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Eur J Cardiothorac Surg 2006;30:20-27
© 2006 Elsevier Science NL

Time-related risk of the St. Jude Silzone heart valve

Gary L. Grunkemeier a , Ruyun Jin a , * , KyungAh Im b , Richard Holubkov c , Elizabeth D. Kennard b , Hartzell V. Schaff d

a Medical Data Research Center, Providence Health System, Portland, OR, United States
b Epidemiology Data Coordinating Center, University of Pittsburgh, Pittsburgh, PA, United States
c Department of Pediatrics, School of Medicine, University of Utah, Salt Lake City, UT, United States
d Division of Cardiovascular Surgery, Mayo Clinic, Rochester, MN, United States

Received 2 December 2005; received in revised form 30 March 2006; accepted 3 April 2006.

* Corresponding author. Address: Providence St. Vincent Medical Center, 9205 SW Barnes Road, LL33, Portland, OR 97225, United States. Tel.: +1 503 216 7276; fax: +1 503 216 7274. (Email: Ruyun.Jin{at}providence.org).


   Abstract
Top
 Abstract
1. Introduction
 2. Material and methods
 3. Results
 4. Discussion
 5. Conclusions
 Appendix A
 References
 
Objective: The St. Jude Medical Silzone heart valve had a silver-impregnated sewing ring designed to reduce the incidence of prosthetic valve endocarditis. Recruitment to the randomized AVERT study comparing Silzone valves with non-Silzone Control valves was stopped because of an increased risk of reoperation for paravalvular leak, but patient follow-up continues. Determining the time-related risk profile of the Silzone valve is important for helping physicians manage the approximately 28,000 patients currently alive with a Silzone valve. Methods: Between 1998 and 2000, 403 Silzone and 404 Control patients were enrolled in AVERT. As of July 2005, there were 1819 Silzone and 1842 Control patient-years of follow-up (mean 4.5, median 5.1 years). Analysis emphasized the use and interpretation of hazard functions, since they are more meaningful than event-free percentages to currently surviving patients. To this end, instead of Cox regression, which estimates the hazard ratio, assuming it is constant over time, we employed primarily Aalen additive regression, which measures the hazard difference, and produces a plot of it over time. We assessed the risks of major paravalvular leak, endocarditis, bleeding and thrombo-embolism. Results: The Silzone valve had a higher initial risk of major paravalvular leak than Control in the mitral (p = 0.02) position, but not in the aortic (p = 0.42) position. Analysis of this risk using additive regression, with all valve positions combined, showed that the initial risk due to Silzone lost statistical significance by 2 years and disappeared by 4 years after implant. In the mitral position, the Silzone valve had a higher initial risk of thrombo-embolism plus bleeding than Control; this risk also lost statistical significance by 2 years and subsided to zero by 4 years. The risks for death and endocarditis were similar for Slizone and Control valves. Conclusions: The additional risks of the Silzone valve, compared to Control, diminish over time and disappear by 4 years after implant. The minimum time after implant of the patients currently alive with Silzone is now well beyond 5 years; thus, these current patients now have a risk profile similar to that of patients with a standard St. Jude valve.

Key Words: Silzone heart valve • Paravalvular leak • Thrombo-embolism and bleeding • Hazard function • Additive regression


   1. Introduction
Top
 Abstract
 1. Introduction
2. Material and methods
 3. Results
 4. Discussion
 5. Conclusions
 Appendix A
 References
 
St. Jude Medical (SJM) introduced the Silzone valve, with a silver-coated sewing ring intended to retard prosthetic valve endocarditis, in May 1997. The CE mark was obtained in September 1997 and FDA approval in March 1998. Subsequently, in July 1998, a large (5 years, 4400 patients planned) randomized trial of Silzone valves versus valves with conventional sewing rings (Control) was begun, called the Artificial Valve Endocarditis Reduction Trial (AVERT), in Europe (7 centers) and North America (12 centers) to evaluate the effectiveness of the Silzone valve in reducing endocarditis [1]. SJM stopped enrollment into the AVERT trial and voluntarily recalled all Silzone valves in January 2000, after only 807 patients had been enrolled, because of a significantly higher rate of explantation for paravalvular leak in the Silzone arm of the study [2]. By that time, approximately 36,000 patients worldwide had received Silzone valves. SJM has continued the follow-up, in fact, intensifying it with an additional echocardiography protocol, to determine the extent and time-relatedness of leak [3]. The important question at this time is, what is the current and future risk for the approximately 28,000 remaining Silzone patients, all of whom are now more than 5 years after implant?


