The objective of this tutorial is to introduce readers to statistical methods for the analysis of survival data that account for competing risks. 0000104274 00000 n 0000001306 00000 n Regardless of how long the duration of follow-up is extended, a subject will not be observed to die of cardiovascular causes once he or she has died of cancer. We summarized continuous variables by using medians and the 25th and 75th percentiles, whereas dichotomous variables were summarized by using frequencies and percentages. An implicit concept in the definition of censoring is that, if the study had been prolonged (or if subjects had not dropped out), eventually the outcome of interest would have been observed to occur for all subjects. Using the same example as above, the subdistribution hazard of cardiovascular death denotes the instantaneous rate of cardiovascular death in subjects who are still alive (ie, who have not yet experienced either event) or who have previously died of noncardiovascular causes. Others refer to such data as time-to-event data or event history data. In survival analysis, we use information on event status and follow up time to estimate a survival function. For each of the 2 causes of death, we regressed the hazard of death on the 11 covariates described above. Each type of event serves as a competing risk, because a diagnosis of cancer before a diagnosis of heart disease or of death precludes either of these latter 2 events from happening first. The overestimates of incidence when using the Kaplan-Meier estimates are moderately large for both cardiovascular death and noncardiovascular death. h�b```f``�a`200 � +�0pL`]%Ȑ{�c ��R9V�3Ni�30HFZX*�����#�|��s�B���ٳՏIl�t겣��v���ų�m��CaC��%?��\�y�%��恎���@,��$��]\;������::��Ʀ�@Z� �L�����q/��bY� �8?����_�� � �2�aq�~�6=�hoH�J��’���w���FK0JK�. This site uses cookies. We considered 11 baseline covariates, which make up the EFFECT-HF mortality prediction model: age, systolic blood pressure on admission, respiratory rate on admission, low sodium serum concentration (<136 mEq/L), low serum hemoglobin (<10.0 g/dL), serum urea nitrogen, presence of cerebrovascular disease, presence of dementia, chronic obstructive pulmonary disease, hepatic cirrhosis, and cancer. Finally, in Discussion, we summarize our tutorial and place it in the context of the existing literature. A distinctive feature of survival data is the concept of censoring. Second, the sum of the 2 Kaplan-Meier estimates of incidence is greater than the estimate of incidence of the composite outcome of all-cause mortality. © American Heart Association, Inc. All rights reserved. In the case study that follows, we examine the incidence of cardiovascular death in patients hospitalized with heart failure. When the complement of the Kaplan-Meier function was used, the estimated incidence of cardiovascular death within 5 years of hospital admission was 43.0%. If one were considering 2 types of events, death attributable to cardiovascular causes and death attributable to noncardiovascular causes, then the cause-specific hazard of cardiovascular death denotes the instantaneous rate of cardiovascular death in subjects who have not yet experienced either event (ie, in subjects who are still alive). By continuing to browse this site you are agreeing to our use of cookies. 0000058135 00000 n The estimated hazard ratios, along with their associated confidence intervals, are reported in Table 2. Dallas, TX 75231 This illustrates the upward bias that can be observed when naively using Kaplan-Meier estimate in the presence of competing risks. Conventional statistical methods for the analysis of survival data assume that competing risks are absent. h�bbd``b`� BH0� �3@Bo��:�R�D�qw�X� �:�5H�d0012��La`� ��@� �s+ However, we know that such estimates of hazard function tended to be highly variable depending on the grouping intervals. The hazard ratio is equal to the exponential of the associated regression coefficient. 0000005255 00000 n 228 0 obj <>/Filter/FlateDecode/ID[]/Index[213 36]/Info 212 0 R/Length 80/Prev 325320/Root 214 0 R/Size 249/Type/XRef/W[1 2 1]>>stream 354 0 obj << /Linearized 1 /O 357 /H [ 1445 629 ] /L 209109 /E 105355 /N 14 /T 201910 >> endobj xref 354 30 0000000016 00000 n A proportional hazards model for the subdistribution of a competing risk. It is important to remember that the 2 models have different interpretations when interpreting the regression coefficients from the cause-specific hazard models and the subdistribution hazard models. A subject who dies of cancer is no longer at risk of death attributable to cardiovascular causes. Conventional statistical methods for the analysis of survival data make the important assumption of independent or noninformative censoring.1,3,6 This means that, at a given point in time, subjects who remain under follow-up have the same future risk for the occurrence of the event as those subjects no longer being followed (either because of censoring or study dropout), as if losses to follow-up were random and thus noninformative. failcodes. Subjects were linked by using an encoded version of the patient’s Ontario health insurance number to the Vital Statistics database maintained by the Ontario Office of the Registrar General. There is a distinct cause-specific hazard function for each of the distinct types of events and a distinct subdistribution hazard function for each of the distinct types of events. Two key properties of the survival function are that S(0) = 1 (ie, at the beginning of the study, the event has not yet occurred for any subjects) and (ie, eventually the event of interest occurs for all subjects). endstream endobj startxref This allows one to estimate incidence in a population where all competing events must be accounted for in clinical decision making. Second, even when the competing events are independent, censoring subjects at the