A 2020 article in JAMA reports the findings of a study that uses data from the National Health and Nutrition Examination Study (NHANES) and from vital records data to quantify the association between physical activity (measured by the average number of "steps per day" measured by accelerometer) and all-cause mortality. The following shows a portion of the abstract from this article:

The authors present the overall results with regards to different levels of adjustment via hazard ratios in the following table (Table 2):

The results in the column "Model 1" have been adjusted for biological sex only (recorded as two levels only, male and female); the results in the column titled "Model 2" have been adjusted for sex and age, and the results in the column titled "Model 3" have been adjusted for age, sex and other characteristics listed in the right side of the above graphic.

Steps per day was measured continuously, and on average participants took 9,124 steps per day (range: 2,000 - 17,600). The relationship between mortality and steps per day was estimated via Cox regression models with a continuous x1 value for the average number of daily steps, i.e.

ln(hazard at time t)=ln(o(t))+^1x1ln(hazard at time t)=ln(o(t))+^1x1

The above table (Table 2) only includes results regarding mortality estimated from this at 3 specific x₁ values: x₁= 4,000 steps per day, x₁ = 8,000 steps per day, and x₁ = 12,000 steps per day.

Using the results from the analysis titled "Model 3", what is the estimated sex-adjusted hazard ratio for persons who took 12,000 steps per day compared to persons who took 8,000 steps per day?

a. 1.0/0.35

b. 0.35 - 0.49

c. ln(0.35 - 0.49)

d. 0.35/0.49