   2. Material and methods
Top
 Abstract
 1. Introduction
 2. Material and methods
3. Results
 4. Discussion
 5. Conclusions
 Appendix A
 References
 
2.1 Clinical material
Between July 1998 and January 2000, 403 patients were randomized to Silzone valves and 404 to Control valves; 398 (98.6%) of the latter were SJM valves with conventional (non-Silzone) sewing rings. We compared the two groups according to treatment (valve) received, rather than intention-to-treat; thus, patients receiving at least one Silzone valve are in the Silzone group for this report. The six non-SJM valves were included in the Control group, since they were a part of the original randomized trial and they had conventional (i.e., non-Silzone) sewing rings. These six valves had no adverse events, so including them does not favor the Silzone group.

Eight patients crossed over in each direction, so there were still 403 Silzone and 404 Control patients. Of the complications evaluated in this study, there were three (one embolism, two bleeds) in patients who were randomized to Silzone but received a Control valve, and one (major leak) in a patient who was randomized to a Control valve but received a Silzone prosthesis. Thus, there was a net loss of two complications in the Silzone group by comparing implanted rather than randomized groups. For the analyses, we combined the mitral (n = 258) and double (n = 75) valve replacement patients into a single group (n = 333). The Silzone and Control groups were similar in each position with regard to preoperative and operative characteristics (Table 1 ). Data on anticoagulation adequacy was also available: of 2506 follow-up encounters for Silzone patients, 1889 International Normalized Ratio (INR) readings were available, and of 2575 follow-up encounters for Control patients, 1895 INR readings were available.


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  		Table 1. Clinical material
 
The complications we considered are major paravalvular leak, thrombo-embolism, thrombosis, bleeding and endocarditis. Since there were only three valve thromboses, all in mitral Silzone valves (one in a mitral valve patient, two in double valve patients), we combined thrombo-embolism and thrombosis (designated as thrombo-embolism). We also created a composite endpoint for analyzing the mitral valve patients by combining thrombosis, embolism and bleeding (TEB). Major paravalvular leak was defined as any episode of paravalvular leak not associated with endocarditis and for which a reoperation or reintervention for repair or explant was performed or planned, or after which the patient died. Bleeding events occurring within 48 h of the start of surgery (12 Silzone, 21 Control) were not considered, since they were more likely due to the procedure than to the prosthesis. All other definitions were according to the STS/AATS guidelines for reporting [4].

Adjudication of thrombo-embolism and valve thrombosis was done by a nine-member Adjudication Committee, which was blinded to the type of valve. Adjudication reduced the numbers of thrombo-embolism from 78 to 56 in Silzone (28% reduction) and from 54 to 42 in Control (22% reduction). Adjudication reduced the numbers of valve thromboses from 5 to 3 in Silzone; there were no valve thromboses for Control. Adjudication of endocarditis, by a single individual who was blinded to the type of valve, reduced the numbers of events from 14 to 7 in Silzone (50% reduction) and from 20 to 4 in Control (80% reduction). Adjudication of two endocarditis events was not completed (one Silzone, one Control) and these were regarded as true. When parts of dates were missing, we imputed 6 for the missing month and 15 for the missing day, unless other information contravened. One bleeding event was missing a date, and the date of last follow-up was used.

As of the data freeze on July 15 2005, Silzone and Control patients had been followed for a mean (median) of 4.5 (5.1) years and a total of 1819 and 1842 patient-years, respectively. A definition of perfect follow-up completeness would be that the status of every patient was determined on the day of the data freeze. By this extreme definition, the ratio of documented follow-up years to perfect follow-up years is 84%. The main reason for computing this stringent metric was to compare follow-up completeness among these subgroups: Silzone 85% and Control 83%; North America 86% and Europe 82%.

2.2 Statistical methods
The most common method of comparing and displaying time-related events is by Kaplan–Meier event-free percentages [5]. But the cumulative hazard function, or better yet its derivative (slope), the instantaneous hazard function, is more meaningful than event-free percentages to currently surviving patients. Thus, we base these analyses on the cumulative hazard and (instantaneous) hazard functions.

