Clinical states of cirrhosis and competing risks
Gennaro D’Amico
1,⇑, Alberto Morabito
2, Mario D’Amico
3, Linda Pasta
1, Giuseppe Malizia
1,
Paola Rebora
4, Maria Grazia Valsecchi
4Summary
The clinical course of cirrhosis is mostly determined by the progressive increase of portal hypertension, hyperdynamic circulation, bacterial translocation and activation of systemic inflammation. Different dis-ease states, encompassing compensated and decompensated cirrhosis and a late decompensated state, are related to the progression of these mechanisms and may be recognised by haemodynamic or clinical characteristics. While these disease states do not follow a predictable sequence, they correspond to varying mortality risk. Acute-on-chronic liver failure may occur either in decompensated or in compen-sated cirrhosis and is always associated with a high short-term mortality. The increasing severity of these disease states prompted the concept of clinical states of cirrhosis. A multistate approach has been considered to describe the clinical course of the disease. Such an approach requires the assessment of the probabilities of different outcomes in each state, which compete with each other to occur first and mark the transition towards a different state. This requires the use of competing risks analysis, since the traditional Kaplan-Meier analysis should only be used in two-state settings. Accounting for compet-ing risks also has implications for prognosis and treatment efficacy research. The aim of this review is to summarise relevant clinical states and to show examples of competing risks analysis in multistate mod-els of cirrhosis.
Ó 2017 European Association for the Study of the Liver. Published by Elsevier B.V. All rights reserved.
Introduction
Cirrhosis is typically classified as compensated or decompensated, based on the absence or presence (or previous history) of variceal bleeding, ascites,
jaundice or encephalopathy.1–3 The significantly
longer survival, usually symptomless, and better quality of life experienced by patients with com-pensated cirrhosis compared to those with decom-pensated cirrhosis, has brought about the concept that compensated and decompensated cirrhosis are distinct clinical states of the disease.4,5Further
disease states have been identified according to the presence of oesophageal varices and to the presence of only one or more disease complica-tions.4,6–10
Development of gastro-oesophageal varices and decompensation usually do not occur below the portal pressure threshold of clinically signifi-cant portal hypertension (CSPH) defined by
hep-atic venous pressure gradient (HVPG) ≥10
mmHg.11–13 Increasing portal pressure, bacterial
translocation, inflammation and hyperdynamic circulation are likely mechanisms of
decompensa-tion,14which progresses to a late decompensation
state characterised by further worsening of liver function associated with other organ dysfunction, while acute-on-chronic liver failure (ACLF) may
occur in any disease state. Histological stages15
of cirrhosis also parallel the progression of portal
hypertension16,17 and clinical states of the
disease.18,19
This body of evidence supports a multistate approach to the clinical course of cirrhosis, which implies a specific statistical methodology, since
the Kaplan-Meier (KM) survival curves20,21 may
not capture clinical state transitions following the occurrence of a competing event, before the event of interest. For example, decompensation before death is not captured by a survival curve of compensated cirrhosis. In this situation, the cumulative incidence function (CIF), based on the Aalen-Johansen estimator allows a more realistic description of the disease course, by providing
the incidence of the competing events.22–24
Herein, the clinical course, competing risks and clinical states of cirrhosis will be reviewed and examples of possible multistate models of the dis-ease will be provided.
The clinical course of cirrhosis
Cirrhosis may result from chronic liver inflamma-tion from any cause, following parenchymal necrosis, activated fibrogenesis, angiogenesis and profound vascular changes. Increased hepatic resistance to blood flow, derived from both mechanical obstacle and vasoconstriction result-ing from endothelial dysfunction and hepatic stel-late cells contraction, gradually leads to portal hypertension. The ensuing adaptive splanchnic vasodilation further contributes to aggravate por-tal hypertension and progressively results in
hyperdynamic circulation.25–27
When established, cirrhosis remains compen-sated for a variably long time, depending on cur-ability of the underlying disease. In this state, persistence of liver damage results in increasing
fibrosis and portal hypertension.16,17,28
Decom-pensation and oesophageal varices may occur
Key point
The clinical course of cir-rhosis encompasses several disease states which require multistate models and competing risks anal-ysis for proper assessment.
Keywords: Cirrhosis; Clinical course of cirrhosis; Portal hypertension; Clinical states of cirrhosis; Competing risks; Cumulative incidence function; Multistate models for cirrhosis. Received 23 July 2017; received in revised form 26 September 2017; accepted 24 October 2017
1
Gastroenterology Unit, Ospedale V. Cervello, Via Trabucco 180, Palermo, Italy
2
Medical Statistics Unit, Università di Milano, Milano, Italy
3
Radiology Department, Università di Palermo, Palermo, Italy
4
Dipartimento di Medicina e Chirurgia Università di Milano-Bicocca, Milano, Italy
⇑Corresponding author. Address: Gastroenterology Unit, Ospedale V Cervello, Via Trabucco 180, 90146 Palermo, Italy. Tel.: +39 091 6802780 or +39 091 6802730; fax: +39 091 6802739.
