Survival Probability in Patients with Sickle Cell Anemia Using the Competitive Risk Statistical Model
1 UEZO - Centro Universitário Estadual da Zona Oeste, Rio de Janeiro, RJ, Brazil.
2 Clinical Hematology Division, Instituto de Hematologia Arthur de Siqueira Cavalcanti. HEMORIO, Rio de Janeiro, RJ, Brazil.
3 School of Medicine/UFRJ - Federal University of Rio de Janeiro, RJ, Brazil.
4 Postgraduate School of Engineering – COPPE/UFRJ.
5 Clementino Fraga Filho University Hospital/UFRJ.
6 Cardeza Foundation, Department of Medicine, Jefferson Medical College, Thomas Jefferson University, Philadelphia, PA, USA.
Received: November 12, 2018
Accepted: January 12, 2019
Mediterr J Hematol Infect Dis 2019, 11(1): e2019022 DOI 10.4084/MJHID.2019.022
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clinical picture of patients with sickle cell anemia (SCA) is
associated with several complications some of which could be fatal. The
objective of this study is to analyze the causes of death and the
effect of sex and age on survival of Brazilian patients with SCA. Data
of patients with SCA who were seen and followed at HEMORIO for 15 years
were retrospectively collected and analyzed. Statistical modeling was
performed using survival analysis in the presence of competing risks
estimating the covariate effects on a sub-distribution hazard function.
Eight models were implemented, one for each cause of death. The
cause‐specific cumulative incidence function was also estimated. Males
were most vulnerable for death from chronic organ damage (p = 0.0005)
while females were most vulnerable for infection (p=0.03). Age was
significantly associated (p ≤ 0.05) with death due to acute chest
syndrome (ACS), infection, and death during crisis. The lower survival
was related to death from infection, followed by death due to ACS. The
independent variables age and sex were significantly associated with
ACS, infection, chronic organ damage and death during crisis. These
data could help Brazilian authorities strengthen public policies to
protect this vulnerable population.
Material and Methods
Statistical analysis. Statistical modeling was performed using Survival analysis in the presence of competing risks.
Basically, three functions are used in survival data: the survival function, the cumulative distribution function, and the hazard function.
In survival analysis, it is common to investigate the lifetime related to a single cause of death. However, there are more complex models, in which the death of the individual is related to one of several possible causes identified in the study. These models are called competing risk models being suitable in studies where individuals are exposed to more than one cause of failure or event.
Gooley et al. define the competing risk as a survival model in which the occurrence of an event prevents or alters the probability of occurrence of another event.
In general, three types of approach are used in the presence of competing risks: 1 - Event-free survival model, using the Cox model considering the time until the occurrence of the first event. This model is not suitable because it does not consider the various risk factors; 2 – Cause-specific hazard model, where the Cox model is used considering one of the events as the main cause and the rest are censored. This approach is also unsuitable because it is not possible to estimate the common effect of a covariate for competing outcomes. Additionally, the sum of the cumulative distribution function for each outcome is different from the cumulative distribution function of the overall curve. It would also be necessary to be valid the assumption of independence between the event of interest and other competing events, considered censorship, which rarely occurs; and 3 – Hazard of subdistribution model, using the cumulative incidence function. This model does not require any assumption of independence of competing risks.
The cumulative incidence function, or subdistribution function, introduced by Kalbleisch & Prentice, is defined as the joint probability
Fine and Gray proposed a regression model implemented on the cumulative incidence function for analyzing competing risks. Modeling is performed by hazard of subdistribution function, defined as the instantaneous hazard of an individual suffering the event for a specific cause, conditional to have survived until a certain time t.
The partial likelihood function is modeled as an extension of the Cox proportional hazards model, weighted by wij.
In each instant tj, in which the event of interest has been observed, the risk set is composed of individuals who have not suffered any event until the time tj, receiving the weight wij=1; and those who have suffered a competing event before this time tj being weighted as wij≤1. Thus, given the occurrence of the event of interest in time tj, for each individual who has suffered a competing event in tj, the greater the distance between points ti and tj, the lower the weigh wij.
In this work, survival analysis was performed using the risk of sub-distribution regression model. These models consider the cumulative incidence function, using a weighting factor for each individual considering all outcomes. Thus, the individual who suffers from the competing event is not censored receiving a weight that decreases gradually with time.
Eight models were implemented, one for each cause of death related to SCDA, as shown in Table 1: Acute Chest Syndrome, Infection, Stroke, Cardiac Causes, Chronic Organ Damage, Death During Crisis, Other (Splenic Sequestration, Hemolytic Crisis or Hepatic Crisis) and Unknown.
|Table 1. Risk of subdistribution regression model.
Figure 1 shows the cumulative incidence function, where one can observe that the lower survival is related to death from infection, followed by death due to ACS. Compared to the model of competing risks, the independent variables age and sex were significantly associated with the outcomes with an asterisk.
Analyses were performed with the use of packages “cmprsk” and “mstate”[14-16] of R software.
A competing risk is an event whose occurrence either precludes the occurrence of another event under examination or fundamentally alters the probability of occurrence of this other event, so it is an ideal model to analyze causes of death in a specific disease with multiple possible causes of death as in SCD. It was used before in other chronic disease but never is SCD in Brazil before.
The competitive risk model was used because it is adequate in survival analysis when there are mutually exclusive events, that is when the occurrence of one event prevents another event occurring. In the article, events are deaths from various causes. The cumulative incidence function (represented by the graph) evaluates for each patient the probability of occurrence of a specific event before a certain time t. The risk sub-distribution model estimates the effect of independent variables for each specific event, considering the presence of competitive risks.
The reasons for the relatively low death rate of females due to chronic organ damage are unknown. Possibilities include gender differences in nitric oxide availability, and the influence of the X-chromosome linked hemoglobin (Hb) F gene which may be protective against organ damage in females. However, Dover’s et al. study was not confirmed by additional studies. In addition, the increase in Hb F by the X-chromosome is minimal in comparison to other studies indicating that Hb F has to be as high as ≥ 8% to be effective. Other determinants of survival such as hyperviscosity, alpha genotypes, and beta haplotypes could not be determined at HEMORIO.
In this article, we used the subdistribution hazard function which evaluates the effect of covariates on the cumulative incidence function for each of the competitive events. This modeling is advantageous because it makes no assumption about the independence of competitive events.
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