Ventricular hypertrophy, age, and date of operation as risk factors

J

THoRAc CARDIOVASC SURG

92:1049-1064, 1986

The Fontan operation Ventricular hypertrophy, age, and date of operation as risk factors One hlUldred two patients, aged 0.7 to 38 years, with a wide variety of cardiac malfonnations underwent the Fontan operation (1975 to April, 1985). Several different techniques were used. All but 17 had previously undergone one or more palliative operations. Follow-up infonnation was obtained in all patients. Overall actuarial survival rate, with time zero being the time of the operation, was 63 % at 6 years with no deaths after that in patients followed as long as out to 9.4 years; that for patients with tricuspid atresia was 81 %. The hazard function (instantaneous risk) for death was highest immediately after operation and merged after about 6 months with a constant hazard extending as long as the patients werefollowed. Elevatedpost-repair right atrial pressure was correlated (p = 0.002)with the probability of death in the early phase, with the risk rising rapidly with pressures above 14 mm Hg, Hypertrophy of the ventricular main chamber was a risk factor for death in both the early (p = 0.007) and late (p = 0.008) phasesof hazard, whichexplainedin part the lesser risk of the Fontan operation in patients with tricuspid atresia. Youngerage, but not older age, was a risk factor for early postoperative death, but this risk was neutralized by recent date of operation. Thus currently there is not a predicted increased risk associated with younger age at operation. In general, the Fontan operation should be done at a young age (2 to 4 years) to avoid increasing ventricular hypertrophy, but older age per se is not a contraindication to the operation.

James K. Kirklin, M.D., Eugene H. Blackstone, M.D., John W. Kirklin, M.D., Albert D. Pacifico, M.D., and Lionel M. Bargeron, Jr., M.D., Birmingham. Ala.

Experience with the Fontan operation, introduced in 1969,1.2 has produced several enigmas. For no obvious reason, the results have seemed to be better in patients with tricuspid atresia than in those with other cardiac anomalies. Young age at operation has seemed to increase the risk of death,' yet the Fontan operation has been successfully performed at 18 months of age as the final step in the repair of the hypoplastic left heart syndrome.' Current experience gives the impression that the results of the operation are better than in earlier

years, yet some hospital survivors still die a few months after the operation. This paper is based on a detailed review of a 10 year experience with the Fontan operation, done in a number of different ways for a wide variety of cardiac anomalies. The data have been analyzed by methods specifically designed to help in the understanding of time-related events, in the hope of resolving the enigmas associated with the Fontan operation and of identifying the determinants of success with the operation. Material and methods

From the Departments of Surgery and Pediatrics and the Alabama Congenital Heart Disease Diagnosis and Treatment Center, University of Alabama at Birmingham Medical Center, Birmingham, Ala. Received for publication Dec. 14, 1985. Accepted for publication Jan. 7. 1986. Address for reprints: Dr. John W. Kirklin, Professor and Surgeon, Division of Cardiothoracic Surgery, University of Alabama at Birmingham, Birmingham, Ala. 35294.

Patients and definitions. All patients (n = 102) undergoing the Fontan operation between 1975 (date of first operation in this institution was June 11, 1975) and April 1, 1985, are included in this study. Their ages at operation ranged from 0.7 to 38 years and the median age was 7.8 years. Very early in the experience strict selection criteria were used, but during most of it the only absolute contraindication to the Fontan procedure 1049

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The Journal of Thoracic and Cardiovascular Surgery

Kirklin et al.

Table I. The AV connection and deaths after the Fontan operation (1975 to April. 1985; n = 102; deaths = 32) Total deaths

Hospital deaths A V connection Concordant Discordant U niventricular Double inlet Common AV valve Right-sided AV valve atresia, dextro-loop* Right-sided AV valve atresia, leva-loop Left-sided AV valve atresia, dextro-loop Left-sided AV valve atresia, leva-loop Ambiguus Total

I

I

CL

No.

44% 0%

29%-60% 0%..61%

9

o

56% 0%

4 0 7

21% 0% 13%

11%..35% 8%..19%

6 I II

32% 50% 20%

16%..46% 7%..93% 14%..28%

0

0%

00/0-85%

0

0%

0%..85%

2

50%

7%..93%

2

100%

39%..100%

4

25%

3%..63%

2

50%

18%..82%

50%

7%..93%

32

31%

260/0-37%

n

No.

16 2

7 0

19 2 54

2 102

p(X')

21

%

I

00/0..61%

50%

7%-93%

21%

16%-26%

0.22

I

%

CL 40%-71% 0%..61%

0.07

Key: A Y, Atrioventricular. CL, 70% confidence limits. 'Tricuspid atresia.

was evidence of poor runoff through the pulmonary arteries (hemodynamic evidence of pulmonary vascular disease or incomplete arborization or very small size of the pulmonary arteries). All cardiac chambers were named according to their morphology and not their position. Thus a morphologic right ventricle was called a right ventricle even though it lay to the left. The internal ventricular architecture was described as being dextro-loop (or right-handed) or levo-loop (left-handed). In the presence of two ventricles, the dominant ventricle was identified, and in the setting of the Fontan operation, the other one was usually hypoplastic or rudimentary, or both. The atrioventricular (AV) valves were described as right or left according to their right- or left-sided position without concern as to whether the morphology was that of a mitral or tricuspid valve. One hundred of the 102 patients had atrial situs solitus, none had atrial situs inversus, and two had atrial isomerism. All types of AV connection are represented (Table I). Seventy-eight patients had ventricular dextroloop, five had questionably dextro-loop, and 16 had levo-loop. Three patients had solitary ventricles. Fiftyone patients had concordant ventriculoarterial connections, 31 had discordant ventriculoarterial connections, 14 had double-outlet right ventricle, two had doubleoutlet left ventricle, three had double outlet from a ventricle of indeterminant morphology, and one had a solitary (aortic) ventricular outlet. All but six patients

had pulmonary stenosis, but in 25 patients it had been produced by pulmonary artery banding. All but 17 of the 102 patients had one or more operations before the Fontan operation. Fifty-one had undergone a Blalock-Taussig or a polytetrafluoroethylene* (PTFE) interposition shunt, three had undergone Potts shunts, and three Waterston shunts. Fourteen patients had previously received a Glenn anastomosis. Fifteen patients had undergone a Blalock-Hanlon type of atrial septectomy. Twenty-four patients had a pulmonary artery band in place at the time of the Fontan operation. Five patients had previously undergone repair of coarctation. Other miscellaneous palliative procedures had been received. (These numbers are not mutually exclusive.) Surgical methods. All operations were done with cardiopulmonary bypass and direct caval cannulation. Since 1977 all patients but two were operated on with aortic cross-clamping and cold cardioplegic myocardial protection.' In 30 patients the Fontan operation was accomplished by making a right atrial-right ventricular connection, in eight of them with a nonvalved conduit, in nine with a valved conduit, and in 13 by a direct right atrial-right ventricular connection, usually with a roof created with Dacron fabric or pericardium. In 72 patients the connection was made between the right *Gore..Tex vascular graft, registered trademark of W. L. Gore & Associates, Inc., Elkton, Md.