above the CSPH threshold (HVPG ≥10 mmHg)13,29 and hence decompensation is more frequent in
patients with oesophageal varices.6,7,10 In
com-pensated cirrhosis, the rate of development of oesophageal varices and of decompensation is
about 7–8% and 5% per year, respectively.11,30,31
Following their appearance, varices grow in
cali-bre at a similar rate30,32 and may rupture in 5%
to 15% of patients per year, with a higher risk in patients with large oesophageal varices and red
signs or Child B-C class.33 The ensuing variceal
bleeding is one of the most critical emergencies
in medicine, with a mortality rate of 10–20%34,35
(it was 50% in the early eighties).36 In untreated
patients, rebleeding and death occur in approxi-mately 60% and 30% of patients, respectively, one
to two years after the index bleeding,37,38 and
are significantly reduced by non-selective beta-blockers plus endoscopic variceal ligation or, in selected patients, by early transjugular
intrahep-atic portosystemic shunt (TIPS).39–41
Ascites is a hallmark of decompensation and is associated with a five-year mortality of about
50%.9,42The progression of the hyperdynamic
cir-culation and the activation of pro-inflammatory
mechanisms14 result in deterioration of renal
function, and ascites may become refractory. The cumulative risk of refractory ascites is in the order of 20% within five years of the development of
ascites.42Two-year mortality following refractory
ascites is approximately 65% and may be reduced
by TIPS in selected patients.43,44
Overt hepatic encephalopathy and/or jaundice typically occur in advanced cirrhosis, rarely as a first sign of decompensation and are associated
with a five-year survival of about 20%.8,10 The
prognostic weight of covert hepatic
encephalopa-thy45remains to be defined, and is possibly more
dependent on the grade I encephalopathy
compo-nent than on minimal encephalopathy.46–48
Renal function is often impaired in patients with advanced cirrhosis, as a consequence of either progressive haemodynamic derangement or acute events such as bleeding, infections or nephrotoxicity. The usual clinical presentation is that of acute kidney injury (AKI), including
hepa-torenal syndrome type 1 or 2.49–51AKI is usually
followed by progressive worsening of renal func-tion, and progressive reduction of mean arterial
pressure, indicating progressive cardiac and
haemodynamic impairment.52One-year mortality,
following renal failure in this advanced disease
state, is in the order of 60%,53,54although it varies
according to the definition used.49–51
Because of bacterial translocation driven by the progression of portal hypertension and liver
dys-function,55 infections are common in advanced
cirrhosis,56–62particularly in patients with ascites.
The inflammatory response is frequently severe
and associated with organ failures.55,60Mortality
may reach 38%,58while discharged patients have
a 30-day readmission rate of 35% and six-month
mortality of 23%.61 Overall mortality within one
year of the infectious episode is 60%.63However,
infections are relatively frequent, as well as being significant events also in compensated cirrhosis, where they are associated with increased risks of
long-term decompensation and mortality.64
Hepatocellular carcinoma (HCC) occurs in 2–8%
patients per year.65–70 The risk is higher in
patients with CSPH, higher body mass index,
oeso-phageal varices and decompensated cirrhosis.70,71
Median survival after HCC detection is nine
months in untreated patients72and approximately
two years in treated patients, ranging from >10 years in Barcelona Clinic Liver Cancer (BCLC) stage 0,73to <6 months in stage D.74
Liver failure, bleeding, HCC, infections, hepa-torenal syndrome, and ACLF are the most frequent causes of death in patients with cirrhosis.
Acute-on-chronic liver failure (ACLF) is charac-terised by acute decompensation, organ failure(s)
and high short-term mortality75–78and may occur
either in compensated or in decompensated cir-rhosis. Organ failures (liver, renal, coagulation, cerebral, respiratory and circulatory) are defined according to the Chronic Liver Failure-Sequential Organ Failure (CLIF-SOFA) score or by its simplified version Chronic Liver Failure-Organ Failure
Assess-ment (CLIF-OF) score.75,76 Severity of ACLF is
graded according to the number of organ failures as ACLF-1, ACLF-2, and ACLF-3. There is a large body of evidence indicating that ACLF is triggered
by a systemic inflammatory response78–82to
sev-eral critical events, which may act as intra- or
extrahepatic factors.83,84Bacterial by-products
ter-med pathogen associated molecular patterns (PAMPS) and damage associated molecular pat-terns (DAMP) released after liver tissue injury play
a key role in triggering inflammation.14Infections
are not only a triggering factor in up to 37% of patients, but they also occur during follow-up in 46% of patients free of infection at ACLF diagnosis, and are associated with a significantly increased
mortality risk in ACLF grades 1–2.85No triggering
factors may be identified in up to 40% of
patients,75,84in whom PAMPs resulting from
sub-clinical bacterial translocation55or DAMPs
result-ing from liver tissue injury86,87may be key-factors.
ACLF is a dynamic syndrome and 28-day mor-tality ranges from 10% to 87% depending on the number of failing organs between day three and
seven.78,77,88The CLIF-C ACLF score enables
pre-diction of mortality risk more accurately than the
MELD, MELD sodium and Child-Pugh scores,89
while another specific prognostic score has been developed for patients with acute decompensation
without ACLF, the CLIF-C AD score.90
In patients with ACLF, 23% of those with mostly alcohol and/or hepatitis C virus (HCV)-related
cir-rhosis,75 and 45–52% of those with mostly
HBV-related cirrhosis83,91may not have history of
pre-vious decompensation. However, in a recently reported study of the incidence of ACLF in outpa-Key point
tients,92 during the first year of follow-up 61 patients developed ACLF: 93% of them had a previ-ous history of decompensation while only 7% did not. The overall incidence rate of ACLF was 7/100 patient-years.
