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Abstract
Aims
The minute ventilation–carbon dioxide production relationship (VE/VCO
2 slope) is widely used for prognostication in heart failure (HF) with reduced left
ventricular ejection fraction (LVEF). This study explored the prognostic value of
VE/VCO
2 slope across the spectrum of HF defined by ranges of LVEF.
Methods and results
In this single‐centre retrospective observational study of 1347 patients with HF referred
for cardiopulmonary exercise testing, patients with HF were categorized into HF with
reduced (HFrEF, LVEF < 40%,
n = 598), mid‐range (HFmrEF, 40% ≤ LVEF < 50%,
n = 164), and preserved (HFpEF, LVEF ≥ 50%,
n = 585) LVEF. Four ventilatory efficiency categories (VC) were defined: VC‐I, VE/VCO
2 slope ≤ 29; VC‐II, 29 < VE/VCO
2 slope < 36; VC‐III, 36 ≤ VE/VCO
2 slope < 45; and VC‐IV, VE/VCO
2 slope ≥ 45. The associations of these VE/VCO
2 slope categories with a composite outcome of all‐cause mortality or HF hospitalization
were evaluated for each category of LVEF. Over a median follow‐up of 2.0 (interquartile
range: 1.9, 2.0) years, 201 patients experienced the composite outcome. Compared with
patients in VC‐I, those in VC‐II, III, and IV demonstrated three‐fold, five‐fold,
and eight‐fold increased risk for the composite outcome. This incremental risk was
observed across HFrEF, HFmrEF, and HFpEF cohorts.
Conclusions
Higher VE/VCO
2 slope is associated with incremental risk of 2 year all‐cause mortality and HF hospitalization
across the spectrum of HF defined by LVEF. A multilevel categorical approach to the
interpretation of VE/VCO
2 slope may offer more refined risk stratification than the current binary approach
employed in clinical practice.
Background ROC (receiver operating characteristic) curve analysis is well established for assessing how well a marker is capable of discriminating between individuals who experience disease onset and individuals who do not. The classical (standard) approach of ROC curve analysis considers event (disease) status and marker value for an individual as fixed over time, however in practice, both the disease status and marker value change over time. Individuals who are disease-free earlier may develop the disease later due to longer study follow-up, and also their marker value may change from baseline during follow-up. Thus, an ROC curve as a function of time is more appropriate. However, many researchers still use the standard ROC curve approach to determine the marker capability ignoring the time dependency of the disease status or the marker. Methods We comprehensively review currently proposed methodologies of time-dependent ROC curves which use single or longitudinal marker measurements, aiming to provide clarity in each methodology, identify software tools to carry out such analysis in practice and illustrate several applications of the methodology. We have also extended some methods to incorporate a longitudinal marker and illustrated the methodologies using a sequential dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver. Results From our methodological review, we have identified 18 estimation methods of time-dependent ROC curve analyses for censored event times and three other methods can only deal with non-censored event times. Despite the considerable numbers of estimation methods, applications of the methodology in clinical studies are still lacking. Conclusions The value of time-dependent ROC curve methods has been re-established. We have illustrated the methods in practice using currently available software and made some recommendations for future research. Electronic supplementary material The online version of this article (doi:10.1186/s12874-017-0332-6) contains supplementary material, which is available to authorized users.