The most common method of assessing risk factors for time-related events is Cox proportional hazards regression [6]. Cox regression estimates the relative risk (hazard ratio) for each risk factor, assuming that the (proportional) influence of a risk factor is constant over time. An alternative but less widely used method is the Aalen linear or additive hazards regression [7,8]. Instead of producing regression coefficients (which are equal to the logarithm of the hazard ratios and assumed to be constant over follow-up) as in the Cox model, the Aalen method produces regression functions that may vary over time—and are closely tied to cumulative hazard functions. Thus, unlike the Cox model, additive regression can naturally model the influence of a risk factor that decreases or even disappears over time.

The Aalen regression program returns the integrated or cumulative regression function. When there is a single dichotomous risk factor, such as Silzone, the cumulative regression function is equal to the difference between the two cumulative hazard functions. Of more interest, especially to current patients, is the (instantaneous) regression function, which in this case is the difference of the two (instantaneous) hazard functions. One way to derive the regression function is to use parametric modeling, such as a Weibull distribution or a Gompertz distribution, to smooth the jagged cumulative regression functions and then take the mathematical derivative (slope) of the resulting smooth curves to produce the regression functions. Aalen regression functions were used to measure the additive risk (hazard) of events over time due to Silzone. More details are provided in Appendix A. The book by Hosmer and Lemeshow contains a good discussion of the Aalen regression model [9].

Details of the statistical methods can be found in Appendix A.


   3. Results
Top
 Abstract
 1. Introduction
 2. Material and methods
 3. Results
4. Discussion
 5. Conclusions
 Appendix A
 References
 
The 5-year Kaplan–Meier event-free percentages are given in Table 2 for death and other events. Cumulative hazard functions were used to compare Silzone with Control valves in the aortic (Fig. 1 ) and mitral (Fig. 2 ) positions.


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  		Table 2. Kaplan–Meier event-free percentages at 5 years
 

Figure 1
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  		Fig. 1. Cumulative hazard curves for the 474 aortic valve patients: (A) major paravalvular leak, (B) prosthetic valve endocarditis, (C) major bleeding event, and (D) thrombo-embolism (thrombosis plus embolism).

 

Figure 2
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  		Fig. 2. Cumulative hazard curves for the 333 mitral/double valve patients: (A) major paravalvular leak, (B) prosthetic valve endocarditis, (C) major bleeding event, and (D) thrombo-embolism (thrombosis plus embolism).

 
3.1 Major paravalvular leak
The cumulative hazard for major leak was higher in both aortic (Fig. 1A) and mitral (Fig. 2A) positions for Silzone patients. With both valve position groups combined, Aalen regression found Silzone significant (p = 0.020) and position not significant (p = 0.21), so the valve positions were combined for the purpose of comparing Silzone with Control.

The number of patients at risk in each valve group at each follow-up time are shown by the thin, somewhat smooth curves in Fig. 3 , indexed by the left-hand vertical axis. The areas under these curves are the total patient-years of follow-up. The cumulative numbers of major paravalvular leaks over time are shown by the thicker step functions, indexed by the scale on the right-hand vertical axis (expanded x10 compared to the left-hand axis). Also shown in this figure are the ‘linearized’ rates of major leak for each valve group, calculated separately for the time intervals before and after 2 years. After 2 years, the rates for Silzone and Control were the same (0.003 or 0.3% per year).


Figure 3
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  		Fig. 3. Time-relationship of major leak to the number of patients at risk. The thinner curves indicate the number of patients (indexed to the left vertical axis) with follow-up to each postoperative time. The area beneath these curves is the total follow-up years. The thicker step functions indicate the cumulative number of major leaks (indexed to the right vertical axis) at each postoperative time. Note that the right vertical axis scale is expanded x10 compared to the left vertical axis scale. A simple comparison of the risks over time, by computing the ‘linearized’ rates for each group before and after 2 years, is shown by the decimal numbers. After 2 years, the linearized rates are the same (0.003 = 0.3% per year).

 
The cumulative hazard functions for Silzone and Control are shown in Fig. 4A, with the parametric fits from the Gompertz distribution superimposed. The significance of the Silzone effect in the Gompertz regression was p = 0.032 (significance of the relative risk for Silzone was p = 0.029 using Cox regression). The cumulative regression function for Silzone from the additive hazard model for major leak is shown in Fig. 4B, along with its point-wise 95% confidence limits. The significance of this regression function was p = 0.022 using Aalen regression. This regression function is the difference between the cumulative hazard functions for the Silzone and Control groups (the step functions in Fig. 4A). Thus, superimposed on this is the difference of the two Gompertz (smooth) curves in Fig. 4A. The derivative (slope) of this smooth curve is the regression function itself, that is, the additive risk due to Silzone. It is shown in Fig. 4C, along with its point-wise 95% confidence limits. The regression function, which is the incremental hazard due to Silzone, becomes nonsignificant by about 2 years (when the lower 95% confidence limit crosses zero), and is estimated to be essentially zero by about 4 years.