The clinical course of cirrhosis may not be
con-sidered as unidirectional anymore (Fig. 1). There is
in fact a large body of evidence that aetiologic cure may result in progressive reduction of fibrosis, and
even regression of cirrhosis93,94 and parallel
reduction of portal hypertension,95–97 reducing
the risk of the major disease complications, when HVPG returns below 12 mmHg. However, even fol-lowing complete aetiological cure, like sustained virologic response in HCV cirrhosis, occurrence of oesophageal varices, decompensation and HCC
have been reported.98–102 Similarly, the risk of
HCC is not fully abolished after successful HBV
suppression.103 Therefore, watchful follow-up of
patients in whom the cause of cirrhosis has been
successfully treated is recommended.104,105
Clinical states in cirrhosis
Several clinical conditions associated with signifi-cantly different outcomes have been proposed as relevant clinical states during the course of the disease4,5,8,10,14,106,107(Fig. 1). However, it is
nota-ble that there is no predictanota-ble sequence of such clinical states and that they may not be considered as progressive disease stages. However, clinical states enable the classification of patients accord-ing to increasaccord-ing mortality risk. Moreover, assess-ing transitions across states may facilitate the description of the clinical course of the disease in a multistate model.
Compensated cirrhosis without varices (state 1). This is the earliest clinical state with a low inci-dence rate of decompensation and very low
mor-tality.4,6,7,10,11 Approximately 50% of patients in
this state13 still have mild portal hypertension
(MPH) (HVPG >5 mmHg and <10 mmHg), while CSPH is already present in the remaining patients. Importantly, liver stiffness measurement (LSM) ≥20–25 kPa alone or in combination with platelet
count and spleen size108–111may identify patients
with compensated cirrhosis, without gastro-oesophageal varices, and a very high probability
of CSPH (specificity 0.90),111while compensated
advanced chronic liver disease (cACLD, or com-pensated cirrhosis) is identified by an LSM >15
kPa.104It is therefore conceivable that the clinical
state of compensated cirrhosis without varices may be split into compensated without CSPH (state 0) and compensated without varices with CSPH (state 1), the latter being associated with higher risk of
developing varices, decompensation11–13 and
HCC.70Moreover, patients with MPH have a very
low or no haemodynamic response to
non-selective beta-blockers (NSBB),13while their HVPG
is significantly reduced by viral eradication in
those with chronic HCV infection,97 suggesting
that the prevention of disease progression in patients without CSPH should be primarily based on aetiological cure of the underlying disease.
Compensated cirrhosis with varices (state 2).
These patients have CSPH13and are at risk of
var-iceal bleeding and decompensation. Thus, they require a different monitoring schedule and
speci-fic treatment according to the severity of
risk.104,107 By competing risks analysis10
five-year event probabilities are: death before decom-pensation 10%, variceal bleeding 8%, one single
non-bleeding decompensating event (mostly
ascites) 20%, more than one decompensating event at the same time 4%.
Decompensation defined by the development of at least one among variceal bleeding, ascites, jaun-dice or encephalopathy, occurs in 4–12% per year.4,6–8,10,11,112–118According to studies8,10using
competing risks analysis, the first decompensating event is most frequently ascites (18–27%), fol-lowed by bleeding (9.5–18%), encephalopathy (2– 7%) and jaundice (1.5%). More than one decompen-sating event at once (mostly ascites plus bleeding) occur in approximately 13% of patients. The first decompensation may also present with ACLF, although its incidence rate is not well defined in
patients without previous decompensation.92
Variceal bleeding (state 3). Patients with bleed-ing alone have better outcomes than patients with ascites without bleeding, and much better
out-comes than patients with bleeding and ascites.8–
10 Better survival rates are also consistently
reported for acute variceal bleeding in patients
whose cirrhosis is otherwise compensated.35,119
According to competing risks analysis, the
reported five-year risks in this state are:8,10death
before other complications 18%–20%, further decompensation 54%–45% and rebleeding before further decompensation 19%.
First non-bleeding decompensation (state 4). Ascites is the most frequent first non-bleeding
decompensating event4,8,10,112–118,120and is in fact
considered the hallmark of decompensation. Although much more rarely, encephalopathy and jaundice may also present as a first non-bleeding
decompensation.8,10 Overall five-year mortality
following the development of any of these decom-pensating events is in the range of 55%– 80%.4,8,10,112,115,118,120–127 Five-year mortality
before the development of further decompensat-ing events is in the order of 25% accorddecompensat-ing to com-peting risks analysis.8,10
Further decompensation (state 5). Following any first decompensating event, most patients develop further decompensation before dying. The most frequent combination is bleeding and ascites, although jaundice and encephalopathy are also
frequent8,10Irrespective of the combination,
five-year mortality may reach 88%.8–10,118
Late advanced decompensation (state 6). The progressive increase in splanchnic vasodilatation, hyperdynamic circulation, bacterial translocation
Key point
ACLF is characterised by acute liver decompensa-tion, organ failure(s) and high 28-day mortality. Systemic inflammatory response to several critical events is the most impor-tant mechanism activating ACLF, even when a clear triggering event is not identifiable (in up to 40% of patients).
Key point
Aetiological treatment of cirrhosis may halt or even reverse the clinical course of the disease, particularly when it is still in a com-pensated state.
Key point
and systemic inflammation result in a more
advanced, late decompensation state where
multi-organ dysfunction becomes clinically
evi-dent.14,49,53,59–63,127–131 Refractory ascites,
infec-tions, persistent encephalopathy and/or jaundice, renal, circulatory and respiratory dysfunctions are typical presentations of this disease state. One-year mortality for these conditions ranges from 60 to 80%.
