1. DR ATHAR KHAN
Associate Professor
Department of Community Medicine
Liaquat College of Medicine & Dentistry
Karachi, Pakistan
matharm@yahoo.com
4/7/19 DR ATHAR KHAN 1
2. INTRODUCTION
โข "Time to event outcome variableโ
โข A time to event variable reflects the time until a participant
has an event of interest (e.g., heart attack, goes into cancer
remission, death).
โข Statistical analysis of these variables is called time to event
analysis or survival analysis even though the outcome is
not always death.
โข "Survival" in this context is remaining free of a particular
outcome over time.
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3. Time to Event Variables
โข Times to event are always positive and their distributions
are often skewed.
โข For example, in a study assessing time to relapse in high
risk patients, the majority of events (relapses) may occur
early in the follow up with very few occurring later. On
the other hand, in a study of time to death in a community
based sample, the majority of events (deaths) may occur
later in the follow up.
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4. Time to Event Variables
โข Standard statistical procedures that assume normality of
distributions do not apply.
โข Specifically, complete data (actual time to event data) is
not always available on each participant in a study due to
incomplete follow-up information.
โข True survival time (sometimes called failure time) is not
known because the study ends or because a participant
drops out of the study before experiencing the event.
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5. Time to Event Variables
โข The event can be death, occurrence of a disease,
marriage, divorce, etc.
โข The time to event or survival time can be measured in
days, weeks, years, etc.
โข For example, if the event of interest is heart attack, then
the survival time can be the time in years until a person
develops a heart attack.
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6. Time to Event Variables
โข Parametric methods assume that the underlying
distribution of the survival times follows certain known
probability distributions. Popular ones include the
exponential, Weibull, and lognormal distributions.
โข A nonparametric estimator of the survival function, the
Kaplan Meier method is widely used to estimate and
graph survival probabilities as a function of time.
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7. Censoring
โข Observations are called censored when the information
about their survival time is incomplete.
โข There are three main types of censoring: right, left, and
interval.
โข The most common is called right censoring.
โข 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).
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8. Censoring
โข 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).
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9. 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.4/7/19 DR ATHAR KHAN 9
10. 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
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11. 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.
What is the likelihood that a participant will suffer an MI over 10
years? 3/7 = 43%
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12. โข 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.
โข 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.
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13. 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%
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14. โข Simple approaches researchers might choose to deal with
censored data are to set the censored observations to
missing or replace the unobserved value of the variable by
zero, the minimum, maximum, mean value, or a randomly
assigned value from the range of possible values.
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15. โข Survival analysis focuses on two important pieces of
information:
โข Whether or not a participant suffers the event of interest
during the study period (i.e., a dichotomous or indicator
variable often coded as 1=event occurred or 0=event did
not occur during the study observation period.
โข The follow up time for each individual being followed.
โข Follow Up Time: Time zero, or the time origin, is the time
at which participants are considered at-risk for the
outcome of interest.
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16. โข Examples of survival times in research
โข Cancer Studies e.g. Leukemia patients [time in
remission] (weeks)
โข Disease-free cohort [time until heart disease] (years)
โข Elderly (60+) population [time until death] (years)
โข Heart transplants [time until death] (months)
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17. The Kaplan-Meier Assumptions
โข 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)
โข 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.
โข The time to an event or censorship (known as the "survival
time") should be clearly defined and precisely measured.
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18. The Kaplan-Meier Assumptions
โข Where possible, left-censoring should be minimized or
avoided.
โข 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
โข There should be no secular trends (also known as secular
changes).
โข There should be a similar amount and pattern of censorship
per group.
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19. months 07 to 140 cutoff.
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26. Video Link
YouTube: How to Use SPSS-Kaplan-Meier Survival
Curve
https://www.youtube.com/watch?v=f4X5csxtJkE
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27. 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
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28. ๏ง Overall censoring was 47/200(23.5%).
๏ง Resumption of smoking was 153/200 (76.5%)
๏ง Resumption of smoking in Hypnotherapy group was 79/104 (76%).
๏ง Resumption of smoking in Nicotine patch group was 74/96(77%).
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31. ๏ง Mean resumption of smoking time was 60 ยฑ 3 months.
๏ง In group-HP, mean resumption time was 58.4 ยฑ 4.31 months.
๏ง On the other hand in group-NP, mean resumption time was
62.2 ยฑ 4.2 months.
๏ง Median resumption of smoking time was 46.8 months.
๏ง In group-HP, median resumption time was 44.4 months.
๏ง On the other hand in group-NP, median resumption time was
49.2 months.
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32. Confidence interval overlapping โ 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.4/7/19 DR ATHAR KHAN 32
34. ๏ง The horizontal axis shows the time to event.
๏ง In this plot, drops in the survival curve occur whenever the
participant resume smoking.
๏ง The vertical axis shows the probability of survival (probability
of resuming smoking).
๏ง 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.
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35. ๏ง Cumulative survival proportion appears to be higher in the
nicotine patch group compared to the hypnotherapy group.
๏ง Hypnotherapy programme prolongs the time until participants
resume smoking (i.e., the event) compared to the other
interventios.
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37. ๏ง Survival curves cross each other (i.e., whether there is an
"interaction" between survival distributions).
๏ง Survival curves are similarly shaped, even if they are above or
below one another.
๏ง As such, a group survival curve that appears "above" another
group's survival curve is usually considered to be
demonstrating a beneficial/advantageous effect.
๏ง Smooth curves are better than step down pattern curves.
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42. 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.
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43. The log rank test
๏ง 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.
๏ง The log rank rest for the data in our example was P = 0.538;
thus the two curves are not statistically significantly different.
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44. ๏ง Log-rank test: what happens later in time.
๏ง Breslow: what happens later in time.
๏ง Tarone: what happens middle in time.
๏ง All three test p-value <0.05 โ significant results
๏ง All three test p-value > 0.05 โ insignificant results
๏ง If mix โ at certain points significant
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