The log-rank test

Survival Analysis in Python

Shae Wang

Senior Data Scientist

Hypothesis testing

A method of statistical inference
Null hypothesis $H_0$: e.g. California and Nevada residents have the same average income.
Alternative hypothesis $H_1$: e.g. California and Nevada residents have different average income.
P-value: what's the likelihood that the data would've occurred if the null hypothesis were true?

Hypothesis testing cartoon.

Log-rank hypothesis testing

Compares survival probabilities $S_i$ between groups at each time $t$

$H_0$: $S_A(t)=S_B(t)$

$H_1$: $S_A(t)\neq S_B(t)$

P-value: if $S_A(t)=S_B(t)$, what's the probability of our data occurring?

Multiple survival curves Multiple survival curves side-by-side.

Running the log-rank test

from lifelines.statistics import logrank_test

logrank_test(durations_A, durations_B, event_observed_A, event_observed_B)

.print_summary()
.p_value
.test_statistic

Log-rank test example

Does the program change when babies start speaking?

t.head(2)

    id  duration  observed
0    1        12         0
1    4         6         1

c.head(2)

    id  duration  observed
0    0        11         1
1    2        14         0

lrt = logrank_test(
    durations_A = t['duration'], 
    durations_B = c['duration'], 
    event_observed_A = t['observed'],
    event_observed_B = c['observed'])

lrt.print_summary()

<lifelines.StatisticalResult: logrank_test>
 null_distribution = chi squared
degrees_of_freedom = 1
         test_name = logrank_test
 test_statistic    p  -log2(p)
           0.09 0.77      0.38

Keep in mind...

Log-rank test is a non-parametric hypothesis test
When using lifelines, data must be right-censored (i.e. subject 3)
Censorship must be non-informative
For a log-rank test between $n>2$ groups, use pairwise_logrank_test() or multivariate_logrank_test()

Censorship cartoon.

Let's practice!

Survival Analysis in Python