ACLF72–75may occur in any disease state and is
associated with six-month mortality from 38% to
96%.77 Patients resolving ACLF, may remain in a
decompensated state with or without organ dys-function or even in a compensated state, although the proportions of these state transitions are not clearly defined.
Management implications of clinical states
of cirrhosis
Recognising different clinical states may have important implications on the most likely clinical outcomes. Hence, clinical states may be used to inform treatment interventions to prevent disease progression. In fact, there is evidence that in com-pensated patients without varices (state 1) the most appropriate approach is aetiological treat-ment, particularly in those with MPH (state 0) in whom NSBBs do not appreciably reduce portal
hypertension.13,97 In these patients, non-invasive
monitoring based on LSM and platelet count may identify patients at risk of CSPH and guide
endo-scopic screening for oesophageal varices.104,109,110
Although timolol (an NSBB) has been proven inef-fective in preventing development of oesophageal
varices,11 since prevention of decompensation is
now recognised as a major management objective
in these patients (states 0–2),104,107other
preven-tative approaches, aiming at reducing intrahepatic resistance and splanchnic flow, should undergo appropriate clinical trials. Patients in states 3–5 should be appropriately treated for the prevention
of bleeding, rebleeding104,107and further
decom-pensation. Patients in state 6 and those with ACLF require a multidisciplinary approach to their man-agement, with access to specific treatments and early selection of candidates for liver transplanta-tion.132–134
Competing risks in cirrhosis
A competing risk is the risk of an event whose occurrence either precludes the occurrence of another event or modifies the probability that it will occur. Along the clinical course of cirrhosis, many clinical conditions, or states, may be charac-terised by competing outcomes which require competing risks analysis to correctly assess the relevant risks. Several such conditions are shown (Table 1), where examples of outcomes of interest are reported together with potentially relevant competing events, according to the baseline condi-tion and the research aim requiring competing risks analysis.135
It is important to note that in decompensated cirrhosis the underlying risk of death is high, with Key point
Refractory ascites, HRS, infections, circulatory dys-function and ACLF are markers of late advanced decompensation and very poor survival, although ACLF may also occur in compensated cirrhosis. Key point
LSM>15 identify cACLD which is equivalent to compensated cirrhosis and values ≥20–25 KPa denote CSPH with 0.90 specificity. MPH (HVPG >5mmHg and <10mmHg), CSPH and gastroesophageal varices are associated with increasing disease severity in compensated cirrhosis. Bleeding alone, any first decompensating event and ≥2 decompensating events are associated with worsening outcome of decompensated cirrhosis.
Increasing fibrosis
METAVIR 4A METAVIR 4B METAVIR 4C
Increasing portal hypertension MPH
HVPG >5 and <10 mmHg
CSPH HVPG ≥10 mmHg
Higher risk of major events HVPG ≥12
Increasing bacterial translocation/inflammation Minimal/absent SAV and normal CO Moderate SAV compensated by ↑ CO Significant SAV no further CO compensation Severe SAV ↓ CO Severe hemodynamics impairment; ↓ organ perfusion
Increasing clinical severity
Compensated cirrhosis Decompensated cirrhosis Late decompensation
No varices Mild PH CSPH Varices (CSPH) Bleeding alone Non-bleeding decompensation ≥2 decompensating events
Refractory ascites; PSE/jaundice; HRS, other organs
dysfunction; ACLF
Aetiological cure ACLF
a median survival of approximately two years.4
This implies that whenever assessing the inci-dence of any further decompensating event, like refractory ascites, hepatorenal syndrome, infec-tions and ACLF, it is important to consider death as a competing event to achieve reliable risk
estimates.135
Competing risks analysis
Recognising competing risks is important because, in the presence of competing risks, the KM
estima-tor21 invariably results in upward biased
esti-mates.22–24,135Competing risks analysis is based
on the CIF which, by using the Aalen-Johansen
estimator,23partitions the probability of any event
into the probabilities that each event occurs first, resulting in an overall event probability (or the sum of the probabilities of each event) correctly ranging from zero to one. The essential difference between the two methods is that the KM estima-tor counts only the events of interest and censors or ignores the competing events, while the Aalen-Johansen estimator correctly counts both the event of interest and the competing events.
As a practical example consider assessing the incidence of oesophageal varices, and the proba-bility of survival without developing varices, in a cohort of patients included in a prospective study
of the natural history of cirrhosis.10Death before
developing varices is clearly a competing event for the occurrence of oesophageal varices. When
using the KM estimator (Fig. 2A) the 20-year
1-KM estimate of the probability of developing varices was 0.61. The 20-year 1-KM cumulative probability of death without varices was 0.46. Since the two risks are mutually exclusive, they are clearly upward biased, summing up to 1.07 instead of ≤1. Notably, when assessing the risk of varices the KM estimator censors death, and when estimating the risk of death without varices it cen-sors the occurrence of varices: for this reason the number of patients at risk per each observation period is identical for the two KM estimates. To show how competing risks analysis works we assessed the risk (1-KM estimate) of the composite outcome (death or varices, whichever occurs first): in this way neither event is censored. By doing this, we have reduced the three-state model (no varices, varices, death) into a two-state model
([no varices]? [varices or death]), the situation
where the KM method may be safely applied.20,21
This estimate in our cohort is plotted (Fig. 2B
[1-KM curve]) together with the CIF of each of the two competing events obtained by the competing risks analysis. It may be seen that the 1-KM esti-mate for the risk of the composite outcome death or varices (0.79) corresponds exactly to the sum of each of the two risks (0.53 varices + 0.26 death = 0.79 composite) computed by the competing risks
Table 1. Examples of clinically relevant outcomes and potentially relevant competing events according to several baseline conditions and specific research aims.