Volume 92 Number 6 December 1986

atrium and pulmonary artery. In 37, and almost routinely in the last few years, the right atrial-pulmonary arterial connection was made as a direct one. In 24 other patients, the connection was also direct but was roofed with a Dacron or pericardial patch. In 11 additional patients, the right atrial-pulmonary arterial connection was made with a heterograft valved extracardiac conduit. In an attempt to relate the results of the multivariate analysis to specific techniques for performing the Fontan operation, we defined these techniques in terms of the risk-determining variables identified by the multivariate equation. The classical Fontan operation (see Table V) is defined as a right atrial-right ventricular connection by a nonvalved Dacron conduit in which the conduit was attached to a linear right atriotomy and right ventriculotomy. The Bjork modification is defined as a right atrial-right ventricular connection in which the right atrial appendage is used as the conduit." The roofed atrial flap connection of right atrium to right ventricle has the atrial flap as the posterior part of the conduit and a contoured Dacron roof anteriorly.' In some instances the direct right atrial-pulmonary arterial connections':" were made to a circular opening in the roof of the atria produced by excising a part of the atrial wall. In other instances they were made to a linear atriotomy or by the use of an atrial flap in the posterior part of the connection and a contoured Dacron roof anteriorly. Right atrial-pulmonary arterial connections were also made in some patients via a heterograft valved Dacron tube, anastomosed proximally to a right atriotomy or to the base of the amputated atrial appendage. Study methods. The original hospital records, records of cardiac catheterization and angiocardiography, operative records, and autopsy reports were reviewed in each case. Follow-up records and studies were all reviewed, as well as correspondence with referring physicians and families. The detailed morphology of the cardiac anomaly was reviewed and recategorized in each case by means of the preoperative cineangiograms and two-dimensional echocardiograms, the operative notes, and, when available, autopsy records. The degree of hypertrophy (increase in wall thickness) of the ventricular main chamber (usually literally the large chamber but in all instances the chamber generating systemic blood flow) was graded as o to 6 from a review of cineangiographic and surgical findings, made without knowledge of the outcome after operation. The increase in size (diastolic volume) of the ventricular main chamber was graded 0 to 6 in the same manner. Every patient had recently been seen or contacted for

Fontan operation

105 1

complete follow-up information. The date of follow-up was May, 1985, the median follow-up time was 33 months, and the range 3.8 months to 9.5 years. Data analysis. After all the information on each patient had been accumulated and verified, actuarial analysis of survival, using the time of operation as time zero, was made by the Kaplan-Meier method,'? as were several stratified actuarial curves that were then compared by determining the p value by the Gehan II Wilcoxon technique. A hazard function (the instantaneous risk in patients not yet experiencing the event under study) for death as a time-related event was then determined by the method of Blackstone, Naftel, and Turner. l2 , 13 A multivariate analysis was made in the hazard function domain to determine the incremental risk factors for death. Variables were retained in the multivariate analysis if their p value was <0.1. Comparisons were made between the patients' survival and hazard functions and those of an age-sex-race matched general population from the 1976 United States life tables. Selective predictive and comparative nomograms and digital displays were made by solving the multivariate equation with certain values entered for the risk factors. Simple contingency tables were also made for variables of interest; discrepancies were apparent between some of the usually univariate contingency tables and the results of the multivariate analysis. A few univariate logistic analyses were also used. Demographic variables entered into the analyses were the continuously variable ones of age, height, weight, and body surface area, the dichotomous (yes/no) ones of race and gender, and logarithmic transformations of the continuous variables. Clinical continuous variables entered were New York Heart Association (NYHA) functional class and hematocrit, as well as the dichotomous ones of a previous Glenn anastomosis, systemicpulmonary artery shunt, and pulmonary artery banding. Morphologic variables entered as dichotomous ones were as follows: large left ventricle, dominant left ventricle, large right ventricle, dominant right ventricle, AV concordant connection, AV discordant connection, double-inlet ventricle, right AV valve atresia and stenosis and incompetence, left AV valve atresia and stenosis and incompetence, the ventricular loop (or handedness), ventriculoarterial concordant or discordant connection, double-outlet right ventricle, pulmonary atresia, bifurcation and/or right, left pulmonary arterial stenosis, "classical tricuspid atresia" (that is, atrial situs solitus, ventricular dextro-loop, right AV valve atresia, and either concordant or discordant ventriculoarterial connection), and "pulmonary atresia with intact ventricular

The Journal of

1 0 5 2 Kirklin et al.

Thoracic and Cardiovascular Surgery

100 90

80

'i

70

';

60

..

:-

(53)

(1.4)

.

::I

en

... •.. C

50

U

40

A.

30

•

20 10 0

0

3

2

4

567

8

10

9

Years after Operation

Fig. 1. Actuarial survival rate, including hospital deaths, after the Fontan operation (1975 to April, 1985; n = 102; deaths = 32). Each patient who died is represented by a circle. The vertical bars describe the 70% confidence limits. The dashed line indicates survival without further deaths. The dash-dot-dash line near the top is the survival of an age-sex-race matched general population. The 30 day actuarial survivorship is 79% (CL 75%-83%),3 months 74% (CL 69%-78%), and 3 years 71% (CL 66%-76%). Not depicted in this and other actuarial analyses is the patient with the longest follow-up (who had tricuspid atresia and died after her second reoperation 9.5 years after the original Fontan operation) because the actuarial method cannot estimate the survival rate in this setting. The patient is represented in the parametric hazard and survivorship presentations.

Table

n.

The morphology and deaths after the Fontan operation (1975 to April, 1985; n = 102; deaths Hospital deaths

Morphology

n

No.

TrICUspId atresia Others

54 48

7 14

102

21

Total p(x')

I

Total deaths Cl

No.

29%

8%-19% 22%-37%

II 21

21%

16%-26%

32

%

13%

0.04

I

= 32)

I

% 20% 44% 31%

I

CL

14%-28% 36%-52% 26%-37%

0.01

Key: CL, 70% confidence limits.

septum." Morphologic variables entered as continuous ones were ventricular hypertrophy grade (0 to 6, zero being normal) and enlargement grade (0 to 6) as well as the ratio of the enlargement and hypertrophy and the difference between the degree of hypertrophy and that of enlargement. Surgical variables entered as continuous ones were the date of operation and aortic cross-clamp time when cardioplegia was used. Surgical variables entered as dichotomous ones were the use of cardioplegia and repair of pulmonary stenosis separate from the making of an atriopulmonary connection. The dichotomous variables concerned with the Fontan operation that were entered were atrial-right ventricular connec-

tion with a linear atriotomy or atrial excision or atrial flap and with a roof or a nonvalved or valved extracardiac conduit; atriopulmonary connection with a linear atriotomy or atrial excision creating a circular opening or a flap and with a direct connection or a roof or a valved extracardiac conduit; with either AV connection or atriopulmonary connection, use of the right atrial appendage as the conduit, use of a roof in the venous pathway, and use of a valved or nonvalved extracardiac conduit in the pathway; complex atrial baffle, either for septal shifting or incorporation of right or common AV valve; right AV valve closure; and left ventricle as the systemic pumping chamber.

