**Introduction**

**Why do we need special methods to analyze survival data?**

_{surviving}/N

_{total}) (3). Such an approach is usually called a direct method and, in the above example, it would take longer than five years to calculate the 5-year survival rate. All patients who were followed up for less than five years, whether alive or dead would have to be excluded from the calculation. This is a disadvantage of the direct method as it goes against the rule of intention-to-treat analysis. Another disadvantage of the direct method of calculation (3) is that we cannot calculate the mean survival time before we know all survival times (4) (e.g. until all patients die). In some cases, it could take decades. In the direct method, some of the censored surviving times would be discarded, although they contain valuable information about survival up to some point in time.

**Figure 1. Survival times usually do not have normal distribution. The histogram presents a follow-up (months) of 152 patients from the study (10). The normal distribution was calculated and is presented by a dashed line (empirical data were not compared using one-sample normality test).**

**About censoring**

**Actuarial (life-table) method and Kaplan-Meier method**

_{died}/N

_{exposed}or N

_{died}/(N

_{total in interval }- N

_{cencored}/2). The method assumes that censored observations contribute only halfway to the number of patients currently at risk (during given time interval), and that is called actuarial assumption. Someone who lived up to the 8

^{th}time interval had to live through seven previous time intervals, so their risk of dying accumulates. It should be noted that proportions of dying and surviving add up to 1 (proportion dying = 1 – proportion surviving). A cumulative proportion dying is gradually increasing with each time interval, as it is multiplied with proportion dying in preceding time intervals, while a cumulative proportion surviving is decreasing and represents the survival rate up to the time interval. Life-table method is useful when death and censored observations are already organized in time intervals, which is rarely the case in biomedical research.

**Figure 2. Survival curves from the study (10) created using Kaplain-Meier estimation. The survival curve itself (upper), with designated censored events (middle), and survival curve with the upper and lower 95% confidence interval curves (lower). Time is shown in months.**

**Calculating survival using Excel sheets**

**Figure 3. Data from the entry page of the workbook. Each patient from the study (10) is designated with a serial identity number (ID, column A). Survival times were calculated from the start date (column B) and the date of last control (column C) for each patient (in months, column D) or were entered directly. Each patient is designated with a status indicator (column E: 0 – censored, 1 – dead).**

**Figure 4. Numerical results of survival data analysis from the workbook summarizing the number of patients from the study (10), median follow-up time with data range (in months, in this example), median survival time, and survival rate at 60 months with respective standard error and 95% confidence interval.**

**Comparing two survival curves**

^{2}-test. There are different types of log-rank tests, some named after respective authors, that slightly differ in their calculations (Cox-Mantel, Peto, Mantel-Haenszel, and some others) (8). When test statistic is obtained, the P-value is read from the normal or c

^{2}-distribution for one degree of freedom (depending on the type of log-rank calculation used). The slope of survival curve at some point in time is termed hazard and represents the rate of dying for that follow-up time.