Survival analysis & Kaplan Meire

SURVIVAL ANALYSIS
DR ATHAR KHAN
LIAQUAT COLLEGE OF MEDICINE & DENTISTRY
matharm@yahoo.com

4/20/2020 DR ATHAR KHAN 2
The surprising thing about young fools is how many
survive to become old fools.
—Doug Larson

Biomedical
Sciences
Engineering
Social
Sciences

OUTCOME VARIABLE

Case 2,4,6 are SE because they enter in the study
after the start of study but included in analysis

Survival analysis, or more generally, time-to-event analysis,
refers to a set of methods for analyzing the length of time until
the occurrence of a well-defined end point of interest.
START
Time to event is outcome variable
Binary outcome (event has occurred versus it has not occurred)
EVENT
Death/Occurrence/Reoccurrence
/Survival after treatment
TIME
Survival time, time-to-event, time to-
detection, failure time, relapse-free
survival time (also called disease-free survival
time), event-free survival.

Survival analysis is a statistical method which analyses data to
predict the time of occurrence of one or more event.
Survival time is time from the start of the study till the
occurrence of event is called survival time.
Survival in this context is remaining free of a particular outcome
over time.
Event-free survival which is the proportion of subjects who have
not yet experienced an event.
START EVENT
Complete remission/Relapse
TIME
Survival time, time-to-event, event time, time
to-detection and failure time

Cancer Studies e.g. Leukemia patients [time in remission]
(weeks)
Disease-free cohort [time until heart disease] (years)
Elderly (60+) population [time until death] (years)
Heart transplants [time until death] (months)
START
The time to event or survival time can be measured in days,
weeks, years, etc.
EVENT
Death/Occurrence/Reoccurrence
/Survival after treatment
TIME
Survival time, time-to-event, time to-
detection and failure time

Whether or not a participant suffers the event of interest during
the study period (i.e., a dichotomous variable) often coded as
1=event occurred or 0=event did not occur during the study
observation period.
Survival analysis focuses on two important pieces of information
The follow up time for each individual being followed.
Follow Up Time: Time zero, or the time origin, is the time at
which participants are considered at-risk for the outcome of
interest.

Types of Survival Analysis
▪ Non-parametric survival
▪ Kaplan-Meier method
▪ Life table method
▪ Nelson-Aalen method
▪ Parametric survival
▪ Exponential
▪ Weibull
▪ Gompertz
▪ Log-logistic

▪ Comparing survival distributions
▪ The log-rank test (also known as the Mantel log-rank test,
the Cox Mantel log-rank test, and the MantelHaenszel test)
is the most commonly used test for comparing survival
distributions.
▪ Breslow’s test (also known as Gehan’s generalised
Wilcoxon test)

▪ Survival models
▪ Survival models are used to quantify the effect of one or
more explanatory variables on failure time. This involves
specification of a linear-like model for the log hazard.
▪ Cox proportional hazards model

Censoring
• Observations are called censored when the information
about their survival time is incomplete.
• There are three main types of censoring: right, left, and
interval.
• The most common is called right censoring.
• This can occur when a participant drops out before the
study ends (the participants observed time is less than the
length of the follow-up).

Censoring
• When a participant is event free at the end of the
observation period (the participant's observed time is
equal to the length of the follow-up period).

An observation is left-censored if its initial time at risk is unknown. This will
occur if we do not know when a participant experienced for the first time the
condition of interest. For example, when an individual contracted a disease.

INTERVAL CENSORING In many applications, the time of the
event may be known only up to a time interval, especially when
the time is established by periodical examinations

During the study period, three participants suffer myocardial infarction (MI), one
dies, two drop out of the study (for unknown reasons), and four complete the 10-
year follow-up without suffering MI.

• An important assumption is made to make appropriate use
of the censored data. Specifically, we assume that
censoring is independent or unrelated to the likelihood of
developing the event of interest.
• This is called non-informative censoring and essentially
assumes that the participants whose data are censored
would have the same distribution of failure times (or times
to event) if they were actually observed.

In survival analysis we analyze not only the numbers of participants who suffer
the event of interest (a dichotomous indicator of event status), but also the times
at which the events occur.
What is the likelihood that a participant will suffer an MI over 10
years? 3/10 = 30%

The Kaplan-Meier Assumptions
• The event status should consist of two mutually exclusive( 2
events cannot both occur at the same time) and collectively
exhaustive states (at least one of the events must occur)
• The event status is mutually exclusive because the outcome for
a case can either be censored or the event has occurred. It
cannot be both.
• The time to an event or censorship (known as the "survival
time") should be clearly defined and precisely measured.