Volume 92 Number 6 December 1986

Fontan operation 1 05 3

100

Tricuspid Atresia (n=54)

90

_______________________C)53)

80

'ii

70

..

60

Co)

40

..

.;> :::I

fit

c:

•.. D• o

_

( 14) Double inlet AV connection (n= 19) ----------------------_.

50

(3)

Other Morphology (n=29)

(~) -

30

- - - - - - - - -

20 10 0

0

2

3

4

567

8

9

10

Vear. After Operation

Fig. 2. Actuarial survival rate, including hospital deaths, after the Fontan operation, according to the cardiac malformation (1975 to April, 1985; n = 102; deaths = 32). The representation is as in Fig. I. AV, Atrioventricular.

The same variables plus post-repair left atrial pressure were entered into a multivariate linear regression correlation analysis of post-repair mean right atrial pressure (P RA ) , measured in the intensive care unit about 2 hours after the operation. Seventy-five patients were alive and had measurement of P RA at that time, but in only 54 was mean left atrial pressure (P LA) also measured, and the latter group was used for the analysis. However, an analysis of the 75 patients without entering P LA gives entirely similar results except for the P LA• Results Survival. Among the 102 patients undergoing a Fontan operation, actuarial survival rate, including hospital deaths, was 63% (CL * 560/0-70%) at 6 years, with 14 patients followed beyond that time and as long as 9.5 years (Fig. 1). Twenty-one (21%; CL 16%-26%) patients died in the hospital; hospital and late deaths occurred less frequently in patients with tricuspid atresia than in those with other cardiac malformations (Table II). The actuarial survival rate, including hospital deaths, out to 9 years, of patients with tricuspid atresia was 81%, higher (p = 0.01) than that of the other groups (Fig. 2). There was an initially high but rapidly falling hazard function (instantaneous risk of death), which began immediately after the operation and merged into the 'Confidence limits.

Table m. Modes of death after the Fontan operation (1975 to April, 1985; n = 102; deaths Mode of death

No.

Q

= 32)

of 32

Acute cardiac failure Subacute cardiac failure Chronic sequelae of elevated systemic venous pressure' Sudden Neurologict After reoperationj

13 6 7

41 % 19% 22%

I 2 3

3% 6% 9%

Total

32

100%

'Persistent pleural, pericardial, and ascitic fluid accumulation; or hepatomegaly and intractable edema. tin one, cerebral embolism was associated with the neurologic death. tin one, after a second operation for removal of an atrial thrombus; in another, after repair of dehiscence of tricuspid valve closure; in a third, after takedown of Fontan operation and creation of a systemic-pulmonary artery shunt.

constant phase by about 6 months after the operation (Fig. 3). The constant phase of risk, which was higher than the hazard function of the matched general population, continued throughout the period of observation. Modes of death and the post-repair PiiA. Most patients died of acute or subacute cardiac failure (Table III), but in many of these the P RA was considerably elevated and appeared to be the limiting factor in cardiac performance. In seven other patients, death occurred with chronic sequelae of elevated systemic

10 5 4

The Journal of Thoracic and Cardiovascular Surgery

Kirklin et al.

0.20 0.18

.. I

0.16

..

0.14

.c c o

0.12

:Ii

0.10

:SIII

0.08

a

0.06

•

0.04 0.02

\

..

3

6

9

12

15

18

21

24

Months after Operation

Fig. 3. The hazard function (instantaneous risk of death in patients still living) after the Fontan operation (1975 to April, 1985; n = 102; deaths = 32). The dashed lines enclose the 70% confidence limits. There are an early rapidly falling phase and a constant phase that extends thorughout the period of observation. The dash-dot-dash line, barely visible at 0.002, represents the hazard function of an age-sex-race matched general population.

!100

C o 90

:Ii

CO 80 C 70

i i.c 60

..

: 50

a '0 40

i

30

=:

20

J

10

>-

i

o

It

0 5

P=.002

10

15

20

25

Right Atrial Pressure (mmHg) in Intensive Care Unit

30

Fig. 4. Nomogram of the probability of death within 6 months of the Fontan operation, according to the post-repair right atrial pressure in the intensivecare unit about 2 hours after operation. The dashed lines enclose the 70% confidence limits. The equation for the nomogram is in the hazard function domain, with right atrial pressure identified as a risk factor in the early hazard phase by univariate analysis (see Appendix A).

venous pressure. Atrial thrombosis or embolization, or both, were associated with the death of two patients. Post-repair P RA in the intensive care unit about 2 hours after the operation was strongly positively correlated with the probability of death in the early hazard

phase (Fig. 4). The risk of death within 6 months of operation was less than 12.5%if the P RA was less than 14 mm Hg at that time, but the risk was 22% (CL 17%-28%) when the P RA was 16 mm Hg and 43% (CL 34%-54%) when it was 19 mm Hg.

Volume 92 Number 6 December 1986

Fontan operation

Table IV. Linear regression correlation analysis of post-repair PRA in the intensive care unit about 2 hours after termination of cardiopulmonary bypass (1975 to April, 1985; n = 54) Correlates Simultaneous PiA Demographic Age (In) Clinical NYHA Class (I-V) Morphologic Main chamber hypertrophy (0-6) Pulmonary atresia with intact ventricular septum Pathway construction Atrial appendage as conduit Atriopulmonary heterograft valved conduit Roofed A V connection Direct atriopulmonary connection with linear atriotomy Surgical Aortic cross-clamp time (min) Intercept

p Value

0.45 ± 0.111

0.0002

-0.7 ± 0.38

0.07

1.1 ± 0.43

0.01

1.3 ± 0.54

0.02

2.4 ± 1.25

0.06

2.9 ± 0.82

0.001

2.5 ± 1.21

0.04

3.5 ± 0.96 1.7 ± 0.80

0.0008 0.04

0.028 ± 0.011 I

Table V. Post-repair P RA after the Fontan operation (various procedures), predicted from the linear regression correlation equation (Table IV). Procedure

Coefficient ±SD

1055

RA-RV connection Classical Fontan operation Bjork modification Connection by a roofed RA flap Heterograft valved extracardiac conduit, RA anastomosis at: Linear atriotomy Base of appendage RA-PA connection Anastomosis to circular RA wall defect Anastomosis to linear right atriotomy Anastomosis via RA flap and Dacron roof Heterograft valved extracardiac conduit, RA anastomosis at: Linear or circular atriotomy Base of appendage

Predicted P1fA (mmHg)

14 (11-16) 17 (14-19) 17 (15-20)

16 (14-19) 20 (18-23) 14 (11-16) IS (13-18) 14 (11-16)

16 (14-19) 19 (16-22)

Key: P;v:, Right atrial mean pressure. RA, Right atrium. RV, Right ventricle. PA. Pulmonary artery. Note: Post-repair Pn is entered as 8, age as 4 years, preoperative NYHA class as II. main chamber hypertrophy as I. pulmonary atresia "no," and aortic cross-clamp time as 80 minutes. (See Material and methods for definitions of procedures.)

