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Table 2.

Regression Models Assessing the Relationship Between Components of the CHADSVASc Score and the Hazard of Hospitalization for Stroke

View this table:
Table 3.

Regression Models Assessing the Relationship Between Components of the CHADSVASc Score Plus Comorbidities of Interest With the Hazard of Hospitalization for Stroke

A comparison of the calibration of the Cox and Fine-Gray regression models utilizing the variables constituting the CHA 2 DS 2 VASc score is illustrated in Figure 4 . The Cox regression model consistently overpredicted the incidence of stroke across all ranges of predicted risk, in contrast to the Fine-Gray model, which displayed better calibration.

Figure 4.

Calibration of models to predict stroke risk using Fine-Gray and Cox regression models. Predicted and observed incidence of stroke at 5 y by decile of predicted risk from Fine-Gray model ( A ) and Cox model ( B ).


We used a population-based cohort of elderly patients with AF to illustrate the impact of competing risks on the estimated incidence of stroke. The incidence of the competing risk, death without stroke, was 9-fold higher than that of stroke. Accordingly, the incidence of stroke was consistently overpredicted by the Kaplan–Meier complement. In the overall cohort, the incidence of stroke was estimated at 7.5% (95% CI, 7.4%–7.7%) by the Kaplan–Meier method, compared with an estimated incidence of 5.4% (95% CI, 5.3%–5.5%) using the CIF. This translates to a 39% relative overestimation of stroke incidence by the Kaplan–Meier method. The degree of bias increased in strata with a higher incidence of the competing risk. Patients with non-CHADSVASc comorbidity had a significantly lower 5-year incidence of stroke than their healthier counterparts in univariable comparisons (4.6%; 95% CI, 4.4%–4.8%; versus 5.9%; 95% CI, 5.7%–6.0%). However, the Kaplan–Meier method led to a different conclusion, predicting a comparable 5-year stroke incidence among patients with non-CHADSVASc comorbidity (7.7%; 95% CI, 7.4%–8.0%) relative to those without one (7.5%; 95% CI, 7.3%–7.7%). Thus, the Kaplan–Meier method resulted in an estimated stroke incidence that was two-thirds higher than the CIF estimate among patients with comorbidities.

Interestingly, the upwards bias in stroke incidence was greater in patients with higher CHADSVASc scores. This is because higher CHADSVASc scores were associated with an increased incidence of competing risks. Accordingly, the relative overestimation in 5-year stroke incidence was 19% among patients with a score of 1, and 40% in patients with scores ≥2. Thus, the use of suboptimal statistical methods can lead to risk overestimation that is amplified among patients for whom anticoagulation would typically be recommended. This could lead to a falsely inflated expectation of benefit by biasing the risk-benefit assessment in favor of anticoagulation. Furthermore, the calibration of the Fine-Gray model was substantially better than that of the Cox model, which systematically overpredicted stroke risk in the validation cohort. This is an important limitation, particularly for diseases like AF which mostly affect older patients with a large burden of comorbidity.

An important observation is that the observed incidence of stroke in our cohort is lower than anticipated from the seminal studies reporting on the heightened risk of stroke in patients with AF. The 5-year cumulative incidence of stroke was only 5.4% (95% CI, 5.3%–5.5%), despite 47% of the cohort not filling a single prescription for warfarin in the 90 days after the index date. Based on a median CHADS score of 2 and CHADSVASc score of 4, the expected stroke incidence is 4% per year. This is consistent with other reports on the decreasing risk of stroke associated with AF over the past 20 years, even among nonanticoagulated patients.

The decreasing stroke incidence underscores the need to reappraise which patients are expected to benefit from long-term anticoagulation for primary stroke prevention because the net benefit of anticoagulation for stroke prophylaxis was demonstrated in patients with higher event rates. A meta-analysis of randomized controlled trials of warfarin in patients with AF reported 282 strokes over 8946 patient-years (≈3.1 per 100 patient-years) in antiplatelet-treated patients. A more recent meta-analysis demonstrating the benefit of direct oral anticoagulants relative to warfarin reported a stroke incidence of 3.8% over ≈2 years’ median follow-up in warfarin-treated patients. Anticoagulation is currently recommended for patients with a CHADSVASc score of ≥2, which has been reported to be associated with a 2.2% annual stroke risk. The risk-benefit balance of anticoagulation for primary prevention of stroke in patients with AF becomes more ambiguous if the absolute stroke risk is lower. Accordingly, treatment decisions about stroke prophylaxis in elderly patients today may be better aided with risk estimates that more accurately reflect contemporary absolute risk. This would require consideration of the impact of competing risks, as illustrated with our data and that of others. Competing risks would also be a relevant consideration when predicting the risk of bleeding associated with anticoagulation.

Comparisons of the Cox and Fine-Gray regression models also provide interesting insights into how the impact of the stroke risk factors should be perceived. We should emphasize, however, that the magnitude of the hazard ratio from the cause-specific hazard model (ie, the Cox model) is not directly comparable to the magnitude of the effect of the covariate on the risk of stroke derived from the Fine-Gray model. Comparison of the 2 regression methods suggests that passive comorbidities which do not substantially affect stroke rate can decrease observed stroke incidence. This would be mediated by their association with a higher competing risk of death without stroke. Thus, it may be useful to account for comorbidities which may not directly affect the rate of the cardiovascular outcome of interest, but which could substantially increase the risk of death, thus reducing the observed incidence of the event of interest.

