| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
J Thorac Cardiovasc Surg 1999;118:973-975
© 1999 Mosby, Inc.
LETTERS TO THE EDITOR |
Associate Editor
Reply to the Editor:
We are indebted to Dr Wormuth for drawing attention to inaccurate terminologyrelated to so-called survival analysis that has crept into our Association’sannual meeting (and into submitted manuscripts). Communication is the essenceof such meetings and of the Journal; yet communicationcontroversies continue even within cardiothoracic surgery in the area of medicalterminology. These pale, however, in comparison with those in the arena ofsurvival analysis. When presenters and authors deem it necessary to selectan adjective to qualify their estimates of time-related events, they findno universally accepted term! Even the general name for the analyses performedis not agreed on, in part because the methodology is widely applicable: survivalanalysis, survival modeling, survival data analysis, actuarial analysis, lifetable, life-history analysis, life data analysis, life-testing, failure-timedata, event-history analysis, and censored data analysis (I may have missedsome). We see survival analysis in the narrow context of death and other time-relatedmorbid events in cardiothoracic surgery; however, historically, it has rootsin other disciplines that continue to contribute to its development, includingdemography, annuities and insurance, and life-history of machinery in industry.These are further generalized to competing risks, multiple decrement, Markovprocess, and other names, not to mention the host of names associated withbiomathematical models! The terms have come from different, often independent,historical roots, but they all relate to the general mathematical and statisticaltheory of counting processes (martingales).
History.
The word actuarial comes from the Latin actuarius, secretary of accounts. The most notable actuariuswas the Praetorian Prefect Domitius Ulpianus, who produced a table of annuityvalues early in the 3rd century AD.
1 This table continued to be usedin Europe through the 18th century and even into the early 19th. With theemergence of both solid population data and the science of probability, modernso-called life tables were produced by Edmund Halley 2 (of comet fame) in 1693. He was motivated, as wasthe actuarius Ulpianus, by economics as related to human survival (annuities,life insurance). Workers in this combined area of demography and economicscame to be called actuaries in the late 18thcentury. Importantly for this discussion, the methodology of the actuary variedwidely. In the 19th century the actuary of the Alliance of London, BenjaminGompertz, 3 developed physiologicallybased mathematical models of the dynamic human processes of birth and deathto characterize survival. This model-based, completely parametric (equationswith constants estimated from data) methodology was substantially differentfrom the simple empiric counting methodology of Halley.
In the 300 years since Halley, a multitude of methods has been developed,and often reinvented, in actuarial science, demography, statistics, industry,and medical science. They all have the common goal of estimating the distributionof the intervals between a designated time zero and the occurrence of an event.In modern times, they also imply a suite of methodology applicable to incompletedata. That is, they permit estimates of at least portions of the distributionto be made when, for many subjects, the time of the event’s occurrenceis only known to be beyond the last time of observation (so-called right censoring,one of several types of incomplete data).
Estimators versus adjectives.
With this background I come to the crux of Dr Wormuth’s concerns.When authors speak or write of actuarial survival, are they communicatinginaccurately the method or formula applied to data to obtain survival estimates(the estimator), or are they simply using a historically rooted generic adjectiveto identify that the estimates are based on time-to-event data? My personalopinion is that they are using an adjective to identify a general type ofdata and its analysis rather than identifying a specific estimator. Dr Wormuthbelieves that they are specifying the estimator. Regardless, we routinelyadvise authors against use of any adjective in front of the word "survival"(and against the use of the further qualifier "rate") becauseit is unnecessary. They can simply state "Survival was...."The "Methods" section of the manuscript should identify the estimatorused to obtain the survival estimates.
The Kaplan-Meier estimator.
As Dr Wormuth states, these days the most commonly used estimator forsurvival and other time-related morbid events in medicine is the product-limitestimator described by Kaplan and Meier 4 and called the Kaplan-Meier estimator. It represents the unlikelysynthesis of its two authors, one working with life-times of vacuum tubesin the repeaters in telephone cables buried in the ocean and the other workingwith medical follow-up studies. They were forced to generate a joint paperby the editor of the Journal of the American StatisticalAssociation, who recognized that their individual submissions onthe subject of "failures" in the face of incomplete informationwere really about the same subject.
