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Table 3

Illustrative example to show differences between three statistical approaches comparing the effect of treatments on functional outcomes “truncated due to death.” We consider the population of patients eligible for the ABC trial and for each patient, generate the potential outcome under control by mimicking characteristics of the control group from the ABC trial such that 62% of the patients receiving the control would experience death by 12 months, the mean cognition among survivors is 42, and based on the composite outcome, as described in the manuscript, 50% of the patients will survive past 72 days (25% of patients will survive to 12 months with cognition score >39). Assuming the monotonicity assumption holds, potential outcomes under intervention were derived based on the effect of the intervention on mortality and the functional outcome among always survivors (for a total of six scenarios). For each scenario, the true population value of the treatment effect defined by the survivors analysis, the SACE and composite endpoint approach are displayed

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When the intervention has no effect on mortality (scenarios 1 and 2), there are no mortality benefiters, only always survivors (38%) and always diers (62%) ( table 3 ). In this case, the SACE approach and survivors analysis produce the same results regardless of whether there is no effect (scenario 1) or a positive effect of the intervention on cognition (scenario 2). Further, when the intervention has no effect on mortality, the SACE can be estimated directly from trial data without making any additional assumptions. The composite endpoint approach identifies that there is no difference in the distribution of the potential composite outcomes in scenario 1 (rank statistic=0) and the shift in the distribution of cognition scores among always survivors in scenario 2 (rank statistic >0).

In scenarios 3 through 6, the intervention has a positive effect on mortality, which results in no change to the proportion of always survivors (38%) but creates a stratum of mortality benefiters (21%, table 3 ). When the intervention has a positive effect on mortality, the SACE approach and survivors analysis will not necessarily provide the same results; whether or not these approaches are equivalent depends on characteristics of the mortality benefiters. In scenarios 3 and 4, the effect of the intervention is to promote survival in more robust patients with high cognition such that the 12 month cognition scores among the always survivors and mortality benefiters under intervention have the same distribution. In these scenarios, the survivors analysis and the SACE provide the same results ( table 3 ). Alternatively, in scenarios 5 and 6, the effect of the intervention is to sustain less healthy individuals, creating a heterogeneous group of survivors (hearty always survivors and frail mortality benefiters). In these scenarios, the survivors analysis underestimates the SACE regardless of whether or not the intervention improves cognition among always survivors (eg, scenario 5: survivors analysis −7 v SACE 0) and use of the survivors analysis could lead to erroneous conclusions about the efficacy of the intervention on cognition. In scenarios 3 through 6, the composite endpoint approach identifies the shift in the distribution driven by the effect of the intervention on mortality and, in scenarios 4 and 6, on cognition.

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Editor’s Note: This article was the first published in the June 2008 World Cities Summit edition of ETHOS .

At the dawn of a new century, broad demographic, economic and environmental forces are giving American cities their best chance in decades to thrive and prosper. The renewed relevance of cities derives in part from the very physical characteristics that distinguish cities from other forms of human settlement: density, diversity of uses and functions, and distinctive design.

Across the United States (U.S.), a broad cross section of urban practitioners—private investors and developers, government officials, community and civic leaders—are taking ambitious steps to leverage the distinctive physical assets of cities and maximise their economic, fiscal, environmental and social potential.

A special class of urban interventions—what we call “transformative investments”—is emerging from the millions of transactions that occur in cities every year. The hallmark of transformative investments is their catalytic nature and seismic impact on markets, on people, on the city landscape and urban possibilities—far beyond the geographic confines of the project itself.

Recognising and replicating the magic of transformative investments, and making the exception become the norm is important if U.S. cities are to realise their full potential.

THE URBAN MOMENT The U.S. is undergoing a period of dynamic change, comparable in scale and complexity to the latter part of the nineteenth century. Against this backdrop, there is a resurgence in the importance of cities due to their fundamental and distinctive physical attributes.

Cities offer a broad range of physical choices—in neighbourhoods, housing stock, shopping venues, green spaces and transportation. These choices suit the disparate preferences of a growing population that is diverse by race, ethnicity and age.

Cities are also rich with physical amenities—mixed-use downtowns, historic buildings, campuses of higher learning, entertainment districts, pedestrian-friendly neighbourhoods, adjoining rivers and lakes—that are uniquely aligned with preferences in a knowledge-oriented, post-industrial economy. A knowledge economy places the highest premium on attracting and retaining educated workers, and an increasing proportion of these workers, particularly young workers, value urban quality of life when making their residential and employment decisions.

Finally, cities, particularly those built in the nineteenth and early twentieth centuries, are compactly constructed and laid out along dense lines and grids, enhancing the potential for the dynamic, random, face-to-face human exchange prized by an economy fuelled by ideas and innovation. Such density also makes cities perfect agents for the efficient delivery of public services as well as the stewardship of the natural environment.

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