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Placebo cases needed The interim read had 95 cases, 90 of which were in the placebo group. 90 is 94.74% of 95. Moderna reported 94.5% effective. The next read is at least 151 cases which could go higher depending on how many cases are confirmed on the day the count reaches 151. I estimate the final read will be on between 151 and 160. The 95 cases already reported on are part of whatever becomes the final count. If the final count is 151, then 56 new cases are needed (151-95). If the final count is at 160, then 65 new cases are needed, 10 of which are recorded on the day 151 was reached (150 yesterday, not enough + 10 today). We already know the ratio of the first 95. It was 90-5, placebo to vaccine. I wondered what percentage of new cases are in the placebo group in order to boost 94.5% effective to at least 95.0% effective. Obviously, the percentage must be more than 95% because we are trying to move the overall percentage from 94.5% to at least 95.0%. This percentage varies depending on the number read between 151 and 160. While percentages can be fractional hence converted into a theoretical fractional case, there is no such thing as a real fractional case. A person either meets the covid 19 criteria or doesn't. Actual cases are whole people. There are no fractions. Therefore, in calculating how many placebo people are in each percentage category, any fraction of a person must be rounded up. Otherwise, the percentage result will be slightly below the desired. I also wondered how few new placebo cases would bring the overall percentage effective to at least 90%. Again, it obvious the percentage of placebo in the new group must be substantially below 94.5 percent in order to drag down the overall percentage to not less than 90%. Here is the result of my study. It calculates what percentage of new cases are needed to make the overall percentage 95.0%. The second table illustrates how low the percentage of new placebo cases can go before the overall percentage drops below 90%.
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