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. The magnitude of overestimation in the KM method depends on the incidence rate levels of competing events. This conditional probability can be estimated in a study as the probability of surviving just prior to that time multiplied by the number of patients with the event at that time, divided by the number of patients at risk. Because of this, RFS and KM CIR are often calculated at failure times only. In the Cox model, relapse and TRM are considered jointly in the outcome; in the Fine and Gray model, they are considered individually. Examples of competing risks in HSCT studies include: incidence of acute GVHD and 100-day death without development of acute GVHD, death due to disease and due to transplant-related complications, and relapse and chronic GVHD for long-term survivors. We will compare each method to its counterpart in standard survival analysis, and show why the latter are inadequate in the presence of competing risks. The difference in the cumulative incidence of TRM was confounded by the bone marrow stem cell use. One hundred and fifty-two patients over the age of 50 who underwent T cell–replete HLA-matched allogeneic transplantation from 1997 to 2002 at our institution were included. It may also be calculated by the incidence rate multiplied by duration: {\displaystyle CI (t)=1-e^ {-IR (t)\cdot D}\,.} 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. The KM estimate of incidence of relapse at a specified time point is then the probability of relapse-free survival just prior to that time, multiplied by the number of relapses at that time, divided by the number of patients at risk (that is, alive, relapse-free, and not lost to follow-up) just prior to that time. The 3-year cumulative incidence of TRM (CIT) was 50% after myeloablative transplantation, but was 32% after nonmyeloablative transplantation (P = 0.01). stcurve also plots the cumulative subhazard or cumulative incidence function (CIF) after stcrreg. Notably, the RFS and KM CIR at t = 40 was the same as the ones at t = 35, even though the calculation is slightly different. 3 ISSN: 1078-0432. The CR analysis of relapse and TRM is an appropriate method to answer these more advanced questions. The corresponding call to plot is the same as with cumulative incidence curves: We can also plot cumulative incidence curves for other families. Copyright &© by the contributing authors. We can use the plot method for objects of class absRiskCB, which is returned by the absoluteRisk function, to plot cumulative incidence curves. This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. The patient with the third smallest observed time died from relapse at t = 35, and thus the RFS at t = 35 was 0.79, i.e., the second patient who was alive and thus censored at t = 20 was excluded from the denominator of the number of patients at risk just prior to t = 35 because this patient's survival information beyond t = 20 is unknown. For example, in allogeneic HSCT for patients with hematologic malignancies, both relapse and TRM are of equal importance to patients as well as physicians. Cumulative incidence is NOT opposite of survival in general. Philippe Armand, Corey Cutler, Stephanie Lee, Robert Gray, David Harrington, and Jerome Ritz. This is a more complex statistic than just comparing two proportions with a, The most commonly used statistic is called the. 3, it seems that nonmyeloablative transplantation is associated with an increased risk for relapse. The probability of the event is the number of deaths at each point in time (just 1 here, but it is possible to have more than 1 at the same time) divided by the number in the cohort at that time. If the KM method is used to estimate the cumulative incidence of relapse in the presence of TRM, patients dying of TRM are censored. 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. Example 2b.
The Fine and Gray method is based on proportional hazards model, whereas the Klein and Andersen method is based on the pseudovalues from a jackknife statistic from the cumulative incidence curve. 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. 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. The 4-year CIT was 50% using the CR method and 59% using the KM method.