time of the occurrence of a competing event may lead to incorrect conclusions because the event probability being estimated is interpreted as occurring in a setting where the censoring (eg, the competing events) does not occur. Similarly, a 10-year increase in age increased the cause-specific hazard of cardiac death by 52%, whereas it increased the cause-specific hazard of noncardiac death by 31%. In Figure 2, 3 additional curves have been added to the cumulative incidence functions described in Figure 1: estimates of the incidence of each of the 2 outcomes derived from the complement of the Kaplan-Meier estimate of the survival function, along with the sum of the incidence of each outcome derived from the 2 Kaplan-Meier survival functions. Evaluating health outcomes in the presence of competing risks: a review of statistical methods and clinical applications. We refer the interested reader to introductions and reviews of differing levels of statistical depth.8–13,15,17–21 We summarize our recommendations in Table 3. The analysis of survival data plays a key role in cardiovascular research. First, as anticipated, the Kaplan-Meier estimate of incidence of each of the 2 outcomes is larger than the corresponding estimate derived from the CIF. In a study examining time to death attributable to cardiovascular causes, death attributable to noncardiovascular causes is a competing risk. That is, one may directly predict the cumulative incidence for an event of interest using the usual relationship between the hazard and the incidence function under the proportional hazards model. The impact of incorrectly treating competing events as censoring events in these analyses has practical importance. We have provided a brief, nontechnical, introduction to statistical methods to account for the presence of competing risks. The regression coefficients are interpreted as log-hazard ratios. The initial sample consisted of 18 284 patients hospitalized with HF. We refer the interested reader elsewhere for further background on these methods and others for the analysis of survival data.1–7. Instead, authors and analysts are encouraged to use the CIF. This indirect effect of the prognostic factor for cardiovascular death occurs because noncardiovascular death cannot occur in those who die of cardiovascular causes and hence have a decreased risk for that event. To be concrete, a strong prognostic factor for the cause-specific hazard for cardiovascular death might lead to an apparent decrease in the cumulative incidence for noncardiovascular death when such factor has no effect on the cause-specific hazard for noncardiovascular death. trailer << /Size 384 /Info 349 0 R /Root 355 0 R /Prev 201899 /ID[<6f7e4f80b2691e9b441db9b674750805>] >> startxref 0 %%EOF 355 0 obj << /Type /Catalog /Pages 352 0 R /Metadata 350 0 R /Outlines 57 0 R /OpenAction [ 357 0 R /XYZ null null null ] /PageMode /UseNone /PageLabels 348 0 R /StructTreeRoot 356 0 R /PieceInfo << /MarkedPDF << /LastModified (D:20010516161112)>> >> /LastModified (D:20010516161112) /MarkInfo << /Marked true /LetterspaceFlags 0 >> >> endobj 356 0 obj << /Type /StructTreeRoot /ClassMap 65 0 R /RoleMap 64 0 R /K 296 0 R /ParentTree 297 0 R /ParentTreeNextKey 14 >> endobj 382 0 obj << /S 489 /O 598 /L 614 /C 630 /Filter /FlateDecode /Length 383 0 R >> stream The need to carefully consider which model is appropriate to address the research question is illustrated in the case study below, in which the effect of cancer is shown to have a different effect on the subdistribution hazard of cardiac death in comparison with its effect on the cause-specific hazard of cardiac death. Researchers should select the appropriate method to address the study objectives and ensure that the analysis results are interpreted correctly. The Cox model relates the covariates to the hazard function of the outcome of interest (and not directly to the survival times themselves). Even when the competing events are independent, the Kaplan-Meier estimator yields biases in the probability of the event of interest. %%EOF This study was supported by the Institute for Clinical Evaluative Sciences (ICES), which is funded by an annual grant from the Ontario Ministry of Health and Long-Term Care (MOHLTC). We categorized cause of death as cardiovascular versus noncardiovascular: 10 215 (63%) patients died during the 5 years of follow-up. Customer Service We encourage analysts to take full advantage of the range of statistical methods for the analysis of survival data that have been developed in the statistical literature. Competing risk of death: an important consideration in studies of older adults. CIFs can be estimated in R using the cuminc function in the cmprsk package; in SAS, one can use the %CIF macro; Stata permits estimation of the CIF using the stcurve function. 142, Issue Suppl_3, October 20, 2020: Vol. 0000002439 00000 n Although such probabilities may be of theoretical interest, they are of questionable relevance in many practical applications, and generally lead to overestimation of the cumulative incidence of an event in the presence of the competing events.8–11. Koller et al15 found that competing risks were present in a large majority of studies published in a sample of high-impact journals. Cumulative incidence functions and Kaplan–Meier estimates. In the absence of competing risks, the survival function, S(t), describes the distribution of event times: S(t) = Pr(Tt). 0000101596 00000 n The American Heart Association is qualified 501(c)(3) tax-exempt They found that the standard Cox model overestimated the 10-year risk of coronary heart disease in comparison with the estimate from the Fine-Gray model. Trained cardiovascular nurse abstractors collected data on patient demographics, vital signs and physical examination at presentation, medical history, and results of laboratory tests.