However, survival analysis has been extended beyond estimating survival rates in cancer patients. It is also been used to estimate survival following total joint replacement. In this case, it is not so easy to define a \u2018hard end point\u2019. Later, we will discuss the implications of an end point that is not \u2018hard\u2019 in more detail.<\/p>\n\n\n\n
For now it is important to realise that: In survival analysis it is essential to define a \u2018hard end point\u2019 for the event of interest.<\/strong><\/p>\n\n\n\n Life Table Survival Analysis<\/strong><\/p>\n\n\n\n It is easiest to explain life table survival analysis<\/strong> with an example. Lets look at 10 patients who have been diagnosed with cancer. The date of diagnosis is shown in the 2nd<\/sup> column of the table below. Analysis was performed on 1\/2\/2001.<\/p>\n\n\n\n Patients who were alive at 1\/2\/2001, had this date inserted in the 3rd<\/sup> column (date last follow up). If the patient died, the date of death was inserted in the 3rd<\/sup> column. The 4th<\/sup> column indicates which patients died and which patients were alive:<\/a><\/p>\n\n\n\n The data can also be shown in a graph:<\/p>\n\n\n\n Patients who died are indicated in black and survivors in grey.<\/p>\n\n\n\n Next, the follow up between the two events (date of diagnosis and date of death \/ last follow up) is calculated for every patient:<\/p>\n\n\n\n In total, there are 10 patients. All these patients have a follow up between 0 and 5 years. However, some patients have a follow up that is longer than others. This has to be taken into account if we want to calculate the probability of survival.<\/p>\n\n\n\n The probability of survival is calculated at yearly intervals<\/em><\/strong> (see table below). We started with 10 patients. Therefore, there were 10 patients at the beginning of year 1. From the table we can see that all patients had a follow up of more than 1 year. Therefore, at the start of the 2nd<\/sup> year there were still 10 patients.<\/p>\n\n\n\n Five patients had a follow up between 1 and 2 years. Two of these two patients died and 3 patients were still alive at review. The 3 patients who were still alive have only been observed for part<\/em><\/strong> of the second year. They could still die during the remainder of that year. These 3 patients are called withdrawn from follow up<\/em><\/strong>.<\/p>\n\n\n\n Patients who have been withdrawn from follow up are also called \u2018censored\u2019<\/em><\/strong>; in other words the event of interest (death) was not observed. Similarly, patients are called \u2018uncensored\u2019<\/em><\/strong> if the event of interest (death) was observed. So, in the 2nd<\/sup> year, 2 patients were uncensored<\/em> and 3 patients were censored<\/em>.<\/p>\n\n\n\n At the beginning of the 3rd<\/sup> year there were 5 patients left. 2 patients had a follow up between 2 and 3 years. One of these patients died (uncensored) and 1 patient withdrew from follow up (censored). Consequently, at the start of the 4th<\/sup> year there were only 3 patients left. Two patients withdrew from follow up during the 4th<\/sup> year and none died. This left only 1 patient at the start of year 5. This patient had a follow up of just over 4 years and consequently withdrew during the 5th<\/sup> year. All these figures have been inserted in the table below:<\/a><\/p>\n\n\n\n It must be clear that the number of patients at the start of a year, minus the patients withdrawn in that year minus the patients who died in that year make up the number of patients at the start of the next year. In other words: the number of patients at the start of a year minus the number censored<\/em><\/strong> minus the number uncensored<\/em><\/strong> in that year equals the number at the start of the next year. <\/p>\n\n\n\n![\"\"](\"http:\/\/pcool.dyndns.org:8080\/statsbook\/wp-content\/uploads\/survival1.png\")
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