Clinical condition Event of interest Potentially relevant competing events
Aims of competing risks analysis Compensated cirrhosis
Decompensation Death Decompensation; death before decompensation
Specific
decompensating event
Death; other decompensating events
First event to occur in compensated cirrhosis
ACLF Death; decompensation ACLF before overt decompensation; death before ACLF
HCC Death; decompensation HCC in compensated cirrhosis; death before HCC
MPH (HVPG >5 and <10 mmHg)
Oesophago-gastric varices
Death; decompensation Development of varices before decompensation; death before varices and decompensation
CSPH (HVPG ≥10 mmHg)
Oesophago-gastric varices
Death; decompensation Development of varices before decompensation; death before varices and decompensation
Oesophageal varices Bleeding Death, decompensation Assessment of bleeding before decompensation Decompensated cirrhosis
Variceal bleeding Rebleeding Death; decompensating
events
Incidence of rebleeding before other decompensating events
Variceal bleeding Rebleeding Death Incidence of rebleeding; death before rebleeding
Ascites Refractory ascites Death Incidence of refractory ascites; death before refractory ascites
Ascites Other decompensating
events
Death; other decompensating events
First new clinically relevant event; death before other events ≥1 decompensating
events
Other decompensating events
Death; other decompensating events
First new clinically relevant event; death before other events Any type of
decompensation
ACLF; HCC; HRS Death ACLF, death before ACLF; HCC, death before HCC; HRS, death before
HRS Late decompensation
Refractory ascites Death OLT Death before OLT; OLT
Major infections Death OLT Death before OLT; OLT
Renal failure Death OLT Death before OLT; OLT
Acute on chronic liver failure
Death OLT Death before OLT; OLT
ACLF, acute-on-chronic liver failure; CSPH, clinically significant portal hypertension; HCC, hepatocellular carcinoma; HRS, hepatorenal syndrome; HVPG, hepatic venous pressure gradient; OLT, orthotopic liver transplantation; MPH, mild portal hypertension.
Key point
analysis. The example shows that the competing risks analysis partitions the risk of any of the com-peting events (whichever occurs first) into the risk that each of the competing events occurs first. Therefore, the real risk of developing varices in the included cohort of patients was 0.53 as esti-mated by the CIF and not 0.61 as estiesti-mated by the KM estimator. Moreover, censoring death like it was not a clinically relevant event does not make
sense and is technically wrong.135The
correspond-ing real probability of dycorrespond-ing before developcorrespond-ing varices was 0.26 and not the 0.46 1-KM estimate. By considering any death (before or after varices) we could have correctly estimated the overall mor-tality by the KM estimator, however this estimate would not consider the possible change of mortal-ity risk after the development of varices.
Another example of a situation where the com-peting risks analysis should be applied is the assessment of the probability that a clinically rel-evant event will be the first to occur among sev-eral events. In such a situation all the assessed events are mutually exclusive, because only one of them may be the next to occur, and the sum of all the probabilities shall range between zero and one. However, by the KM model the sum of the probabilities obtained may be higher than one, because per each assessed event, the occur-rence of the competing events is ignored or cen-sored. For example, looking for the next event to occur in a cohort of 377 patients with
compen-sated cirrhosis,10the 1-KM estimates showed that
20-year cumulative risk of death was 0.63, ascites
0.51, variceal bleeding 0.35 and HCC 0.28 (Fig. 3A),
yielding a total probability of 1.77, which is of course impossible for mutually exclusive risks. In fact, this analysis does not provide us with the probability of the next event to occur, but instead gives us the 20-year cumulative risk of each event, independently of the occurrence of other events, in a hypothetical world where death (or the other events) do not exist. In particular, the KM curve on death is the correct estimate of the overall mortal-ity, as defined before. Note that, as already men-tioned, death is censored when estimating the risk of each of the other events, while for any other event of interest, patients experiencing the com-peting events are still at risk of the event of inter-est. Competing risks analysis showed that the 20-year probability of being the next event to occur was 0.29 for ascites, 0.16 bleeding, 0.15 HCC,
0.12 death summing up to 0.72 (Fig. 3B). In a
sim-ilar study117 it was erroneously concluded that
HCC was the first event to occur based on a 17-year 1-KM cumulative risk of 0.55 compared with 0.35 ascites, 0.27 jaundice, 0.10 bleeding, 0.03 encephalopathy, summing up to a total probability of 1.3. An inference from this study would be that HCC is the most likely first event in an ideal world where the other events do not exist.
