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 model).

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.

In
left censoring observation ends before a given point in time. In right censoring the subject is last seen alive at a given
time and is not followed up subsequently. Interval censoring, a mixture of left and right censoring, occurs between two given
time given points in time. Right censoring is more common than left censoring. Random censoring occurs uniformly throughout
the study, is not related to outcome, and is not biased. Non-random censoring is due to investigator manipulation and can
cause bias. Progressive censoring occurs in studies in which entry and censoring times are different for each subject. 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.