Introduction In many cancer studies, the main outcome under assessment is the time to an event of interest. The generic name for the time is survival time, although it may be applied to the time ‘survived’ from complete remission to relapse or progression as equally as to the time from diagnosis to death. If the event occurred in all individuals, many methods of analysis would be applicable. However, it is usual that at the end of follow-up some of the individuals have not had the event of interest, and thus their true time to event is unknown. Further, survival data are rarely Normally distributed, but are skewed and comprise typically of many early events and relatively few late ones. It is these features of the data that make the special methods called survival analysis necessary. This paper is the first of a series of four articles that aim to introduce and explain the basic concepts of survival analysis. Most survival analyses in cancer journals use some or all of Kaplan–Meier (KM) plots, logrank tests, and Cox (proportional hazards) regression. We will discuss the background to, and interpretation of, each of these methods but also other approaches to analysis that deserve to be used more often. In this first article, we will present the basic concepts of survival analysis, including how to produce and interpret survival curves, and how to quantify and test survival differences between two or more groups of patients. Future papers in the series cover multivariate analysis and the last paper introduces some more advanced concepts in a brief question and answer format. More detailed accounts of these methods can be found in books written specifically about survival analysis, for example, Collett (1994), Parmar and Machin (1995) and Kleinbaum (1996). In addition, individual references for the methods are presented throughout the series. Several introductory texts also describe the basis of survival analysis, for example, Altman (2003) and Piantadosi (1997). TYPES OF ‘EVENT’ IN CANCER STUDIES In many medical studies, time to death is the event of interest. However, in cancer, another important measure is the time between response to treatment and recurrence or relapse-free survival time (also called disease-free survival time). It is important to state what the event is and when the period of observation starts and finishes. For example, we may be interested in relapse in the time period between a confirmed response and the first relapse of cancer. CENSORING MAKES SURVIVAL ANALYSIS DIFFERENT The specific difficulties relating to survival analysis arise largely from the fact that only some individuals have experienced the event and, subsequently, survival times will be unknown for a subset of the study group. This phenomenon is called censoring and it may arise in the following ways: (a) a patient has not (yet) experienced the relevant outcome, such as relapse or death, by the time of the close of the study; (b) a patient is lost to follow-up during the study period; (c) a patient experiences a different event that makes further follow-up impossible. Such censored survival times underestimate the true (but unknown) time to event. Visualising the survival process of an individual as a time-line, their event (assuming it were to occur) is beyond the end of the follow-up period. This situation is often called right censoring. Censoring can also occur if we observe the presence of a state or condition but do not know where it began. For example, consider a study investigating the time to recurrence of a cancer following surgical removal of the primary tumour. If the patients were examined 3 months after surgery to determine recurrence, then those who had a recurrence would have a survival time that was left censored because the actual time of recurrence occurred less than 3 months after surgery. Event time data may also be interval censored, meaning that individuals come in and out of observation. If we consider the previous example and patients are also examined at 6 months, then those who are disease free at 3 months and lost to follow-up between 3 and 6 months are considered interval censored. Most survival data include right censored observations, but methods for interval and left censored data are available (Hosmer and Lemeshow, 1999). In the remainder of this paper, we will consider right censored data only. In general, the feature of censoring means that special methods of analysis are needed, and standard graphical methods of data exploration and presentation, notably scatter diagrams, cannot be used. ILLUSTRATIVE STUDIES Ovarian cancer data This data set relates to 825 patients diagnosed with primary epithelial ovarian carcinoma between January 1990 and December 1999 at the Western General Hospital in Edinburgh. Follow-up data were available up until the end of December 2000, by which time 550 (75.9%) had died (Clark et al, 2001). Figure 1 Figure 1 Converting calendar time in the ovarian cancer study to a survival analysis format. Dashed vertical line is the date of the last follow-up, R=relapse, D=death from ovarian cancer, Do=death from other cause, A=attended last clinic visit (alive), L=loss to follow-up, X=death, □=censored. shows data from 10 patients diagnosed in the early 1990s and illustrates how patient profiles in calendar time are converted to time to event (death) data. Figure 1 (left) shows that four