More insight into the reason why the use of the KM estimator is correct only in two-state settings is provided by the relationship between rate (or incidence rate) and risk. This has been thoroughly
explained elsewhere.22,135Here we only recall that
while the incidence rate is the ratio D/Y (number of
0.0 0.2 0.4 0.6 0.8 1.0 0 60 120 180 240 1-KM estimate 0.46 0.61 Months Varices Death Probability Varices or death estimated by 1-KM Varices (CIF) Death (CIF) 0.79 0.53 0.26 0.0 0.2 0.4 0.6 0.8 1.0 Probability Patients at risk 243 153 98 74 52 0 60 120 180 240 Months 243 153 98 74 52
A
B
Fig. 2. Development of oesophageal varices and mortality in 243 patients free of varices at diagnosis of compensated cirrhosis.10(A) 1-KM estimates of the cumulative risks of developing oesophageal varices (death censored) and of dying before developing varices (varices censored). The sum of the two risks is higher than 1 (0.46 + 0.61 = 1.07). (B) Cumulative incidence of varices and of death assessed by the competing risks analysis CIF, estimated by the Aalen-Johansen estimator. The 1-KM estimate of the composite endpoint (death or development of varices) is also plotted to show how the CIF partitions the risk of any event in the risks of each event (0.53 + 0.26 = 0.79). (A, B) The abscissa denotes the number of months of observation and the numbers below the abscissa are the number of patients at risk per each observation period. Note that the number of patients at risk per each observation period for the two KM plots in (A) is the same because when estimating the risk of death without developing varices, the KM estimator censors the occurrence of varices and when estimating the risk of varices it censors deaths. Therefore, per each observation period the number of patients at risk is the number at risk at the beginning of the previous observation period – (n developing varices + n death + n with truncated observation) for both curves. For the same reason, the number of patients at risk in the competing risks analysis and in the 1-KM plot in the right side of the figure are the same as those in the plots of the left side. CIF, cumulative incidence function; KM, Kaplan-Meier.
Key point
subjects developing the disease/the total amount of person-time at risk), the risk is the ratio D/N, (number of subjects who develop the disease/ number of subjects disease-free at the beginning
of the observation time).136 Therefore, while the
incidence rate is essentially an average measure of the speed of occurrence of the event of interest, assuming a constant hazard over time, and is expressed as the number of events occurring per unit of time, the risk is a measure of the cumula-tive probability of the event in a given observation time. Consequently, while the cumulative risk may not decrease over time (because D either increases or is constant with time), the incidence rate may increase, remain near constant or decrease.
It may be noted that while in two-state set-tings, there is a direct one to one relationship between rate and risk, because the number of sub-jects at risk and of events taken as a basis for cal-culations is the same for rate and risk, in a multistate setting (competing risks) this unique relationship is lost, because the number of sub-jects at risk decreases whenever one of the com-peting events occurs. In fact, here the interest is in the next event to occur, and the risk depends on more than one rate of events.
In other words, the KM assumes that there is only one event of interest and that only this will contribute to reduce the number of patients at risk. When more than one event causes the reduc-tion of patients at risk, like in the competing risks situation, the Aalen-Johansen estimator correctly
estimates the risk that each of several events of interest occurs first, by the CIF.
These concepts also imply that the association of covariates with the rate of one event of interest may be different from their association with the risk of that event, in the presence of competing
risks. For this reason, the Cox model137may not
be appropriate to estimate the risk of events in
dif-ferent groups135 in a competing risks setting,
because it assumes a one to one relationship between rate and risk.
Building multistate models in cirrhosis
Clinical states should be conceived as a flexible concept and specific clinical states should be defined whenever a specific prognostic questionmakes it appropriate (Table 1). As an example, in
the same study of the clinical course of cirrhosis
referred to earlier,10the 20-year cumulative
prob-ability of death (1-KM) was 0.62, in 377 patients with compensated cirrhosis, and 0.93 after pensation in 224 patients who developed
decom-pensation during the follow-up (Fig. 4A).
However, in clinical practice, it might also be of interest to know the probability of decompensa-tion and of death before decompensadecompensa-tion. These probabilities are appropriately assessed by the
competing risks analysis (Fig. 4B), which shows a
20-year cumulative probability of 0.58 and 0.14 for decompensation and death before decompen-sation, respectively. The probability of death after
Key point
In two-state settings there is a direct one to one relation between rate and risk, this is lost in multi-state settings, where the number of subjects at risk decreases at any time one of the competing events occurs. Death Ascites Bleeding HCC Cumulative risks by the KM estimator 0.63 0.51 0.35 0.28 0.12 0.29 0.16 0.15 Cumulative incidence by the Aalen-Johansen estimator
0.0 0.2 0.4 0.6 0.8 1.0 0 60 120 180 240 Months Probability Patients at risk 377 309 251 207 141 377 288 219 160 120 377 292 231 164 125 377 304 244 178 131 0.0 0.2 0.4 0.6 0.8 1.0 0 60 120 180 240 Months Probability 377 276 201 142 106 Death Ascites Bleeding HCC
A
B
decompensation is already known by the KM anal-ysis and the full three-state model is shown (Fig. 4C).
In a multistate model it is also possible to assess the probability of patients in the earliest state occupying one of the other possible states
after a certain observation time.135In the
three-state model above, the possible outcomes along the disease course are: alive still compensated, alive decompensated, dead before decompensa-tion, dead after decompensation. The relevant state occupation probabilities may be estimated by the Aalen-Johansen estimator, which is an extension of the KM estimator for multistate mod-els. Statistical software for this kind of analysis are available in the R statistical package (msSurv or
mstate routins).138 State occupation probabilities
for the above model are shown (Fig. 4D) at
differ-ent observation times over the whole disease course. The probability of being alive in a decom-pensated state is low, and this is coherent with the current knowledge that patients who
transi-tion in the decompensated state have a very low survival time. The analysis also shows that 20 years after the diagnosis of compensated cirrhosis there is a 41% probability of death after decom-pensation, and 34% of being alive in a compen-sated state.
A schematic representation of a hypothetical multistate model encompassing the whole course of cirrhosis is shown (Fig. 5).
