CURRICULUM IN CARDIOLOGY: STATISTICAL PAGES Year : 2016  Volume : 2  Issue : 3  Page : 187189 The basics of Kaplan–Meier estimate Aakshi Kalra Institute of Economic Growth, Delhi University, New Delhi, India Correspondence Address:
Concept behind Kaplan–Meier Test Before describing further, it would be important to understand the concept of censoring first. All those participants who are lost to followup or they drop out of the study or if the study ends before they die or have an outcome of interest come under the ambit of censored cases. It will be important to remember that the results may be biased if the dropout is related to both outcome and treatment. For each interval, survival probability is calculated as patients surviving divided by patients at risk. The denominator does not include “censored” participants. The data of the participants are stored using dates and time. The probability of surviving to any point is estimated from cumulative probability of surviving each of the preceding time intervals, that is, calculated as the product of preceding probabilities.[2] Although the probability calculated at any given interval is not very accurate because of the small number of events, the overall probability of surviving to each point is more accurate. It is based on estimating conditional probabilities at each time point the event occurs. Plotting confidence intervals can be useful in visualizing the differences in survival curves. The involved mathematical computations are beyond the scope of this article. Interpretation of Kaplan–Meier Curves The lengths of the horizontal lines along the Xaxis of serial times represent the survival duration for that interval. Vertical axis represents estimated probability of survival. Precision of estimates depends on the number of observations. Survival estimates can be unreliable toward the end of a study when there are small numbers of subjects at risk of having an event. Nonetheless, it is important to note that this test does not control for covariates and requires categorical predictors. It also cannot accommodate for timedependent variables.[3],[4],[5],[6],[7] Understanding Through Examples The description can be best illustrated by an example. Consider a hypothetical longitudinal research study involving 10 endstage heart failure patients who were followed up for 6 months to identify how many survived for the 1st month, 2 months, and so forth. Ideally, data of all ten patients should be available at the end of the study, but this may not hold true in practice. The estimation of survival probabilities may differ at every followup depending on the number of participants retained in the study at that point. As shown in [Figure 1], of the 10 participants, one died after 2 months of initiation of the study and another 2 participants dropped out at the end of 4 months. By the concept of censored cases, the probability of surviving up to the 1st month is 100% = 10/10, but fraction surviving beyond 2 months is 9/10. Similar calculations can be done for each month, but these would be cumulative. There are many online free to access websites which provide calculators for Kaplan–Meier estimate. One of the websites is VassarStats, a website for statistical computation (http://vassarstats.net).[8] Quoting the same example as cited above and illustrating in VassarStats; on the website, under the section of “Clinical Research Calculators,” click on “Kaplan–Meier Survival Probability Estimates.” Then, a prompt appears on the screen regarding time period. Fill in the time intervals/endpoints according to the study and data related to participants consequently. This will provide calculated survival probabilities with confidence intervals as shown in [Figure 2].{Figure 1}{Figure 2} Source: Table template from VassarStats website. There is another calculator “MedCalc” with a free trial version (https://www.medcalc.org/manual/kaplanmeier.php).[9] Consider the same aforesaid example (arbitrary data) but with two patient groups 1 and 2. [Figure 3] shows the data of 10 participants distributed across 2 groups of comparison. The data are entered as patient group in column 1, survival time period in column 2, and the last column for censored cases (marked 0 for censored else 1 for those who reached the endpoint). Time period for the study was 6 months. Upon entering data, go to survival analysis and under that Kaplan–Meier test. There would be a prompt for assigning columns under survival time, endpoint, and factor. This will produce a survival curve along with other details [Figure 4]. Detailed process is given on the website of MedCalc.{Figure 3}{Figure 4} Conclusion The Kaplan–Meier test is a descriptive nonparametric estimate of the survival function, which takes all observations including failures and censored into consideration. It is commonly used to describe survivorship of study population and frequently used to compare two study populations through graphical presentation. Financial support and sponsorship Nil. Conflicts of interest There are no conflicts of interest. References