0.02

5.4

Key: AV, Atrioventricular. In, Natural logarithm. NYHA, New York Heart Association. Prx, Left atrial mean pressure. PI!A, Right atrial mean pressure.SD, Standard deviation. Note: Sixty-one percent (r') of the variability in PI!A is explained by the correlates. The coefficients, with appropriate multiplication in the case of continuous variables, may be directly converted to PI!A in millimeters of mercury.

A correlation analysis (Table IV) indicates that the post-repair P RA was strongly influenced by the postrepair P LA, The mean value for the simultaneously observed PRAPLA was 7 ± 3.4 mm Hg (mean ± standard deviation), with a range of 0 to 16 mm Hg. Other variables were also correlated with the post-repair P RA• When these variables were clustered so as to describe certain typical surgical procedures, the postrepair P RA A can be predicted assuming a post-repair P LA of 8 mm Hg (Table V). Incremental risk factors for death. The emergence of the grade (severity) of hypertrophy of the main ventricular chamber as a risk factor for death in both the early and late phase in the multivariate analysis (Table VI) accounted for some of the risks that were otherwise ascribed to several of the cardiac anomalies treated with the Fontan operation,

Thirty-seven (69%; CL 61%-76%) of the 54 patients with tricuspid atresia had ventricular hypertrophy grade oor 1 whereas 14 (29%; CL 22%-37%) of 48 with other morphology had this grade; the median grade of hypertrophy was 1 in patients with tricuspid atresia and 2 in those with other morphology. The correlation of the severity of the ventricular hypertrophy with age at operation and presence of a pulmonary artery band was a weak one by univariate analysis (Table VII). By multivariate linear regression analysis, omitting tricuspid atresia from the analysis because of its overwhelmingly powerful effect, neither older age at operation (p = 0.21), nor presence of a pulmonary artery band (p = 0.21), nor ventricular outflow obstruction (n = 13) were retained as correlates with main chamber ventricular hypertrophy. The correlates retained with a p value <0.1 (intercept 1.31) were morphologies other than tricuspid atresia (p = 0.05), double-inlet ventricle (p = 0.002), grade (0-5) of left AV valve incompetence (p = 0.(02), and left AV valve atresia (p = 0.03); the coefficients, respectively, were 0.34 ± 0.172, 0.7 ± 0.22, 1.1 ± 0.35, and 0.7 ± 0.32. The importance of ventricular hypertrophy as a risk factor was also evident from contingency table and logistic analysis (Table VIII). Its continuing importance,

The Journal of Thoracic and Cardiovascular Surgery

1 0 5 6 Kirklin et al.

Table VI. Incremental risk factors for death after the Fontan opeation, including in-hospital and late deaths (1975 to April. 1985; n = 102; deaths = 32) Time of influence (hazard phase)

Incremental risk factors Demographic variables Younger age Morphologic variables Main ventricular chamber hypertrophy (Grade 0-6) Left-sided AV valve atresia Left-sided AV valve incompetence Right and/or left pulmonary artery stenosis Surgical variables Earlier date of operation Interaction with age Direct atriopulmonary connection with linear atriotomy Longer aortic cross-clamp time

Early and decreasing p value

Table YD. The relation of age at operation and presence of a pulmonary artery band to the severity (grade) of main chamber hypertrophy Main chamber hypertrophy (grade) 0 I 2 3 4 5 6

Constant and throughout p value

0.009 0.007

0.008

0.002 0.02 0.02

0.004 0.03 0.0004 0.009

Key: AV, Atrioventricular. Note: The variables entered into the analysis are listed in Material and methods. The equations and coefficients are in Appendix B.

even in the current era, was predicted by solution of the multivariate equation (Table IX). The morphology of the dominant chamber and the internal architecture did not emerge as incremental risk factors in the multivariate analysis. Neither did they appear to be a risk factor by contingency table analysis (Table X). Younger age was a risk factor for death in the early phase in the early years of this experience (Fig. 5), but older age was not a risk factor in either the early or late phase. This was also reflected in univariate contingency table and logistic analysis (Table XI). Although simple contingency table analysis disclosed no improvement as regards survival in the recent years of this experience (Table XII), multivariate analysis indicated that, when other factors were considered, earlier date of operation was a risk factor (Table VI). In addition, a mathematical interaction of this with young age resulted in the decreased risk of death in the current era being especially evident in younger patients (Fig. 6). As a result, the predicted probability of death within 6 months of a Fontan operation in a patient with no or mild ventricular hypertrophy in 1985 was less than 2%, with no difference imposed by the age of the patient. However, the

Total P (for trend)

n 1 50 34 15 2

102

Age (yr) (mean ± SE) 1.3 ± ± ± ±

9.5 11.6 II 15

0.95 I.71 2.6 5.5

10.5 ± 0.84 0.15 0.14

PA band No. 0 8 II 6

25

I

% ofn

0% 16% 32% 40%

25% 0.17 0.18

Key: PA, Pulmonary artery. SE, Standard error.

70% confidence limits for the 2-year-old patient are wider than those for older patients (see Fig. 5). Left-sided AV valve atresia (see Table I) increased the risk of death in the early phase of hazard (Table VI). Important left-sided AV valve incompetence also increased the risk of death in the early phase. Stenosis of the right or left pulmonary artery, or both, increased the risk of death in the early phase. Nineteen patients (seven of whom died in the hospital after operation and three of whom died later) had stenosis of the right or left pulmonary artery, or both. Fourteen of these had diffuse narrowing of both pulmonary arteries; four had one or more discrete narrowings; and one had stenosis at the origin of both pulmonary arteries. The presence of a pulmonary artery band was not a risk factor for death. Among the 25 patients with pulmonary artery bands, four had secondary bifurcation stenosis (not included in the 19) but with large left and right pulmonary arteries, and the repair of these was easily incorporated into the Fontan-type repair. Neither a pulmonary artery band nor a single previous systemic-pulmonary artery shunt was a risk factor for death, and neither correlated with right and/or left pulmonary artery stenosis. A longer aortic cross-clamp time was a risk factor for death in the early phase after operation. However, this was evident only when there was considerable main ventricular chamber hypertrophy and aortic cross-clamp time greater than 96 minutes (Fig. 7). The only type of surgical connection between right atrium and pulmonary artery that was a risk factor in the multivariate analysis for death was a direct right atrial-pulmonary arterial connection in which a linear