Competing risks and clinical research
As shown in previous sections in this article, the most obvious field of application for competing risks analysis is the study of the clinical course of diseases in every situation where relevant compet-ing risks are identified.A second relevant field where competing risks should be appropriately accounted for is prognosis research. A major aim of this type of research is to find accurate predictors of a disease outcome in a given time. The hypothesis underlying this research is that one or more among several patient or disease characteristics may be linked to the dis-ease outcome through a causal mechanism (causal factors) or through indirect association (predictive factors). In studies of causal factors, the hypothesis is that some biological mechanism links the candi-date predictor to the event under study. In this type of study the interest is in assessing whether the event occurs earlier in patients presenting the candidate causal factor than in those without, thus focussing on the rate, not the risk. In this
sit-uation, the cause specific Cox model138is
appro-priate, since it looks at the instantaneous rate of only the event of interest and may disclose a cau-sal effect when all the potential confounders are accounted for.
When the interest is in identifying factors asso-ciated with the occurrence of the event of interest (risk predictors), competing events, which may modify the risk of the event of interest must be accounted for. In this type of research, the stan-dard Cox model is not appropriate because it ignores the competing events and may result in upwards biased estimates similar to the KM estimator. A specific multiple regression propor-tional hazards model has been developed for
com-peting risks, by Fine and Gray.139 This model
provides the sub(distribution)-hazard ratio (sHR), which measures the relationship between the candidate predictive factor and the outcome, accounting for both the association between the factor and the outcome and for the modifying effect of the competing events on this association. Although it does not have a meaningful interpreta-tion, it allows for risk predictions in individual patients.140
Therefore, it is important when planning research on prognostic indicators, to ensure that the statistical method used is appropriate for the specific research aims. The Cox model should be
Compensated
Decompensated Death
0.58 0.14
0.93
Decompensation
Death before decompensation 0.14 0.58
Death probability Compensated n = 377 0.62 Decompensated n = 224 0.93 1-KM estimates 0 20 40 60 80 100 Prediction probabilities % 10 5 7 78 59 18 10 13 10 13 31 46 8 17 41 34 100 Alive, decompensated
Alive, compensated Dead after decompensation Dead without decompensation
Competing risks analysis (Aalen-Johansen estimator) 0.0 0.2 0.4 0.6 0.8 1.0 0 60 120 180 240 Months Patients at risk 377 309 251 186 141 224 62 35 23 10
A
B
C
D
Event probability 0.0 0.2 0.4 0.6 0.8 1.0 0 60 120 180 240 Months 377 274 203 146 109 0 60 120 180 240 Months Patients at riskused to study causal associations, while the Fine and Gray model is more appropriate for risk pre-diction in individual patients, in the presence of
competing risks.140
An example of how the two models may yield different results is provided by an analysis per-formed to investigate the role of oesophageal varices on the risk of decompensation in patients with compensated cirrhosis, accounting for death
as a competing risk, in 377 compensated
patients.10Platelet count and the Child-Pugh score
were also included to adjust for other important
prognostic indicators in cirrhosis.4 Both models
found a significant association between varices and decompensation: the cause specific Cox model (hazard ratio 1.51, 95% CI 1.14–1.99) suggested a potential causal role (possibly through some plau-sible biological mechanism like more advanced portal hypertension), whereas the Fine and Gray model (sub-hazard distribution ratio 1.43, 95% CI 1.08–1.89) suggested a significant difference in the risk of decompensation in patients with and without oesophageal varices. Moreover, both models showed a significant effect of platelet count and Child-Pugh score on the risk. The indi-vidual patient risks predicted by the two models are plotted against the observed risks (estimated
by the Aalen-Johansen estimator [Fig. 6]) to show
how the Cox model tends to overestimate the risk in the presence of competing risks, compared to the Fine and Gray model.
A third research area where competing risks analysis may help to interpret observations may be treatment efficacy research. This is usually based on risks comparison without accounting for competing risks. To illustrate how competing risks analysis may provide more insight into the interpretation of results, we report an extended analysis accounting for competing risks of a previ-ously published randomised, double-blind, clinical trial of octreotide vs. placebo for rebleeding, in
patients with cirrhosis over 42 days.141 The trial
showed a barely significant reduction of rebleed-ing with octreotide (p = 0.04, log rank test) (Fig. 7): 42/101 patients rebled in the placebo group and 27/101 in the octreotide group; there were eight and ten deaths, respectively. Compet-ing risks analysis showed that the reduction in rebleeding risk with octreotide was slightly higher than found by the KM estimator, and that five of ten deaths in the octreotide group occurred before rebleeding, compared to only one of eight in the placebo group. This observation, together with the higher number of rebleeding episodes and of blood unit transfusions in the placebo group sug-gests that octreotide was associated not only with a reduction in the rebleeding risk, but also with a lower severity of rebleeding episodes.
