Analysis/Event History Analysis:
Proportional Hazards Models
(Week 17)
Definitions...
• Event history = Series of episodes/spells of
time spent in discrete states.
(Can be thought of in terms of transition
times, or durations/waiting times)
• Survival analysis = Duration of time to a
permanent transition into a different state.
Variables...
(in a survival analysis)
• Dependent variable: Survival (to a given
duration)
• Independent variables: An individual’s chance
of ‘survival’ can be affected both by
background characteristics which remain
constant over time and by time-varying
factors.
A complication...
• Censoring = When an individual is still in the
original state and their final survival duration
is thus as yet unknown.
• Censored cases need to be included in
analyses to avoid biases. (Where censoring is
related to the event history process in some
way, biases can still occur).
Looking at the risk
of not surviving over time
• Hazard rate = probability of event occurring
between time t and time t+1.
• Hazard function [ h(t) ] = frequency curve for
times at which events occur.
A key form of model...
• Proportional hazards model:
log h(t) = log h0(t) + b1x1 + b2x2 + ...
• The model is proportional in the sense that the
hazard functions have the same shape but differ
in magnitude, i.e. the hazard rate for two
individuals differs by a constant multiplicative
factor (e.g. the hazard for the first is consistently
twice the hazard for the second).
The pros of not being parametric...
• Unlike some other models used for analyzing
duration data, proportional hazards models do
not require a researcher to specify a form for the
hazard curve (technically speaking, they are semiparametric rather than parametric).
• These models are thus well-suited to situations
where a researcher is more interested in the
difference between the hazards for different
groups than in the way in which hazards vary with
duration.
a.k.a. Cox regression
The classic paper which introduced proportional hazards
models (and highlights their relationship with a standard
demographic tool: the ‘life table’ - see Hinde 1998: Ch. 4;
Newell, 1988: Ch. 6) is:
Cox, D.R. 1972. ‘Regression models and life tables’ (with
discussion), Journal of the Royal Statistical Society (Series
B), 34.2: 187-220.
• According to the Web of Science (Social Sciences Citation
Index) this has been cited 26,919 times...
But...
• Marsh and Elliott (2009) suggest that there
are some advantages to discrete time hazard
models, in which a form can be specified for
the hazard function.
• Discrete time models are also easier to
integrate more than one time-dependent
covariate into.
Similarities to logistic regression
• For a short discussion of proportional hazards
alongside a discussion of logistic regression
see:
Rose, D. and Sullivan, O. 1996. Introducing
Data Analysis for Social Scientists (2nd
Edition). Buckingham: Open University Press.
[Chapter 12].
Applications to marital formation
and marital dissolution
• Lampard, R. 1994. ‘An Examination of the
Relationship between Marital Dissolution and
Unemployment’. In Gallie, D., Marsh, C. and Vogler,
C. (eds) Social Change and the Experience of
Unemployment. Oxford: OUP. [264-298].
• Lampard, R. and Peggs, K. 1999. ‘Repartnering: the
relevance of parenthood and gender to cohabitation
and remarriage among the formerly married’, British
Journal of Sociology, 50.3: 443-465.
But it isn’t just me! (Examples...)
• South, S.J. and Lloyd, K.M. 1995. ‘Spousal
alternatives and marital dissolution’, American
Sociological Review, 60.1: 21-35.
• Reinhold, S. 2010. ‘Reassessing the Link
Between Premarital Cohabitation and Marital
Instability’, Demography 47.3: 719-733.
• Aryal, T.R. 2007. ‘Age at first marriage in
Nepal: Differentials and Determinants’, Journal
of Biosocial Science 39.5: 693-706.
A useful textbook?
• Kleinbaum, D. 2011. Survival Analysis: A SelfLearning Text (3rd edition). New York: SpringerVerlag.
• Other texts listed in the module reading list
are quite technical...