Our analysis has several limitations. Our study was not designed to generate a prediction model for stroke after AF. The outcome definition was limited to hospitalizations for stroke, and we did not identify strokes that led to death before hospital presentation. Moreover, our inclusion criteria stipulated age ≥66 years and a hospitalization event to select patients with a large burden of comorbidities and a higher risk of nonstroke death. This was done to illustrate the concepts of competing risks in a clinically meaningful manner. However, this means that our observations should not be extrapolated to younger, healthier patients with a lower risk of death.


The incidence of death without stroke was 9-fold higher than that of stroke in this cohort of patient with AF. Accordingly, there is the potential for substantial bias if competing risks are ignored when estimating the incidence and risk of stroke. Our analyses illustrate that the Kaplan–Meier survival functions and Cox regression models overestimate risk if used in a setting in which competing risks are incorrectly assumed to be absent. Where this assumption cannot be verified, one should account for competing risks in the manner most appropriate for the purpose of the analysis. The concepts we present here likely apply to other settings where the patient population is elderly or carries a high burden of comorbidity.

Sources of Funding

Funding for this project was provided by the Heart and Stroke Foundation of Canada. This study was supported by the Institute for Clinical Evaluative Sciences (ICES), which is funded by an annual grant from the Ontario Ministry of Health and Long-Term Care (MOHLTC). Dr Abdel-Qadir was supported by a Fellowship from the Canadian Institutes of Health Research and salary support from the University of Toronto Clinician-Scientist Training Program. Dr Lee is supported by a midcareer research award from the Heart and Stroke Foundation and the Ted Rogers Chair in Heart Function Outcomes. Dr Austin is supported in part by a Career Investigator Award from the Heart and Stroke Foundation. Dr Tu was supported by a Tier 1 Canada Research Chair in Health Services Research and an Eaton Scholar award. The opinions, results, and conclusions reported in this article are those of the authors and are independent from the funding sources. No endorsement by ICES or the Ontario MOHLTC is intended or should be inferred.




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Small Business Economics

, Volume 33, Issue2 , pp 141–149 | Cite as

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Policy makers often think that creating more start-up companies will transform depressed economic regions, generate innovation, and create jobs. This belief is flawed because the typical start-up is not innovative, creates few jobs, and generates little wealth. Getting economic growth and jobs creation from entrepreneurs is not a numbers game. It is about encouraging the formation of high quality, high growth companies. Policy makers should stop subsidizing the formation of the typical start-up and focus on the subset of businesses with growth potential. While government officials will not be able to “pick winners,” they can identify start-ups with a low probability of generating jobs and enhancing economic growth. By eliminating incentives to create these low probability companies, policy makers can improve the average performance of new businesses.


Economic growth Entrepreneurship Entrepreneurship Award Winner Job creation New firm formation

Scott A. Shane is the 2009 Winner of the . This essay is the Prize Lecture given upon receipt of the Award on 12May 2009 in Stockholm, Sweden. More information about the Prize and previous Winners is available at This lecture draws on Scott Shane’s new book: (Yale University Press, 2008).

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Policy makers believe a dangerous myth. They think that start-up companies are a magic bullet that will transform depressed economic regions, generate innovation, create jobs, and conduct all sorts of other economic wizardry. Leading economist Edward Lazear ( 2005 , p. 649) has even claimed that “the entrepreneur is the single most important player in a modern economy.” So they provide people with transfer payments, loans, subsidies, regulatory exemptions, and tax benefits if they start businesses. Any businesses.

Take, for example, the remarks of former U.S. President George W. Bush who said, in a speech to the Small Business Week Conference (Bush 2006 ): “Small businesses are vital for our workers…. That’s why it makes sense to have the small business at the cornerstone of a pro-growth economic policy…. The Small Business Administration is working hard to make it easier for people to start up companies. We understand that sometimes people have got a good idea, but they’re not sure how to get something started…. And so we’ve doubled the number of small business loans out of the SBA since I came to office.”

Or take a speech by British Prime Minister Gordon Brown to the International Monetary Fund (Brown 1998): “Britain cannot be properly equipped while we have productivity levels 40 per cent below America, and 20 per cent below France and Germany, so over the next year, in partnership with industry, we intend to examine and begin the task of dismantling every barrier to productivity, prosperity and employment creation. That will require policies to promote entrepreneurship and small business development.”

This is bad public policy. Encouraging more and more people to start businesses won’t enhance economic growth or create a lot of jobs because start-ups, in general, aren’t the source of our economic vitality or job creation.

You might be startled by this position, going, as it does, against the grain of most popular arguments. It might even seem illogical to you. After all, companies like SAP in computer software, Google in Internet search, and Genentech in biotechnology, are all examples of wildly successful start-ups. And the list need not stop there. EasyJet and Wal-Mart were also start-up companies not too long ago. So, surely, these companies must have contributed to economic growth?

Yes, of course, they have. But, those companies are not typical start-ups. In the United States, the typical start-up is a company capitalized with about $25,000 of the founder’s savings that operates in retail or personal services (Hurst and Lusardi Roger Vivier Gommette Turtle ballerinas ZLTMs
). Odds are pretty good that it is a home-based business (Pratt 1999 ), and the founder aspires to generate around $100,000 in revenue in five years (Haynes LE SILLA Embellished denim platform sneakers rHvuXlk
). The vast majority of people founding new businesses aren’t entrepreneurs in the sense of people building companies that grow, generating both jobs and wealth. Rather, they are founding wage-substitution businesses that have more in common with self-employment than with the creation of high growth companies. 1

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