Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Table 3 contd.ZSecond decimal place of Z3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.00073.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.00053.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.00033.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.00023.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.00023.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.00013.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.00013.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.00013.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00004.0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Area under the curve in the lower tailQuestion 2: What percentage of subjects have an SBP below 110 mm Hg?Similarly to in Question 1, we can calculate that Z = –1.33. As the standardnormal distribution is symmetrical about zero, the area below –1.33 is equal to thearea above 1.33; this area equals 0.0918. Thus, 9.18% of subjects have an SBPlower than 110 mm Hg.The area under the curve within a certain rangeQuestion 3: What proportion of subjects have an SBP between110 and 160 mm Hg?This can be calculated in three steps:Step 1: The proportion above 160 mm Hg, as calculated in Question 1, is 2.28%.Step 2: The proportion below 110 mm Hg, as calculated in Question 2, is 9.18%.Step 3:The proportion of subjects with an SBP between 110 and 160 mm Hg:= 1 – (proportion above 160 mm Hg + proportion below 110 mm Hg)= 1 – (2.28% + 9.18%) = 89.54%The area under the curve in two-sided symmetric tailsQuestion 4: What proportion of subjects have an SBP above130 + 15 mm Hg and below 130 – 15 mm Hg?The areas described here are known as two-sided percentages, as they cover theobservations symmetrically in both the upper and lower tails. The proportionsgiven in Table 3 are one-sided areas in the each tail (α). To determine a two-sidedproportion, we simply double the area (denoted as 2α).181