When planning randomised controlled trials (RCTs) the cause specific hazard Cox model should always be used, as the interest lies in causal rela-tionships. However, to estimate the risk of an
event it may also be important to account for rel-evant competing risks, because the sample size estimation may be different according to whether relevant competing risks are accounted for or not. As an example, if one would plan an RCT to pre-vent the formation of oesophageal varices based on the baseline risk of 0.61 calculated by the KM
estimator (Fig. 2A), with the hypothesis of a
haz-ard ratio of 0.7 for the two treatments,
a
= 0.05and b = 0.20, the total number of events needed
would be 247 (two-sided test with arms of equal
Compensated State 0: no varices, MPH LSM >15 and <20 or HVPG >5 and <10 mmHg State 1: no varices, CSPH LSM ≥20 or HVPG ≥10 mmHg State 2: Varices (= CSPH) Decompensated End state DEATH State 3: bleeding State 4: first non-bleeding decompensation State 5:
second decompensating event
State 6: late decompensation:
refractory ascites, persistent PSE or Jaundice, infections,renal, other organs dysfunction
ACLF
Fig. 5. Schematic representation of a comprehensive multistate model for the clinical course of cirrhosis. ACLF, acute-on-chronic liver failure; CSPH, clinically significant portal hypertension; HVPG: hepatic venous pressure gradient; LSM, liver stiffness measurement; MPH, moderate portal hypertension; PSE, portosystemic encephalopathy.
Observed risk
0.0 0.2 0.4 0.6 0.8 1.0
Predicted probability Cox model
Fine and Gray model
0.0 0.2 0.4 0.6 0.8 1.0
Fig. 6. Calibration of predicted probabilities of decompen-sation, according to the Cox model and to the Fine and Gray model, adjusted for the presence of oesophageal varices, platelet count and Child-Pugh score in a cohort of 377 patients with compensated cirrhosis at diagnosis.10Predicted probabilities are computed according to each of the two models in nine groups of patients of approximately equal size. Per each group the median predicted probability of decompensation is plotted against the median observed risk. The dashed line represents perfect correspondence between predicted and observed risks. The figure shows that the Cox model tends to overestimate predicted probabilities.
Key point
size) and the total number of patients included would need to be 452. Instead, by using the 0.53 risk derived by the competing risks analysis, accounting for death before the formation of
varices (Fig. 2B), the total number of patients
needed would be 520 under the assumption of a
hazard ratio of 0.7 as before.142 Therefore, it is
likely that even if the correct hypothesis has been made, the trial would be underpowered if the competing risk of death has not been
appropri-ately accounted for.143
Conclusions
The clinical spectrum of cirrhosis encompasses several clinical states, from a very early state of compensated cirrhosis with subclinical portal hypertension, to the late decompensation state
with extreme hyperdynamic circulation, bacterial translocation and inflammation. The progression across such states does not occur through a pre-dictable sequence, because of the variable inter-play between pathophysiological mechanisms. Therefore, a multistate approach provides a more realistic description of the disease course. Mul-tistate models require competing risks analysis to assess the probabilities of transition across states and appropriate multiple regression models to investigate prognostic indicators, because the traditional KM estimator and the Cox model may provide biased results in the presence of compet-ing risks. These concepts should be thoroughly accounted for when planning clinical research either of prognosis or of treatment efficacy in cirrhosis.
Financial support
P. Rebora was supported by the grant of the Italian Minister of Education, University and Research (MIUR) – Italy SIR 2014 (RBSI14LOVD).
Conflict of interest
The authors declare no conflicts of interest that pertain to this work.
Please refer to the accompanyingICMJE
disclo-sureforms for further details.
Authors’ contribution
Gennaro D’Amico: review concepts and project, data collection, elaboration of examples, text and figures. Alberto Morabito: statistical concepts and data analysis for examples. Mario D’Amico: data collection; cohort study for the examples included in the review; text revision. Linda Pasta: responsible for the cohort study used for the examples included in the review. Giuseppe Mal-izia: review project and text revision. Paola Reb-ora: statistical concepts, examples and text revision. Maria Grazia Valsecchi: statistical con-cepts, examples, text revision.
Supplementary data
Supplementary data associated with this article
can be found, in the online version, at
https://doi.org/10.1016/j.jhep.2017.10.020. Rebleeding 0.40 Death 0.01 Rebleeding 0.26 Death 0.05 0 7 14 21 28 35 42 Death 0.08 Rebleeding 0.41 Rebleeding 0.28 Death 0.10 Death probability 0.0 0.2 0.4 0.6 0.8 1.0
A
B
C
D
Placebo 1-KM estimate Octreotide 1-KM estimate Octreotide Competing risks analysis (Aalen-Johansen estimator) PlaceboCompeting risks analysis (Aalen-Johansen estimator) 101 82 77 71 67 101 99 99 97 94 65 61 94 93 Days 0 7 14 21 28 35 42 66 97 82 80 71 87 97 95 94 90 74 71 89 89 Days 0 7 14 21 28 35 42 101 81 76 70 66 64 60 Days 0 7 14 21 28 35 42 97 82 80 74 71 71 60 Days Death probability 0.0 0.2 0.4 0.6 0.8 1.0 Death probability 0.0 0.2 0.4 0.6 0.8 1.0 Death probability 0.0 0.2 0.4 0.6 0.8 1.0 Patients at risk Patients at risk Patients at risk Patients at risk
Fig. 7. Estimates of rebleeding and death risks in a double blind, placebo controlled randomised clinical trial of octreotide.141(A, B) 1-Kaplan-Meier estimates in (A) the placebo group and in (B) the octreotide group, respectively. (C) Placebo group and (D) octreotide group: rebleeding and death cumulative incidence functions, estimated by the Aalen-Johansen estimator in the same trial. The fig. shows that deaths occurred mostly after rebleeding in the placebo group, while half of the total deaths in the octreotide group occurred before rebleeding. (A–D) The abscissa denotes the number of months of observation and the numbers below the abscissa are the numbers of patients at risk per each observation period.
Key point
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