A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and 15.0 mL per minute per 1.73 m2 of body surface area or ii. a late start group, where dialysis was initiated when their GFR was 5.0 to 7.0 mL per minute per 1.73 m2 of body surface area. The primary outcome was total mortality. There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years. 10.86 What test can be used to compare the mortality rates in the two groups? 10.87 Implement the test in Problem 10.86, and report a two-sided p-value. In planning the study it was anticipated that 400 subjects would be enrolled per group and that the 3-year mortality risk would be 36% in the late start group and 26% in the early start group. 10.88 How much power would the study have if it had occurred under the planned mortality rates and sample size?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A study was performed among patients with progressive chronic kidney disease to assess the optimal time for the initiation of dialysis (Cooper et al. [22]). Patients were randomized to either
i. an early start group, where dialysis was initiated when their estimated glomerular filtration rate (GFR) was between 10.0 and 15.0 mL per minute per 1.73 m2 of body surface area or
ii. a late start group, where dialysis was initiated when their GFR was 5.0 to 7.0 mL per minute per 1.73 m2 of body surface area.
The primary outcome was total mortality.
There were 404 patients assigned to the early start group, of whom 152 died. There were 424 patients assigned to the late start group, of whom 155 died over the same time period. Patients were enrolled from July 2000 to November 2008 and were followed for 3 years.
10.86 What test can be used to compare the mortality rates in the two groups?
10.87 Implement the test in Problem 10.86, and report a two-sided p-value.
In planning the study it was anticipated that 400 subjects would be enrolled per group and that the 3-year mortality risk would be 36% in the late start group and 26% in the early start group.
10.88 How much power would the study have if it had occurred under the planned mortality rates and sample size?
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