patients had a nonfatal relapse, one was lost to follow-up, and seven patients died (five from ovarian cancer). In the other plot, the data are presented in the format for a survival analysis where all-cause mortality is the event of interest. Each patient's ‘survival’ time has been plotted as the time from diagnosis. It is important to note that because overall mortality is the event of interest, nonfatal relapses are ignored, and those who have not died are considered (right) censored. Figure 1 (right) is specific to the outcome or event of interest. Here, death from any cause, often called overall survival, was the outcome of interest. If we were interested solely in ovarian cancer deaths, then patients 5 and 6 – those who died from nonovarian causes – would be censored. In general, it is good practice to choose an end-point that cannot be misclassified. All-cause mortality is a more robust end-point than a specific cause of death. If we were interested in time to relapse, those who did not have a relapse (fatal or nonfatal) would be censored at either the date of death or the date of last follow-up. Lung cancer clinical trial data These data originate from a phase III clinical trial of 164 patients with surgically resected (non-small cell) lung cancer, randomised between 1979 and 1985 to receive radiotherapy either with or without adjuvant combination platinum-based chemotherapy (Lung Cancer Study Group, 1988; Piantadosi, 1997). For the purposes of this series, we will focus on the time to first relapse (including death from lung cancer). Table 1 Table 1 A sample of times (days) to relapse among patients randomised to receive radiotherapy with or without adjuvant chemotherapy Radiotherapy (n=86) 18, 23a, 25, 27, 28, 30, 36, 45, 55, 56, 57, 57, 57, 59, 62, …, 2252a, 2286a, 2305a, 2318a, 2940a Radiotherapy+CAP (n=78) 9, 22, 35, 53, 76, 81, 94, 97, 103, 114, 115, 126, 147, 154, …, 2220a, 2375, 2566, 2875b, 3067b CAP=cytoxan, doxorubicin and platinum-based chemotherapy. a Lost to follow-up and considered censored. b Relapse-free at time of analysis and considered censored. gives the time of the earliest 15 and latest five relapses for each treatment group, where it can be seen that some patients were alive and relapse-free at the end of the study. The relapse proportions in the radiotherapy and combination arms were 81.4% (70 out of 86) and 69.2% (54 out of 78), respectively. However, these figures are potentially misleading as they ignore the duration spent in remission before these events occurred. SURVIVAL AND HAZARD Survival data are generally described and modelled in terms of two related probabilities, namely survival and hazard. The survival probability (which is also called the survivor function) S(t) is the probability that an individual survives from the time origin (e.g. diagnosis of cancer) to a specified future time t. It is fundamental to a survival analysis because survival probabilities for different values of t provide crucial summary information from time to event data. These values describe directly the survival experience of a study cohort. The hazard is usually denoted by h(t) or λ(t) and is the probability that an individual who is under observation at a time t has an event at that time. Put another way, it represents the instantaneous event rate for an individual who has already survived to time t. Note that, in contrast to the survivor function, which focuses on not having an event, the hazard function focuses on the event occurring. It is of interest because it provides insight into the conditional failure rates and provides a vehicle for specifying a survival model. In summary, the hazard relates to the incident (current) event rate, while survival reflects the cumulative non-occurrence. KAPLAN–MEIER SURVIVAL ESTIMATE The survival probability can be estimated nonparametrically from observed survival times, both censored and uncensored, using the KM (or product-limit) method (Kaplan and Meier, 1958). Suppose that k patients have events in the period of follow-up at distinct times t 1
[1]Division of Cardiovascular Medicine, Department of Medicine
Brigham and Women's Hospital
75 Francis Street
Boston
MA
02115
USA
[2]
Brigham and Women's Hospital Center for Clinical Investigation
Boston
MA
USA
[3]Noninvasive Cardiovascular Imaging Program, Department of Medicine (Cardiovascular
Division) and Department of Radiology
Brigham and Women's Hospital
Boston
MA
USA
[4]Heart Institute, Department of Pediatrics, Cincinnati Children's Hospital
University of Cincinnati College of Medicine
Cincinnati
OH
USA
Author notes
[*][*
]Correspondence to: Anju Nohria, Division of Cardiovascular Medicine, Brigham and Women's
Hospital, 75 Francis Street, Boston, MA 02115, USA. Phone: +1‐617‐525‐7052; Fax: +1‐617‐264‐5265.
Email:
anohria@
123456bwh.harvard.edu
This is an open access article under the terms of the
http://creativecommons.org/licenses/by-nc-nd/4.0/ License, which permits use and distribution in any medium, provided the original
work is properly cited, the use is non‐commercial and no modifications or adaptations
are made.
History
Date
revision received
: 04
November
2021
Date
received
: 24
September
2021
Date
accepted
: 24
November
2021
Page count
Figures: 3,
Tables: 6,
Pages: 10,
Words: 3994
Funding
Funded by: Brigham and Women's Hospital
, doi 10.13039/100005292;
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