Volume 92 Number 6 December 1986

Fontan operation

1057

vrn. The relation (univariately) of the grade (severity) of hypertrophy of the main ventricular chamber to death after the Fontan operation (1975 to April. 1985; n = 102; deaths = 32)

Table

Total deaths

Hospital deaths

Main chamber hypertrophy (grade)

No.

n 1

o

2 3

50 34 15

7 7 7

4

2

o

102

21

o I

Total

I

%

I

0% 14% 21% 47% 0%

CL

No.

o

0%-85% 90/0-21% 13%-30% 310/0-63% 0%-61%

%

I

2

0% 20% 29% 67% 100%

32

31%

10

10 10

p(x')

0.08

0.002

p (logistic)

0.04

0.0004

1

CL 0%-85% 14%-28% 21%-40% 500/0-81% 39%-100% 26%-37%

Key: CL, 70% confidence limits.

Table IX. Predicted 6 month survival (essentially, survival through the early phase of hazard) after the Fontan operation. according to the grade (severity) of main ventricular chamber hypertrophy in patients 5 and 20 years old Main chamber hypertrophy

Age (yr)

%

5

99.4% 99.5%

20

Grade 1

Grade 3

Grade 4

6 mo survival

6 mo survival

6 mo survival

I

CL

%

98.8%-99.7% 99.0%-99.8%

94%

I

92%

CL

%

850/0-96% 88%-97%

73% 79%

1

CL 51%-88% 59%-91%

Key: CL, 70% confidence limits. Note: The predictions are a solution of the multivariate equation (Table V and Appendix B), in which aortic cross-clamp time was entered as 80 minutes, all other morphologic variables as "no," direct atriopulmonary connection with a linear atriotomy as "no," and date of operation as 1985.

Table X. Death after the Fontan operation according to the ventricular morphology and internal architecture (loop) (1985 to April. 1985; n = 102; deaths Ventricular dominance and architecture Donunant LV

Dextro-loop Levo-loop Dominant RV Dextra-loop ?Dextra-loop Leva-loop Solitary ventricle LV and RV Indeterminant Codominant ventricles Dextra-loop Leva-loop Total

= 32)

Hospital deaths n

No.

85 71 14 10

18 14 4 2

4

2

5 I

3 2 I

4

3

o o o o o I

I

I

o

102

21

CL

No.

21% 20% 29% 20% 50% 0% 0% 0% 0% 0% 25% 33% 0%

16%-27% 15%-26% 150/0-46% 7%-41% 18%-82% 0%-32% 0%-85% 00/0-46% 0%-61% 0%-85% 3%-63% 4%-76% 0%-85%

25 20 5 4

21%

16%-26%

32

%

r

p(x') for dominance categories Key: CL. 70% confidence limits. LV. Left ventricle. RV. Right ventricle.

0.8

I

4

o

o

I

o I

2

2

o

1

Total deaths

% 29% 28% 36% 40% 100% 0% 0% 33% 0% 100% 50% 67% 0% 31% 0.8

I

CL 24%-35% 220/0-35% 21%-53% 22%-61% 62%-100% 0%-32% 0%-85% 4%-76% 0%-61% 15%-100% 18%-82% 24%-96% 0%-85%

260/0-37%

The Journal of Thoracic and Cardiovascular

1 0 5 8 Kirklin et al.

Surgery

..

11I100

.c C 0

:IE

\

90

CD 80 C

.. ....

:c j

.c

70

Date of Operation

III 50

...

--

40

#.

30

:0 III

10

0 A.

0

C

0

'9••

~ 20

..

.a

Tricuspid Atresia

;;'9.. '#

60

.

. --

-- - - ::- - :- _

~"

0

,

10

5

15

20

Age (Years) at Operation

25

30

Fig. 5. Nomogram of a solution of the multivariate equation (Table V) showing the probability of death within 6 months of the operation (essentially, in the early phase), according to the age of the patient and the year of operation, in patients with main ventricular chamber hypertrophy grade 1 (essentially, patients with tricuspid atresia). The other morphologic variables were entered as "no." The aortic cross-clamp time of 80 minutes was entered, using cold cardioplegic myocardial protection and linear atriotomy, as "no." The dashed lines enclose the 70% confidence limits. The widely spaced dotted line represents an extension of the probability curve beyond the actual experience; the short solid line near the upper end of the extension indicates that the experience in 1980 did include one infant 1 year of age.

Table XI. Deaths after the Fontan operation, accordingto the age of the patient at operation (1975 to April, 1985; n = 102; deaths = 32) Age at operation (yr) :S

1 2 4 10 20

I

Hospital deaths

<

n

1 2 4 10 20

3 6 12 39 28 14

3 3 5 7 2 1

100% 50% 42% 18% 7% 7%

102

21

21%

Total p (logistic)

No.

I

%

<0.0001

I

Total deaths CL

53%-100% 24%-76% 25%-60% 11%-27% 2%-16% 10/0-22% 16%-26%

No.

3 3 7 9 7 3 32

I

% 100% 50% 58% 23% 25% 21% 31%

I

CL

53%-100% 24%-76% 40%-75% 16%-32% 160/0-36% 10%-38% 26%-37%

0.004

Key: CL. 70% confidence limits.

atriotomy was used at the site of the connection (Table VI). An additional multivariate analysis of the correlates with death was made into which the post-repair P RA was entered along with all the variables entered into the multivariate risk factor analysis. Post-repair P RA appeared as a correlate (p = 0.01) with death in the early phase, along with the variables already identified by the multivariate risk factor analysis.

Reoperation. Thirteen patients underwent a cardiac reoperation after the first Fontan operation. Four patients had a Glenn operation on the day of the Fontan procedure because of high post-repair right atrial pressure, and all died. Two patients had their Fontan operation taken down subsequently, because of persistently high post-repair P RA ; in one (who died) a PTFE interposition shunt was substituted, and in the other

Volume 92 Number 6

Fontan operation

December 1986

..

10 5 9

~100

Tricuspid Atresia

C

o 90

:::E

CD 80 C 70

Age (years) at Operation

.

:c j

30 10

60

5 2

1979

1977

1981

Date of Operation

1985

1983

Fig. 6. Nomogram from a solution of the multivariate equation (Table V) showing the relation between data and age at operation and the probability of death within 6 months of operation. The grade of main ventricular chamber hypertrophy was entered as 1 (essentially, tricuspid atresia). Other variables were entered as in Fig. 5, and the presentation is as in Fig. 5.

