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Presentation at a Training
Program on Biostatistics for physician managers working in Public Health
Administration, Qassim Province on May 1, 2013 by Professor Omar Hasan Kasule
Sr MB ChB (MUK), MPH (Harvard), DrPH (Harvard) EM: omarkasule@yahoo.com
1.0 INTRODUCTION TO
SURVIVAL ANALYSIS
Survival
analysis is used to study survival duration and the effects of covariates on
survival. It uses parametric methods (Weibull, lognormal, or gamma) or
non-parametric methods (life-table, Kaplan-Maier, and the Proportional
hazards).
Time
is measured as time to relapse, length of remission, remission duration,
survival after relapse, time to death, or time to a complication.
The
best zero time is point of randomization. Other zero times are: enrolment, the
first visit, first symptoms, diagnosis, and start of treatment.
Problems
of survival analysis are censoring, truncation, and competing causes of death.
Censoring
is loss of information due to withdrawal from the study, study termination,
loss to follow-up, or death due to a competing risk. Clinical trials analysis
based on the intention to treat is more conservative than censored analysis.
In
left truncation, only individuals who survive a certain time are included in
the sample. In right truncation only individuals who have experienced the event
of interest by a given time are included in the sample.
Competing
causes of death are one cause of censoring that bias survival estimates.
2.0 NON-REGRESSION SURVIVAL ANALYSIS
Two non-regression methods are used in
survival analysis: the life-table and the Kaplan-Maier methods.
The life-table methods better with large
data sets and when the time of occurrence of an event cannot be measured
precisely. It leads to bias by assuming that withdrawals occur at the start of
the interval when in reality they occur throughout the interval.
The Kaplan-Maier method is best used for
small data sets in which the time of event occurrence is measured precisely. It
is an improvement on the life-table method in the handling of withdrawals. The
assumption could therefore create bias or imprecision. The Kaplan-Maier method
avoids this complication by not fixing the time intervals in advance.
3.0
REGRESSION METHODS FOR SURVIVAL ANALYSIS
The
Proportional hazards, a semi-parametric method proposed by Sir David Cox in
1972, is the most popular regression method for survival analysis. It is used
on data whose distribution is unknown.