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. Therefore, the difference in the cumulative incidence of TRM (Fig. Note that results from the CR regression analysis were not presented in the published article (8). 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). More specifically, the cumulative incidence of relapse in the presence of TRM as a competing risk, denoted as CICRrel, is calculated aswhere SKMrel,TRM(t) denotes the KM estimate of survival probability for the joint events of relapse and TRM. Of the 40 patients with myeloablative transplantation who died of TRM, 35 received bone marrow stem cells. However, if there is more than one type of event (or failure), and if these events are dependent, KM estimates are biased. Because the simple relationship between a single end point and a single crude hazard does not hold in the presence of competing risks, Fine and Gray (6) and Klein and Andersen (7) proposed a direct regression modeling of the effect of covariates on the cumulative incidence function for CR data. This bias arises because the KM method assumes that all events are independent, and thus, censors events other than the event of interest. In both models, the type of transplantation was not a significant factor for outcome after adjusting for pretransplant characteristics. Two curves jump at the same time whenever relapse occurs, but the magnitude of each jump is smaller in the CR method. This is illustrated in example 2c. (8)] shows cumulative incidences of relapse and TRM using the CR method after myeloablative and nonmyeloablative transplantation. This difference is smaller compared with the difference in CIR. The costs of publication of this article were defrayed in part by the payment of page charges. Software packages for the KM method and Cox proportional hazards regression model are available in S-plus, SAS, and SPSS. Of these 152 patients, 81 underwent myeloablative and 71 underwent nonmyeloablative transplantation. Comparison of cumulative incidence of relapse between the KM and CR methods using a numerical example. Relapse and TRM are not independent in this setting because these two events are likely related to immunologic effector mechanisms following HSCT, whereby efforts to reduce TRM may adversely affect the risk of relapse; moreover, patients who die from TRM cannot be at further risk of relapse. 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. (in our example, 0.100 x 0.125 x 0.143 x 0.200 x 0.333 x 0.500 = 0.0000595), This is because there is a discrete jump in the. In contrast, in the Cox model for relapse and TRM combined, the HR for bone marrow as compared with peripheral blood stem cell use was 1.13 (P = 0.71). In order to calculate cumulative incidence, you need to understand or least accept on faith the following. So the probability … Using the same data set presented in example 2a, Fig. B, comparison of cumulative incidence of TRM between the KM and CR methods. The combination of the second and third approaches is a comprehensive approach that addresses general as well as specific study questions. However, if you are comparing risk of, say, herpes outbreak (where one individual may have several outbreaks over the duration of the study), the cumulative incidence curve will account for the total volume of outbreaks. This is because the standard Cox model is not designed to answer what risk factors contribute to relapse in the presence of the competing risk of TRM. Re: Cutomize competing-risk cumulative incidence curve.
eISSN: 1557-3265 Although this is indicated in the Cox model of relapse and TRM combined events in Table 2 (β = −0.39, HR = 0.68, P = 0.053), it is unknown from this model whether this is due to relapse or TRM prevention. In addition to estimating the cumulative incidence of an event, it is often of interest to determine whether there is a difference in the cumulative incidence rates among different groups. When the two methods were compared in a real data example, results from both approaches were in close agreement (7). Cumulative Incidence in Competing Risks Data and Competing Risks Regression Analysis, Biomarker Analysis from the BERIL-1 Study, Radiation and TGFβ Blockade in Metastatic Breast Cancer, Cancer Epidemiology, Biomarkers & Prevention, Estimating Cumulative Incidence in the Presence of Competing Risks, Comparison of Cumulative Incidence Curves in the Presence of Competing Risks. This conditional probability can be estimated in a study as the number of patients who are alive or event-free without loss to follow-up at that time, divided by the number of patients who were alive just prior to that time. This option is particularly useful if you want to add the cumulative incidence curve to an existing plot, e.g., adding the adjusted smooth curve to a Kaplan-Meier curve. There were 51 patients with relapse: 23 after myeloablative and 28 after nonmyeloablative transplantation. In the example of the myeloablative versus nonmyeloablative HSCT study, presentation of CIR without CIT would be misleading because even though the CIR is higher in the nonmyeloablative transplantation compared with the myeloablative transplantation, the CIT is lower. If the patient with the fourth smallest observed time, t = 40, dies from TRM, then the KM method treats this as no event, and thus censors the observation. 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 many cancer treatments, efforts have been made to decrease disease recurrence but often at the cost of increased toxicity due to the treatment. The graphical display of the cumulative incidence function (i.e., failure probabilities) over time is intuitive and appealing. It is a fundamental theorem of probability that the cumulative probability of two independent events is the product of their individual probabilities.
At t = 55, the RFS drops to 0.63, and the KM CIR increases to 0.37. Similarly, in Fig.
However, one could not know the effect of competing risks a priori unless CR analysis is done. As in any other regression analysis, modeling cumulative incidence functions for competing risks can be used to identify potential prognostic factors for a particular failure in the presence of competing risks, or to assess a prognostic factor of interest after adjusting for other potential risk factors in the model. The second approach is correct, but is too limited to address various important research questions. These curves can be further customized. Example 2c. Fine and Gray (6) and Klein and Andersen (7) proposed a method for direct regression modeling of the effect of covariates on the cumulative incidence function for competing risks data.
The KM CIR at t = 35 was thus 0.21. However, methods for estimating cumulative incidence function must be clearly understood.
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