Table XII. Deaths after the Fontan operation, according to the date of operation (1975 to April. 1985; n = 102; deaths = 32) Year of operation

1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 (3 rno) Total p (logistic)

Hospital deaths n

No. I

4 2 9 8 2 14 18 18 24 2 102

o

I

%

I

Total deaths CL

o

0% 0% 50% 0% 38% 50% 14% 39% 17% 17% 0%

0%-85% 0%-38% 7%-93% 0%-19% 17%-62% 70/0-93% 5%-31% 25%-54% 7%-31% 9%-28% 00/0-61%

21

21%

16%-26%

o 1

o 3 1 2 7

3 4

0.8

No.

1

I

%

1 3 4 1 2 7 6 6 1

100% 0% 50% 33% 50% 50% 14% 39% 33% 25% 50%

32

31%

o

I

CL

15%-100% 00/0-38% 70/0-93% 15%-56% 27%-73% 70/0-93% 5%-31% 250/0-54% 21%-48% 15%-37% 70/0-93%

260/0-37%

0.7

Key: CL, 70% confidence limits. Note: In the years 1984 and 1985, seven patients with tricuspid atresia (ages 6 to 37 years) underwent repair with no hospital deaths and one death 23 months postoperatively (in a patient with dextrocardia, large right ventricle, and two previous shunting procedures).

(who lived) the ventricular septal defect was simply enlarged. Two patients (who lived) underwent closure of an overlooked partial unroofing of the coronary sinus (coronary sinus-left atrial fistula), one later on the day of the Fontan operation and the other 2 months postoperatively. One other patient (who lived) underwent closure of a residual atrial septal defect.

Three patients underwent revision of the Fontan operation 42, 82, and 95 months postoperatively because of obstruction that developed in the pathway to the pulmonary artery. The patient reoperated on at 95 months had thrombosis in the right atrium and conduit, and this recurred and necessitated a second reoperation 14 months later after which she died. The other two

The Journal of Thoracic and Cardiovascular Surgery

Kirklin et al.

10 6 0

.: 50

•

•

45

:c

Main Chamber Hypertrophy Grade

1985

C\I C 40

=

..•

~ ~

35

30

..&

25

-..

0 20

! 15 :.. = 10 :a

•

5

A.

0

.a o

3

._•._•._.c.c

<.<.

40

30

50

60

70

80

-.:.:.:.:.:.:.:.~.-. ... 1

:.:.:.:.-..

90

100

Aortic Cross-clamp Time (min)

110

120

Fig. 7. Nomogram of the relation of the length of the aortic cross-clamptime during cold cardioplegic myocardial protection to probability of death within 2 weeksof operation, depicted for patients with main ventricular chamber hypertrophy grade 1 and those with hypertrophy grade 3. Note the expanded vertical axis. The nomogram is a solution of the multivariate equation (Table V) and the presentation is as in Fig. 5. The year of operation was entered as 1985 and the age as 4 years. The other morphologic variables in the multivariate equation were entered as "no," and "direct atriopulmonary anastomosis with linear atriotorny" as "no." There is no evident effect of cross-clamp times up to 120 minutes in patients with hypertrophy grade 1. The lower 70% confidence limit of the curve for main chamber hypertrophy grade 3 rises by 96 minutes of cross-clamp time to that of the upper confidence limit of a cross-clamptime of 30 minutes; thus there is an evident differencein the probabilityof death within 2 weeks when the cross-clamp time is longer than 96 minutes.

Table XIll. Functional status at the time of last follow-up in patients surviving after the Fontan operation (1975 to April. 1985; n = 102) n

Percent * 79% 14% 4%

IV Unknown

55 10 3 0 2

Dead

32

31%t

Total

102

NYHA Class

I II III

3%

Key: NYHA. New York Heart Association.

* Percent of 70 survivors. tPercent of 102.

patients lived. One other patient (who died) underwent reclosure of the tricuspid valve orifice 15 months after the Fontan operation. In four additional patients, a pericardial window into the pleural space was made late postoperatively because of persistent pericardial effusions. Functional status late postoperatively. Ninety-three

percent of the surviving patients are in NYHA functional class I or II (Table XIII). One patient is playing on a lacrosse team. Discussion Material and methods. Common denominators of success with the Fontan operation are difficult to identify because of the variability of the cardiac morphology that is treated, the different surgical techniques that are used, and the many other factors that seem to relate to the probability of success. As we attempt to understand determinants of success by identifying the risk factors for death and other unfavorable events, the results of multivarite analysis may conflict with those of simple analysis. Whereas the simple analyses, such as contingency tables, are records of what has been achieved, in complex situations that rarely provide a basis for useful inferences, comparisons, and predictions. Properly conducted multivariate analysis can provide this basis, but with a degree of uncertainty that is quantitated by p values and with a dependence upon the skill and integrity of the analyzers. The parametric hazard function and risk factor

Volume 92 Number 6 December 1986

analysis has been used, because the use of hospital mortality to quantify the early risks of cardiac surgical procedures underestimates them. This appears to be particularly true of the Fontan operation, wherein the early phase of hazard for death does not merge with the low constant phase of death until about 6 months postoperatively. Post-repair P RA• The P RA about 2 hours after the repair was used for the analyses in this study. However, the P RA varies considerably during the early postoperative period, a complexity that could not be taken into account in this study. Nonetheless, the probability of survival through the early hazard phase was strongly influenced by this single value of the post-repair P RA • Post-repair P RA is influenced by the post-repair P LA (influenced in tum by the systolic and diastolic function of the main chamber and by stenosis and/or incompetence at the left-sided AV valve); by the resistance to the flow of blood through the lungs and thus by the pulmonary artery pressure; and by any obstruction that may be present in the pathway between right atrium and pulmonary artery. Since some of these can be favorably influenced by interventions, there is an advantage in continuously monitoring pressure in the left atrium, pulmonary artery, and right atrium during the early postoperative period. The post-repair P RA did not explain all deaths in the early phase of risk, as evidenced by the persistence of many other variables in the correlation analysis with death into which P RA was entered. Also, even a P RA of 14 mm Hg about 2 hours after the repair was associated with an overall mortality of 12.5% during the early phase of risk, and a few patients with such atrial pressures had continuing pleural and pericardial collections of fluid and even of chyle. This may be related to the fact that Smith and colleagues!" have demonstrated in dogs that microvascular permeability to macromolecules is increased after cardiopulmonary bypass, a phenomenon that may be related to the complement activation that occurs during cardiopulmonary bypass.14, 15 Once the increased permeability of pore enlargement occurs, this might progress under the stress of even a modest increase of systemic venous pressure until finally chylomicrons (about ten times larger than the largest plasma protein) pass through the microvascular membranes. Several patients in this experience were observed to have simple serous pleural effusions in the first few postoperative days, which slowly evolved into frank chylothoraces. Even though a direct right atrial-pulmonary arterial connection with a linear atriotomy is the only technical variable identified as a risk factor for death in the