Figure 4
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  		Fig. 4. Three depictions of the difference in major paravalvular leak between Silzone and Control valves. (A) Cumulative hazard functions for Silzone and Control valves (step functions) with smooth parametric fits from the Gompertz distribution. (B) Cumulative regression function from the Aalen model, with 95% confidence limits (step functions). This is the difference between the two step-functions in panel A, and the smooth fit is the difference between the smooth curves in panel A. (C) Aalen model regression function, produced by taking the derivative (slope) of the smooth fit to the cumulative regression function in panel B, with 95% point-wise confidence limits. This equals the difference between the instantaneous hazard functions for Silzone and Control groups, and represents the additive risk of major leak due to Silzone.

 
3.2 Endocarditis
In the aortic position, the initial risk of endocarditis was somewhat higher in the first year for Silzone than for Control, but the risks were similar after that (Fig. 1B). In the mitral position, the risks of endocarditis were similar (Fig. 2B).

3.3 Thrombo-embolism and bleeding
3.3.1 Aortic valves
In the aortic position, the risks of bleeding (Fig. 1C) and thrombo-embolism (Fig. 1D) were virtually identical. The level of anticoagulation was also similar. The mean (standard deviation [SD]) of INR was 2.84 (0.84) for Silzone, based on 1184 INR readings, and 2.81 (0.73) for Control, based on 1104 INR readings (p = 0.72, Mann–Whitney test).

3.3.2 Mitral/double valves
In the mitral/double positions, the initial risks of bleeding (Fig. 2C) and thrombo-embolism (Fig. 2D) were higher for Silzone than for Control. We computed the composite TEB (thrombosis/embolism/bleeding) endpoint and used the Aalen additive regression to quantitate the difference in risk over time (Fig. 5 ).


Figure 5
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  		Fig. 5. Three depictions of the difference in TEB (thrombosis/embolism/bleeding) between mitral/double Silzone and Control valves. (A) Cumulative hazard functions for Silzone and Control valves (step functions) with smooth parametric fits from the Gompertz distribution. (B) Cumulative regression function from the Aalen model, with 95% confidence limits (step functions). This is the difference between the two step-functions in panel A, and the smooth fit is the difference between the smooth curves in panel A. (C) Aalen model regression function, produced by taking the derivative (slope) of the smooth fit to the cumulative regression function in panel B, with 95% point-wise confidence limits. This equals the difference between the instantaneous hazard functions for Silzone and Control groups, and represents the additive risk of TEB due to Silzone.

 
The cumulative hazard functions for TEB are shown in Fig. 5A, along with parametric fits from the Gompertz distribution. The significance of the Silzone effect in the Gompertz regression was p = 0.020 (significance of the relative risk for Silzone was p = 0.026 using Cox regression). The cumulative regression function for Silzone from the additive hazard model for TEB is shown in Fig. 5B, along with its point-wise 95% confidence limits. The significance of this regression function was p = 0.027 using Aalen regression. Superimposed on this is the difference of the Gompertz curves for the two study arms (from Fig. 5A). The regression function itself (derivative of the smooth curve in Fig. 5B) is shown in Fig. 5C, along with its point-wise 95% confidence limits. The regression function, which is the incremental hazard due to Silzone, becomes nonsignificant by 2 years, and essentially zero by 4 years.

Overall, the mean INR was somewhat higher for Silzone (2.88, SD = 0.79, based on n = 705 INR readings) than for Control (2.79, SD = 0.77, n = 791) patients (p = 0.011, Mann–Whitney test). For the patients who had a thrombo-embolic event, the mean INR was similar for Silzone (2.87, SD = 0.86, n = 100) and Control (2.83, SD = 0.94, n = 43) patients (p = 0.45), and for the patients who had a bleeding event the mean INR was higher in the Silzone (2.84, SD = 0.67, n = 88) than in the Control (2.40, SD = 0.56, n = 58) patients (p < 0.001).