The Kaplan-Meier Assumptions
• Where possible, left-censoring should be minimized or
avoided.
• There should be independence of censoring and the event. This
means that the reason why cases are censored does not relate
to the event i.e. non informative censoring
• There should be a similar amount and pattern of censorship per
group.

months 07 to 140 cutoff.

Video Link
YouTube: How to Use SPSS-Kaplan-Meier Survival
Curve
https://www.youtube.com/watch?v=f4X5csxtJkE

H o = normality
If you accept, then assume normality
If you reject, then do not assume normality
If p < then 0.05, reject the H0
Use Kaplan Meier Test

▪ Overall censoring was 47/200(23.5%).
▪ Resumption of smoking was 153/200 (76.5%)
▪ Resumption of smoking in Hypnotherapy group was 79/104 (76%).
▪ Resumption of smoking in Nicotine patch group was 74/96(77%).

▪ Mean resumption of smoking time was 60 ± 3 months.
▪ In group-HP, mean resumption time was 58.4 ± 4.31 months.
▪ On the other hand in group-NP, mean resumption time was
62.2 ± 4.2 months.
▪ Median resumption of smoking time was 46.8 months.
▪ In group-HP, median resumption time was 44.4 months.
▪ On the other hand in group-NP, median resumption time was
49.2 months.

Confidence interval overlapping – No difference
22.6 75.7
35.7 51.2
Since there is a lot of overlap in the confidence intervals, it is unlikely that there is much
difference in the "average" survival time.
If confidence intervals do not overlap between levels, differences in effect on time to event
can be inferred.4/20/2020 DR ATHAR KHAN 53

Kaplan-Meier Survival Curve
0.5
Median Survival
Time

▪ The horizontal axis shows the time to event.
▪ In this plot, drops in the survival curve occur whenever the
participant resume smoking.
▪ The vertical axis shows the probability of survival (probability
of resuming smoking).
▪ In survival analysis the survival probabilities are usually
reported at certain time points on the curve (e.g. 1 year and 5
year survival); otherwise the median survival time (the time at
which 50% of the subjects have reached the event) can be
reported.

▪ Cumulative survival proportion appears to be higher in the
nicotine patch group compared to the hypnotherapy group.
▪ Hypnotherapy programme prolongs the time until participants
resume smoking (i.e., the event) compared to the other
interventions.

Pancanology Explains Kaplan-Meier Graphs
https://www.youtube.com/watch?v=KE1tkZmWhqU
VIDEO

▪ Survival curves cross each other (i.e., whether there is an
"interaction" between survival distributions).
▪ Survival curves are similarly shaped, even if they are above or
below one another.
▪ As such, a group survival curve that appears "above" another
group's survival curve is usually considered to be
demonstrating a beneficial/advantageous effect.
▪ Smooth curves are better than step down pattern curves.

SMOOTH CURVE

The p-value (sig) is the probability of getting a test statistic of at
least 0.379 if there really is no difference in survival times for
treatment groups. As the p-value = 0.538 and is greater than 0.05,
conclude that there is no significant evidence of a difference in
survival times for treatment groups. The estimated time until
resumption is 44.4 months for HP and 49.2 months for NP this
difference is statistically NOT significant (p=0.538) therefore,
both groups have similar time for start of smoking again.

The log rank test
▪ The log-rank test tests the hypothesis that there is no difference
in survival times between the groups studied at all time points in
the study.
▪ The log rank rest for the data in our example was P = 0.538;
thus the two curves are not statistically significantly different.

▪ Log-rank test: what happens later in time.
▪ Breslow: what happens later in time.
▪ Tarone: what happens middle in time.
▪ All three test p-value <0.05 – significant results
▪ All three test p-value > 0.05 – insignificant results
▪ If mix – at certain points significant

KM CURVE EXAMPLES

ONE GROUP

EXERCISE

REFERENCES
• http://sphweb.bumc.bu.edu/otlt/MPH-
Modules/BS/BS704_Survival/BS704_Survival_print.html
• https://statistics.laerd.com/spss-tutorials/kaplan-meier-using-
spss-statistics.php

DR ATHAR KHAN
MBBS, MCPS, DPH, DCPS-HCSM, DCPS-HPE, MBA, PGD-
STATISTICS, CCRP
ASSOCIATE PROFESSOR
DEPARTMENT OF COMMUNITY MEDICINE
LIAQUAT COLLEGE OF MEDICINE & DENTISTRY
KARACHI, PAKISTAN
0092-3232135932

Survival analysis & Kaplan Meire

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