Fontan operation

1061

multivariate equation, the effect of other techniques on the post-repair P RA (see Table IV) suggests that they may also have some relation to the probability of survival. It may be suggested that, in regard to achieving a low post-repair P RA, the most desirable techniques are the classical Fontan operation with a nonvalved conduit between right atrium and right ventricle, a direct pulmonary arterial connection to a circular aperture in the superior wall of the right atrium, and a direct right atrial-pulmonary arterial connection with a right atrial flap and a Dacron roof (see Table V). After the Fontan operation, just a 4 or 5 mm Hg increase in pressure in the pressure-generating system for pulmonary blood flow, systemic veins, and right atrium makes a great difference in prognosis, whereas for example after repair of the tetralogy of Fallot a 30 to 40 mm Hg increase in post-repair peak pressure in the pumping chamber, the right ventricle, is required to affect prognosis. Thus, although the absence of a pumping chamber to the pulmonary circulation is compatible with long life, it restricts the adaptability of the circulatory system. The effect of ventricular hypertrophy on survival. Most studies, including the present one, find the risk of the Fontan operation to be less in patients with tricuspid atresia than in those with other cardiac anomalies. Once the degree of hypertrophy of the ventricular main chamber, even crudely estimated as in this study, was introduced into the analysis, some of the other morphologic variables (such as double-inlet ventricle) were no longer risk factors. For example, a morphologic diagnosis other than tricuspid atresia (with which diagnosis 29% of patients had hypertrophy grade 0 or 1) was no longer a risk factor per se compared with tricuspid atresia (with which diagnosis 69% of patients had hypertrophy grade 0 or 1). An increased size (or volume) of the main ventricular chamber was not found to be a risk factor, perhaps because a large ventricle can have excellent function whereas a hypertrophied one generally has impaired diastolic function. Impaired diastolic function imposes a higher left ventricular diastolic pressure, a higher PIA, and thus a higher PRfI: than would otherwise be present. The risk of post-repair death associated with ventricular hypertrophy is incremented by the action of other risk factors, such as long aortic cross-clamp time (see Fig. 7). This may be related to the difficulty in reperfusing the subendocardium when the ventricle is thick-walled. The effect of age on survival. Fontan and Bauder' observed in their early experience that the prevalence of death early after the Fontan operation was higher in young patients. We 16, 17 made the same observation in

1062

Kirklin et al.

our earlier experiences and in the one herein reported. In the current study, however, multivariate analysis indicates that in the current era young age per se is not a risk factor for death. Before it can be accepted that young age is in reality no longer a risk factor for death after the Fontan operation, other studies should confirm the results just described, as only nine patients less than 2 years of age received the Fontan operation in this experience. Although Fontan and Baudet,' using a univariate analysis, found older age at operation to be a risk factor for death, in the present study older age was not found to be a risk factor when other unfavorable variables were accounted for by the multivariate analysis. The effect of date of operation on survival. Since earlier date of operation was a risk factor in this study, there is reason to believe that the probability of survival of patients operated on recently is higher than that of patients operated on in an earlier era; this improvement is particularly evident in patients coming to operation at a young age (interaction of date of operation effect with that of young age-see Figs. 5 and 6). The process by which the risks have become less in recent years is not known with certainty. It may be that cardiac performance is better and PRX lower early postoperatively than in earlier years, in part because of improved myocardial protection and more efficient operations and in part because of better methods for making a completely nonobstructive pathway from the right atrium to the pulmonary artery. Therapeutic inferences. The Fontan operation should be performed as early in life as is compatible with a low mortality. As indicated by Mair and colleagues," delay beyond 4 or 5 years of age seems disadvantageous. Currently, deferral of the Fontan operation until about 2 to 3 years of age, rather than performing it in the first or second year of life, seems prudent even if a preliminary anastomotic operation or pulmonary artery banding are required in the early months of life. Neither has been shown by multivariate analysis of this experience to be risk factors for death early or late after the Fontan repair. Although older age per se is not a risk factor for death after the operation, left-sided AV valve incompetence or ventricular hypertrophy has developed in many older patients; thus they are at high risk of postoperative death. However, patients who have survived to be first seen at an older age have the same chances of survival after the Fontan operation as do younger patients with other characteristics similar to those of the older patients. There is no indication from this study that the specific morphology of the main ventricular chamber affects the

The Journal of Thoracic and Cardiovascular Surgery

probability of survival; thus there is no reason to avoid the Fontan operation in patients with right (rather than left) ventricular main chambers. Left-sided AV valve atresia as a risk factor for postoperative death may be related to the difficulty of diverting the pulmonary venous blood entering the left atrium to the right-sided AV valve without producing obstruction to that valve. The use of a right atrial flap for partitioning the atria, making the left atrium as large as possible and the right one simply a tube conducting caval blood to the atriopulmonary connection, may help in this regard." Although a direct right atrial-pulmonary arterial anastomosis has been used routinely in the most recent part of the experience here reported, it remains controversial in patients with tricuspid atresia as to whether this procedure or a right atrial-right ventricular connection should be made. There is evidence of enlargement and hemodynamic effectiveness of the originally hypoplastic right ventricle, especially when a valve is positioned in the right atrial-right ventricular connection.v" The effect may not be a powerful enough one, however, to outweigh the technical simplicity and absence of foreign material in the direct right atrial-pulmonary arterial communication. There is evidence from this study to support the idea that a large and round right atrial opening should be made for the right atrialpulmonary arterial connection. The finding that even with cold cardioplegic myocardial protection longer aortic cross-clamp times increase the risk of death early after the Fontan operation (as they do after other operations) indicates the advantages of an efficient surgical technique. However, probably up to nearly 100 minutes of cross-clamp time may be used without added risk, even when marked ventricular hypertrophy exists, and longer when ventricular hypertrophy is mild or absent, and this should be ample for nearly all operations of this type. The occurrence of pulmonary and systemic emboli and right atrial thrombi, also reported by others (AC Dobel, unpublished data), suggests the wisdom of routinely administering warfarin for a few weeks to a few months after the Fontan operation. We appreciate the help of Mr. Rob Brown in data collection and analysis and Dr. David Naftel. We also acknowledge the help of Ms. Debbie Nuby in graphics and editing and Ms. Nancy Ferguson in editing.