Its advantage is a firm basis in probability and statistical theory,widespread availability in commercial statistical computer programs, and itsvisual appeal of presenting the most atomic details of the distribution oftimes to events. We encourage authors to use fully the estimates obtainedby application of this methodology in their graphs, for they provide morevisual information than does unnecessary coarse collapsing of the estimatesinto interval values (as would be the product of the so-called actuarial estimator).
I would also quibble with the statement that "Kaplan-Meier analysisis undertaken at each survival event, death, or censoring." In fact,the Kaplan-Meier estimator provides survival estimates only at uncensoredtimes (death) and not at censored times. Chin Long Chiang 5 described a method that accounts explicitly for thetimes of censoring, but for some reason this more complicated method (requiringmore than counting) has not seen widespread implementation.
Finally, whether or not to connect Kaplan-Meier survival estimates atall, to use a zero order interpolation (straight line) as suggested by DrWormuth, or first-order or higher interpolation (linear interpolation, splineinterpolation) is not a settled issue. Dr Yang-Ming Zhu in my group demonstratedthat both maximum entropy estimation and minimum norm estimation favor atleast some form of interpolation greater than zero (step function) when usinga nonparametric estimator such as that of Kaplan and Meier.
The actuarial estimator.
What seems generally agreed on is that, in contrast to the Kaplan-Meierestimator, the actuarial estimator generates survivorship (freedom from events)estimates within time intervals, rather than at the time of each event. However,the limit as the interval approaches zero is the Kaplan-Meier estimator, aswas described by Böhmer in 1912, long before the seminal paper by EdwardKaplan and Paul Meier.
If I may be allowed to correct Dr Wormuth, the actuarial estimator was,and is, often used in settings in which the exact times of the events areknown. For large populations, grouping of times to death was convenient andsaved computational time. Certainly the introduction of the actuarial estimatorto the medical mainstream by Berkson and Gage 6 at the Mayo Clinic was not motivated by having interval data, butby not having readily available a better method! They called the method theactuarial method because they had obtained it from the 1922 writings of Murphyand Papps for the Actuarial Society of America. I agree with Dr Wormuth that,in most medical settings today, this interval method is considered obsoleteand more exact methods (such as the Kaplan-Meier or Nelson-Aalen 7 estimators) should be used. Further, the word actuarial carries with it the historical connotationof economic inferences from the survival data, which is generally not thecase in medical follow-up reporting.
Today, the exact time of an event may not be known, only that it occurredafter some point in time and before a later time point. This is known as interval-censoreddata. All modern life-table methods (for lack of a generic term for them),including the method of Kaplan and Meier, can be modified to accommodate amixture of data with exact times of events known and interval-censored data.Parametric methods allow mixtures of data representing additional censoringtypes. 8
Summary.
Accuracy and clarity in communication are important. However, this lengthyresponse to the issues raised by Dr Wormuth indicates that communication withinthe subject of so-called survival analysis is not simple! There is lack ofan accepted generic adjective for analyses of time-related events. There ishistorical baggage that suggests that in most medical contexts "actuarial"has implications that are not intended, although its introduction by Berksonat the Mayo Clinic is compelling. One must distinguish between the type ofdata at hand, the estimator applied to that data, and the estimates therebygenerated.
I dare say, in all these regards and including Dr Wormuth and me, thatwe all have a "limited understanding of survival analysis" (forlack of a better phrase with which to characterize it!).
12/8/102963
References
This article has been cited by other articles:
|
|
 |
|
  E. Bodnar and E. H. Blackstone An "actual" problem: Another issue of apples and oranges J. Thorac. Cardiovasc. Surg., January 1, 2006; 131(1): 1 - 3. [Full Text] [PDF]
|
|
|
|
 |
|
 C. Selkane, B. Amahzoune, N. Chavanis, O. Raisky, J. Robin, J. Ninet, and J. F. Obadia Changing management of cardiac myxoma based on a series of 40 cases with long-term follow-up Ann. Thorac. Surg., December 1, 2003; 76(6): 1935 - 1938. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| ANN THORAC SURG | ASIAN CARDIOVASC THORAC ANN | EUR J CARDIOTHORAC SURG |
| J THORAC CARDIOVASC SURG | ICVTS | ALL CTSNet JOURNALS |
