Survival Analysis: Exploring the Concept with Manual Examples and in R

Survival Analysis: Exploring the Concept with Manual Examples and in R

Introduction:

The log-rank test is a statistical test used to compare the survival between two groups. It is also known as the Mantel-Cox test. The test compares the observed number of events in each group to what would be expected if the survival curves were identical. The test is nonparametric, meaning it makes no assumptions about the survival distributions.

In this article, we explain the concept of the log-rank test and provide an example dataset to demonstrate its application. We also provide a step-by-step guide on how to perform the test manually and using R.

After performing the test, we interpret the results and discuss the significance level in rejecting the null hypothesis. Finally, we compare the results obtained manually with the results generated using the survdiff function in R.

Overall, the log-rank test is a useful tool for comparing survival curves between two groups and determining if there is a statistically significant difference in survival between them.

Full Article: Survival Analysis: Exploring the Concept with Manual Examples and in R

Log-Rank Test: Comparing Survival Between Two Groups

In this news article, we will focus on the log-rank test, also known as the Mantel-Cox test, which is used to compare survival between two groups. The log-rank test is a statistical test that compares the observed number of events in each group to what would be expected if the survival curves were identical. The test assumes no assumptions about the survival distributions, making it a nonparametric test.

Dataset:

We will use the following dataset for our example:

Patient Group Time Event
1 1 4.1 1
2 1 7.8 0
3 1 10.0 1
4 1 10.0 1
5 1 12.3 0
6 1 17.2 1
7 2 9.7 1
8 2 10.0 1
9 2 11.1 0
10 2 13.1 0
11 2 19.7 1
12 2 24.1 0

Hypotheses:

For this example, we are interested in comparing Group 1 and Group 2 in terms of survival. We set up the following hypotheses:

Null Hypothesis (H0): Survival curves for Group 1 and Group 2 are identical (S1(t) = S2(t) for all t).
Alternative Hypothesis (H1): Survival curves for Group 1 and Group 2 are different (S1(t) ≠ S2(t) for some t).

Test Statistic:

To perform the log-rank test, we use the following test statistic:

U = ∑j w(y(j))(Oj – Ej)

where U is the test statistic, w(y(j)) is the weight for the jth time point, Oj is the observed number of events in each group at time j, and Ej is the expected number of events in the first group assuming equal hazard rates.

Results:

By filling in the table for the log-rank test by hand, we calculate the test statistic Uobs = 1.275. Using a significance level of 0.05, we compare Uobs to the critical value z0.975 = 1.96. Since |Uobs| < z0.975, we do not reject the null hypothesis. This means that based on the data, we cannot conclude that survival is different between the two groups. Alternatively, we can use the survdiff() function in R to perform the log-rank test. The results from the function provide the test statistic, observed and expected values, and the p-value. Conclusion: In conclusion, the log-rank test is a statistical test used to compare survival between two groups. In our example, based on the data, we do not reject the null hypothesis and cannot conclude that survival is different between Group 1 and Group 2. This test is commonly used in survival analysis to assess the impact of different factors on survival outcomes.

Summary: Survival Analysis: Exploring the Concept with Manual Examples and in R

The log-rank test is a statistical test used to compare survival between two groups. It compares the observed number of events in each group to what would be expected if the survival curves were identical. The test is nonparametric, meaning it makes no assumptions about the survival distributions. In order to perform the test, a test statistic called U is calculated, and if the p-value is less than a certain significance level (usually 0.05), the null hypothesis is rejected. In this article, a step-by-step explanation of the log-rank test is provided, along with an example dataset and code in R to perform the test. The conclusion from the test is that there is no significant difference in survival between the two groups.

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