REFERENCES Fontan F, Mounicot F-B, Baudet E, Simonneau J, Gordo J, Gouffrant J-M: "Correction" de l'atresie tricuspidienne. Rapport de deux cas "corriges" par I'utilisation d'une

Volume 92 Number 6

Fontan operation

December 1986

technique chirurgicale nouvelle. Ann Chir Thorac Cardiavase 10:39-47, 1971 2 Fontan F, Baudet E: Surgical repair of tricuspid atresia. Thorax 26:240-248, 1971 3 Fontan F, Deville C, Quaegebeur J, Ottenkamp J, Sourdille N, Choussat A, Brom GA: Repair of tricuspid atresia in 100 patients. J THORAC CARDIOVASC SURG 85:647-660, 1983 4 Norwood WI, Lang P, Hansen D: Physiologic repair of aortic atresia-hypoplastic left heart syndrome. N Engl J Med 308:23-26, 1983 5 Conti VR, Bertranou E, Blackstone EH, Kirklin JW, Digerness SB: Cold cardioplegia versus hypothermia as myocardial protection. Randomized clinical study. J THORAC CARDIOVASC SURG 76:577-589, 1978 6 Bjork VO, Olin CL, Bjarke BB, Thoren CA: Right atrial-right ventricular anastomosis for correction of tricuspid atresia. J THORAC CARDIOVASC SURG 77:452-458, 1979 7 Stanton RE, Lurie PR, Lindesmith GG, Meyer BW: The Fontan procedure for tricuspid atresia. Circulation 64:(Suppl 2):140-146, 1981 8 Kreutzer GO, Vargas FJ, Schlichter AJ, Laura JP, Suarez JC, Coronel AR, Kreutzer EA: Atriopulmonary anastomosis. J THORAC CARDIOVASC SURG 83:427-436, 1982 9 Doty DB, Marvin WJ Jr, Lauer RM: Modified Fontan procedure. J THORAC CARDIOVASC SURG 81:470-475, 1981 10 Kaplan EL, Meier P: Nonparametric estimation from incomplete observations. J Am Stat Assoc Assn 53:457481, 1958 11 Gehan EA: A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika 52:203223, 1965 12 Blackstone EH, Kirklin JW: Death and other time-related events after valve replacement. Circulation 72:753-767, 1985 13 Blackstone EH, N aftel DC, Turner ME Jr: The decomposition of time-varying hazard into phases each incorporating a separate stream of concomitant information. J Am Stat Assoc (in press) 13a Smith EEJ, Naftel DC, Blackstone EH, Kirklin JW: Microvascular permeability after cardiopulmonary bypass. An experimental study. J THORAC CARDIOVASC SURG (in press) 14 Chenoweth DE, Cooper SW, Hugli TE, Stewart RW, Blackstone EH, Kirklin JW: Complement activation during cardiopulmonary bypass. Evidence for generation of C3a and C5a anaphylatoxins. N Engl J Med 304:497503, 1981 15 Kirklin JK, Westaby S, Blackstone EH, Kirklin JW, Chenowith DE, Pacifico AD: Complement and the damaging effects of cardiopulmonary bypass. J THORAC CARDIOVASC SURG 86:845-857, 1983 16 Cleveland DC, Kirklin JK, Naftel DC, Kirklin JW, Blackstone EH, Pacifico AD, Bargeron LM Jr: Surgical treatment of tricuspid atresia. Ann Thorac Surg 38:447457, 1984

1 06 3

17 Stefanelli G, Kirklin JW, Naftel DC, Blackstone EH, Pacifico AD, Kirklin JK, Soto B, Bargeron LM Jr: Early and intermediate-term (10 year) results of surgery for univentricular atrioventricular connection ("single ventricle"). Am J Cardiol 54:811-321, 1984 18 Mair DD, Rice MJ, Hagler DJ, Puga FJ, McGoon DC, Danielson GK: Outcome of the Fontan procedure in patients with tricuspid atresia. Circulation 72:Suppl 2:8892, 1985 19 Fantidis P, Salvador JC, Ruiz MAF, Amat CG, Martinez VP, Ruiz MC, Diaz FA: A new surgical technique for orthoterminal correction. Experimental development. Ann Thorac Surg 39:450-455, 1985 20 Bull C, de Leval MR, Stark J, Taylor JFN, Macartney FJ, McGoon DC: Use of a subpulmonary ventricular chamber in the Fontan circulation. J THORAC CARDIOVASC SURG 85:21-31, 1983

Appendix A Univariate relationship of P n to the time-related distribution of deaths. The analytical equations described in Appendix B were used, except that only post-repair P RA was entered. Parametric univariate estimate. Early Phase. p = 0.1379, lJ = 0.8662, m = -1, intercept -6.914, PM 0.3511. Constant phase. Intercept -6.330.

Appendix B Structure and risk factors of the time-related distribution of deaths. The parametric method used in the analysis of the event death after the Fontan operation is conceptualized in the cumulative hazard domain ~(t). Cumulative hazard is related to the survivorship function S(t) by the expression S(t) = exp [-~(t)], and to the hazard function >..(t) by its first derivative with respect to time (exp is the base of the natural logarithms). Three additive phases of hazard were considered:

(I) The J.LS are scaling parametric functions and the Gs are parametric functions of follow-up time t. G, represents an early decreasing phase of hazard, G, a constant hazard phase, and G 3 a late rising phase of hazard. In this study, only early and constant hazard phases were identified. The early phase shaping equation is a function of three parameters:

(2)

G,(t) = -mv(plt)V . [I

+ (pit)"

] m I~ I

(3)

G,(t) is the representation of G,(t) in the hazard domain, p represents the half-time for early cumulative hazard, lJ determines the shape of the hazard function in the vicinity of time zero, and m shapes the overall function.

The Journal of Thoracic and Cardiovascular Surgery

1 0 6 4 Kirklin et al.

The scaling parametric function III was made a function of incremental risk factors:

(4) where In is the natural logarithm and ti,'~, = f30

+ f3,x, + f32 X2 + ... + f3kXk

(5)

that is, a linear regression model with f30 as the intercept, f3; the regression coefficient, and X; the value of the risk factor. Equation 4 is the representation of the logistic equation in the cumulative hazard domain. The constant phase shaping function is

Git) = t

(6)

and (7)

The scaling parametric function 112 was made a log-linear function of risk factors: (8)

The form of the regression equation is as in equation 5. All shaping parameters and regression coefficients were estimated simultaneously by the method of maximum likelihood.

Numerical and graphic portrayal of the resulting analyses may be made from the above equations and the parameter estimates given below. To make use of the multivariate regression coefficients, dichotomous variables were entered as a value of 1 when present and 0 when absent. For continuous variables the units of the variables are multiplied by the coefficient in the equation. Parametric estimate. Early phase. Intercept -0.9448, p = 0.1401, v = 0.6309, m =-1. Constant phase. Intercept -6.516. Parametric multivariate estimates. Early phase. p = 0.4561, v = 0.6860, m = -I, intercept 24.16, age (years) at operation (logarithm) -11.83, main chamber hypertrophy grade (0 to 6) 1.511, left-sided AV valve atresia 4.766, left-sided AV valve incompetence 5.112, bifurcation and/or right, left pulmonary arterial stenoses 2.285, date of operation (years since Jan. 1, 1967) -1.852, logarithm of age X date of operation interaction 0.6182, direct atriopulmonary connection via a linear incision 4.189, and aortic cross-clamp time (minutes) with cardioplegia 0.04109. Constant phase. Intercept -8.674, main chamber hypertrophy grade (0-6) 1.195.

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