   4. Discussion
Top
 Abstract
 1. Introduction
 2. Material and methods
 3. Results
 4. Discussion
5. Conclusions
 Appendix A
 References
 
For this analysis, we used the Aalen additive hazard regression rather than the more popular Cox proportional hazard regression. Since the additive model does not require the assumption of proportional hazards, it is more natural for dealing with hazard ratios that change over time, and risk factors that even disappear, as does the Silzone risk in this study. The assessments of the overall significance of Silzone as a risk factor for paravalvular leak and for mitral TEB were highly concordant for the Aalen, Gompertz and Cox regression approaches applied to the AVERT data.

The Cox model has been shown to be robust to violations of the proportional hazards assumption and in fact a test of the proportional hazards assumption for major leak based on the Schoenfeld residuals in this study was not violated (p = 0.37). If the proportional hazards assumption is violated, time-varying covariates can be used to transform risk factors, but this is more difficult. The Aalen regression is easier to implement and more natural in this situation, and also provides an estimate of the time-varying hazard, called the regression function (Figs. 4C and 5C).

The event of primary concern with the Silzone valve, for which the AVERT study was stopped [2], and for which continued intensive study is ongoing [3], is major paravalvular leak. In the present study, the incidence of major leak was higher for Silzone initially, but the risk among Silzone valve recipients decreased to that of the Control group by 4 years after operation (Fig. 4C).

It has been stated that, ‘It is possible that the same mechanism of impaired healing of the sewing ring that leads to PV leakage also leads to increased exposure of thrombo-embogenic surface in some patients.’ [2] A significant increase in early thrombo-embolic events (but not leak) with mitral Silzone valves compared to a noncontemporary group of conventional SJM valves has in fact been reported [10–12]. Since thrombo-embolism and thrombosis are part of the same complex, and the risk of bleeding is increased by the medical treatment of this complex, several authors have advocated combining these events into a single variable [13–15]. Thus, even though its individual components were not statistically significant (Fig. 2), we also computed the composite endpoint of TEB, and found a significant effect due to Silzone in the mitral position only, which also declined to zero by 4 years (Fig. 5C).

These two patient groups were randomized, so the comparisons herein are supported by a good study design. However, the randomization pertained to preoperative variables only. A possible difference between the groups could be in postoperative management, namely anticoagulant therapy. It is possible that some Silzone patients began receiving more aggressive anticoagulant treatment following the 1999 reports of a higher stroke risk in mitral patients [10,11]. We did not find a temporal rise in INR, but the average INR over time was slightly higher for the mitral Silzone patients, and significantly so for the subset of patients who had bleeding events. However, the effect of slightly increased INR should contribute offsetting effects to the risks of bleeding and thrombo-embolic events, so that the net result would be a neutral effect on the risk of the TEB complex.


   5. Conclusions
Top
 Abstract
 1. Introduction
 2. Material and methods
 3. Results
 4. Discussion
 5. Conclusions
Appendix A
 References
 
The excess risks of major paravalvular leak and of TEB in the mitral position due to Silzone diminish over time and disappear by 4 years after implant. Based on the number of Silzone valves currently active in this study (78%, Fig. 6 ), we estimate that fewer than 28,000 of the 36,000 patients who received Silzone valves are still alive with their Silzone valve. Since the implantation of Silzone valves was discontinued in January 2000, the minimum time after implant of these patients is now well beyond 5 years, and our results indicate that they now have a risk profile similar to that of patients with a standard SJM valve.


Figure 6
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  		Fig. 6. Histograms of most recent follow-up by patient status and time post implantation.

 

   Appendix A
Top
 Abstract
 1. Introduction
 2. Material and methods
 3. Results
 4. Discussion
 5. Conclusions
 Appendix A
References
 
Statistical details

Several interrelated functions are used to characterize survival data. The most familiar is the survival or event-free curve, usually estimated by the Kaplan–Meier method [5]. The hazard function describes the instantaneous risk that currently faces an event-free patient, and could be considered the most important of these functions. For technical reasons, the hazard function is difficult to estimate directly, without making parametric (smoothing) assumptions. However, its integral, the cumulative hazard function is easy to produce, either by taking the negative logarithm of the Kaplan–Meier estimate, or by computing directly from the two functions (processes) given in Fig. 3. The thinner curves in Fig. 3 plot the number of patients still at risk and are called the at-risk processes. The thicker curves are called the counting processes and rise one unit for each event (leak). The cumulative hazard functions have a roughly similar shape but for each event they rise a much smaller amount, equal to the inverse of the value of the at-risk process at that point.

