However, this is also confounded by unfavorable risk status at the time of transplantation. This test is obtained by constructing a 2 × 2 table at each distinct failure time, comparing the failure rates between two groups, and then combining tables over time. Analysis is performed by dividing the follow-up time into discrete pieces to calculate probability of survival at each event (survival = probability of no event). When competing risks are present, there are three ways to analyze the data: (a) analysis of the event of interest ignoring CR, (b) analysis of joint events as a single end point, and (c) analysis of CR. Of five patients with nonmyeloablative transplantation, four received bone marrow stem cells and died of TRM. The magnitude of overestimation in the KM method depends on the incidence rate levels of competing events. The detailed calculation of KM estimate for cumulative incidence of relapse (CIKMrel or KM CIR, for the purpose of simplicity) is presented in Table 1 eISSN: 1557-3265 This is illustrated in example 2c. When there are no competing risks, a Mantel-Haenzel log-rank test (2) is used to compare KM cumulative incidence curves. Because the relapse-free survival [SKMrel(t)] in the KM method is always greater than or equal to the relapse- and TRM-free survival [SKMrel,TRM(t)] in the CR method, the cumulative incidence using the KM method is always greater than or equal to the cumulative incidence using the CR method. As previously mentioned, efforts to modify the relapse rate through immune effector mechanisms may adversely affect TRM rates (vice versa is also true), and therefore, relapse and TRM are not independent events. 2A and B occur at the same time in both methods because, irrespective of the method used, the occurrence time of an event does not change. As in our hypothetical example above (Fig. Using a cause-specific Cox regression model is incorrect because it ignores competing risks and treats them as censored. The second approach is correct, but is too limited to address various important research questions. Note that since time is missing, the risk estimate is calculated at the observed failure times. CR regression analysis is also useful to identify other prognostic factors, other than type of transplantation, for each type of failure. The difference lies in the probability of an event-free survival just prior to a certain time. Grant support: National Heart, Lung, and Blood Institute grant HL070149 and National Institute of Allergy and Infectious Diseases grant AI029530. For survfitms objects a different geometry is used, as suggested by @teigentler. Using hypothetical numeric example and real data, we will demonstrate the use of these three methods, compare the results to the results obtained from standard survival analysis, and discuss the source and magnitude of bias that arises from standard methods. In standard survival analyses, when testing a group (or treatment) difference, the usual steps are to present KM survival or cumulative incidence curves, test the difference of these survival curves using a log-rank test, and perform a proportional hazards regression analysis. (8)].

Alternatively, you can use graphics::matplot by specifying gg = FALSE. At t = 40, the relapse- and TRM-free survival (SKMrel,TRM or EFS) in the CR method is 0.68, whereas the RFS in the KM method is 0.79 in Table 1. In the Cox model, relapse and TRM are considered jointly in the outcome; in the Fine and Gray model, they are considered individually. Fitting a CR regression model is also important to confirm whether the difference seen in the cumulative incidence curves is true or confounded by other risk factors. This function plots Cumulative Incidence Curves. In the analysis of CR data, it is important to present both the results of the event of interest and the results of competing risks. Therefore, the survival probability is overestimated and thus cumulative incidence of relapse is also overestimated (as shown in the example below) in the KM method. eg, if event 1 occurs with probability 1/6 and event 2 with probability 1/2, then the probability of both event 1 and 2 occurring = 1/6 x 1/2 = 1/12. Posted 2 weeks ago (39 views) | In reply to viviyeah I have a macro that can create and customize the curves for you: Instead, Gray investigated this issue and proposed a class of tests for comparing the cumulative incidence curves of a particular type of failure among different groups in the presence of competing risks (3). The cumulative incidence of relapse in the presence of TRM as a competing risk (CR) can be calculated similarly as in the KM method. We gratefully acknowledge helpful feedback from Drs. This type of design with staggered entry and administrative censoring is very common within health sciences. NOTE: We request your email address only to inform the recipient that it was you who recommended this article, and that it is not junk mail. Similarly the difference in the cumulative incidence of relapse was confounded by unfavorable prognosis at stem cell infusion. In a competing risks situation, the equivalent steps are to generate cumulative incidence curves using the CR method described above, test the difference between cumulative incidence curves using the Gray method, and perform a CR regression analysis. In the CR method, unlike the KM method, patients dying from TRM are counted as events when calculating the event-free survival, SKMrel,TRM(t), and only patients who are truly alive are considered at risk for relapse. Patients who fail from other causes or who are still alive at the specified time point are censored. In both models, the type of transplantation was not a significant factor for outcome after adjusting for pretransplant characteristics. The 4-year CIT was 50% using the CR method and 59% using the KM method. Cumulative incidence estimates are often derived in cohort studies in which individuals are included during a pre-specified period and subsequently monitored for the disease until an administrative end of follow-up date. Survival probability at a certain time is a conditional probability of surviving beyond that time, given that an individual has survived just prior to that time. stcurve also plots the cumulative subhazard or cumulative incidence function (CIF) after stcrreg. So at 1 month of follow-up there was a death and at that time all 10 original members of the cohort were still in follow-up.
Competing risks occur frequently in cancer research even though their presence may not always be recognized at the time of analysis. In this short vignette, we will introduce the plot method for absoluteRisk objects. To illustrate the KM and CR methods with real data, we considered a typical competing risks data set of relapse and TRM presented in Alyea et al. ↵1 http://biowww.dfci.harvard.edu/~gray/. The RFS at t = 20 (0.9) was multiplied by the incidence rate of relapse at t = 35 because only those patients who were alive just prior to t = 35 were subject to relapse at t = 35. Calculating Cumulative Incidence with the Kaplan-Meier Method. These models distinguish between patients who are still alive and those who have already failed from competing causes and allow direct inference regarding the effects of covariates on the cumulative incidence function.

Of the 40 patients with myeloablative transplantation who died of TRM, 35 received bone marrow stem cells. A hypothetical numeric example and real data are used to compare those three methods in the competing risks data analysis to their respective counterparts in the standard survival analysis. In addition to estimating the cumulative incidence of an event, comparing cumulative incidence curves among different treatment groups is useful when selecting the appropriate treatment for a particular patient. requires date last observed or date outcome occurred on each individual (end of study can be the last date observed) The essence of the Kaplan-Meier (KM) method is having the date each outcome in the cohort occurred. Suppose that there are 10 patients with the ordered failed or censored times shown belowwhere + denotes a censored time, (R) denotes relapse, and (T) denotes death due to treatment-related complications (TRM). For example, suppose we want to change the theme: By default, the plot method uses ggplot2 to produce the curves. More specifically, the cumulative incidence using the KM method, denoted as CIKMrel, is calculated as follows: The KM estimate of cumulative incidence function is simple and useful for a single end point such as relapse. 1 The Cumulative Incidence Function In our earlier discussion we introduced the cause-speci c densities f j(t) = lim dt#0 PrfT2(t;t+ dt) and J= jg=dt which have the property of summing to the overall density f(t) = P j f j(t). At all time points, the sum of RFS and KM CIR was equal to 1 [i.e., SKMrel(t) + CIKMrel(t) = 1].
In order to calculate cumulative incidence, you need to understand or least accept on faith the following. Therefore, the RFS at t = 40 was 0.79, and the corresponding KM CIR was 0.21.

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