# Log Rank Test in R-Survival Curve Comparison

Log Rank Test in R, the most frequent technique to compare survival curves between two groups is to use a log-rank test.

Test hypotheses:

Ho: In terms of survivability, there is no difference between the two groups.

Hi: There is a survival differential between the two groups.

We can reject the null hypothesis and infer that there is enough evidence to claim there is a difference in survival between the two groups if the p-value of the test is less than 0.05 (95% confidence level).

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In R, we can use the survdiff() function from the survival package to do a log-rank test, which has the following syntax:

`survdiff(Surv(time, status) ~ predictors, data)`

The Chi-Squared test statistic and related p-value are returned by the above function

## log-rank test in R.

Following libraries are required for the analysis.

```library("survival")
library("survminer")
library("Rcpp")```

The lung cancer data was utilized from the survival package.

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```data("lung")
```    inst time status age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
1    3  306      2  74   1       1       90       100     1175      NA
2    3  455      2  68   1       0       90        90     1225      15
3    3 1010      1  56   1       0       90        90       NA      15
4    5  210      2  57   1       1       90        60     1150      11
5    1  883      2  60   1       0      100        90       NA       0
6   12 1022      1  74   1       1       50        80      513       0```

Type the following code to compute survival curves:

```fit <- survfit(Surv(time, status) ~ sex, data = lung)
print(fit)```
```Call: survfit(formula = Surv(time, status) ~ sex, data = lung)
n events median 0.95LCL 0.95UCL
sex=1 138    112    270     212     310
sex=2  90     53    426     348     550```

The sort summary table can be accessed based on the below code

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`summary(fit)\$table`
```records n.max n.start events   *rmean *se(rmean) median 0.95LCL 0.95UCL
sex=1     138   138     138    112 325.0663   22.59845    270     212     310
sex=2      90    90      90     53 458.2757   33.78530    426     348     550```

## Visulization

The following code allows us to understand the survival curves in a better way.

```ggsurvplot(fit,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))``` The survival chance is 1.0 at time zero (or 100 percent of the participants are alive).

At time 250, the chances of survival for sex=1 are about 0.55 (or 55 percent) and 0.75 (or 75 percent) for sex=2.

The median survival time for sex=1 is 270 days and for sex=2 is 426 days, indicating that sex=2 has a better survival rate than sex=1.

The following code shows how to perform a log-rank test to determine if there is a difference in survival between sex who received different treatments:

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### Perform log-rank test

```surv_diff <- survdiff(Surv(time, status) ~ sex, data = lung)
surv_diff```
```Call:
survdiff(formula = Surv(time, status) ~ sex, data = lung)
N Observed Expected (O-E)^2/E (O-E)^2/V
sex=1 138      112     91.6      4.55      10.3
sex=2  90       53     73.4      5.68      10.3
Chisq= 10.3  on 1 degrees of freedom, p= 0.001```

The Chi-Squared test statistic is 10.3 with 1 degree of freedom and the corresponding p-value is 0.001. Since this p-value is less than 0.05, we reject the null hypothesis.

In other words, we have sufficient evidence to say that there is a statistically significant difference in survival between the two groups.

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