Several cumulative hazard functions are presented in Figs. 1 and 2. The slope of a cumulative hazard function is its most important feature, since it equals the hazard at each time. The steeper the slope of the cumulative hazard, the higher the risk facing the patient at that time. If the slope is zero, i.e., the curve is horizontal, the hazard is zero. When two cumulative hazard curves are parallel, the hazard is the same for those two groups at that time. The vertical axis is usually labeled as a dimensionless (raw) number, but multiplying by 100 converts it to percentage (although it can exceed 100%). Its slope (the hazard) is then in units of percent per year, for easy comparison with the usual ‘linearized’ event rates.

A.1 Nonparametric survival regression
Cox regression is widely used to assess the influence of a preoperative risk factor on death and other postoperative events [6]. The hazard function for an individual with a certain risk factor is the product of a baseline hazard function and a constant (over time) hazard ratio associated with that risk factor (equal to its exponentiated regression coefficient). The assumption is that the hazard functions for those with and without the risk factor are proportional throughout postoperative time (though they may be of arbitrary shape).

Aalen [7,8] introduced an alternative, additive (or linear) regression model for the hazard function. Here, the hazard for an individual with a certain risk factor is the sum of a baseline hazard function and a regression function that can vary over time. This model does not require the hazard functions for those with and without the risk factor to be proportional, and is ideally suited to a risk factor whose influence changes over time, increasing, decreasing or even disappearing or reversing. The regression function could be thought of as the additional hazard due to that risk factor. In our use of this method, the hazard for a Silzone valve is equal to the underlying hazard of a Control valve plus an additional hazard due to Silzone.

The Aalen method is based on partitioning the risk via decomposition of the cumulative hazard function. When there is a single dichotomous risk factor, e.g., Silzone, the cumulative regression function for that risk factor (Figs. 4B and 5B) is simply the difference between the cumulative hazard functions with and without the risk factor. But the primary interest is in the regression function itself (Figs. 4C and 5C), since it has a direct and intuitive interpretation as the additional risk at each point in time. The regression function is the slope (derivative) of the cumulative regression function; but since the latter is a step function, some smoothing must be done to obtain a continuous regression function.

A.2 Parametric survival regression
The usual (nonparametric) way to smooth a cumulative hazard function or cumulative regression function is to use a kernel density smoothing procedure, which yields a function somewhat akin to a histogram. But this is difficult to do without a large number of events, the result depends on the bandwidth of the kernel (like width of the histogram bins) and the amount of smoothing, and getting confidence intervals is problematic. A smooth approximation can also be obtained by finding a mathematical equation that describes the cumulative regression function; taking its mathematical derivative then yields the regression function itself. Since the cumulative regression function for Silzone is the difference between of cumulative hazard functions for Silzone and Control, we proceeded by: (1) fitting the survival data to a known family of survival functions; (2) getting the equations for the cumulative hazard functions from the best-fitting member of that family (Figs. 4A and 5A); (3) subtracting these equations for Silzone and Control to get the equation for the cumulative regression function (Figs. 4B and 5B); and (4) taking its mathematical derivative to get the regression function (Figs. 4C and 5C). The survival functions considered in step (1) were the six families of distributions implemented in Stata's streg function. The 95% confidence limits for the regression functions were computed by the delta method (using function nlcom in Stata).

A.3 Software
Statistical analyses and graphics were done using Stata 9.1 (Stata Corporation, College Station, TX, USA) and the open-source program R 2.2.0 (R Foundation for Statistical Computing, Vienna, Austria; http://www.R-project.org). The Aalen linear (additive) hazards regression is implemented in the Stata ado file stlh, available at http://www.stata-journal.com/software/sj2-4/st0024/stlh.ado. This program provides graphical output of the cumulative regression functions, their 95% point-wise confidence intervals, and four different statistical tests of the covariate effects based on different weightings (we used weights equal to the size of the risk set) [16]. The Aalen regression procedure is also implemented in the R package addreg, available at http://www.med.uio.no/imb/stat/addreg, and in the SAS macro additive, available at http://www.biostat.mcw.edu/software/addmacro.txt.


   Acknowledgments
 
Data collection and validation for the AVERT study was supported by St. Jude Medical. This research project was supported by Providence Health System.


   References
Top
 Abstract
 1. Introduction
 2. Material and methods
 3. Results
 4. Discussion
 5. Conclusions
 Appendix A
 References
 

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