# Teorema de bayes

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Average Annual Percent Change (AAPC)
As of version 3.3, an important new feature was added to Joinpoint, the Average Annual Percent Change (AAPC). While Joinpoint computes the trend in segments whose start and end are determined to best fit the data, sometimes it is useful to summarize the trend over a fixed predetermined interval. The AAPC is a method which uses the underlying Joinpoint modelto compute a summary measure over a fixed pre-specified interval.
Annual Percent Change (APC) is one way to characterize trends in cancer rates over time. This means that the cancer rates are assumed to change at a constant percentage of the rate of the previous year. For example, if the APC is 1%, and the rate is 50.000 per 100,000 in 1990, the rate is 50 × 1.01 = 50.500 in 1991 and 50.5 × 1.01 =51.005 in 1992. Rates that change at a constant percentage every year change linearly on a log scale. For this reason, to estimate the APC for a series of data, the following regression model is used:
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One advantage of characterizing trends this way is that it is a measure that is comparable across scales, for both rare and common cancers. For example, it is reasonable to think thatrates for a rare cancer and a common cancer could both change at 1% per year, but it is not reasonable to think that a rare cancer and a common cancer would change in the same increments on an absolute (or arithmetic) scale. That is, a cancer with a rate of 100 per 100,000 could be changing by 2 per 100,000 every year, but a cancer with a rate of 1 per 100,000 would probably not change in the sameincrements.
It is not always reasonable to expect that a single APC can accurately characterize the trend over an entire series of data. The joinpoint model uses statistical criteria to determine when and how often the APC changes. For cancer rates, it is fit using joined log-linear segments, so each segment can be characterized using an APC. For example, cancer rates may rise gradually for aperiod of several years, rise sharply for several years after that, then drop gradually for the next several years. Finding the joinpoint model that best fits the data allows us to determine how long the APC remained constant, and when it changed.
Average Annual Percent Change (AAPC) is a summary measure of the trend over a pre-specified fixed interval. It allows us to use a single number todescribe the average APCs over a period of multiple years. It is valid even if the joinpoint model indicates that there were changes in trends during those years. It is computed as a weighted average of the APC's from the joinpoint model, with the weights equal to the length of the APC interval.
• How is the AAPC computed?
• What are the relative advantages and disadvantages of reporting an AAPCover APCs?
• What is the advantage of reporting an AAPC over an APC computed by fitting a single line (on a log scale) to the data?
How is the AAPC computed?
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AAPC is derived by first estimating the underlying joinpoint model that best fits the data. The accompanying figure shows the joinpoint model for prostate cancer incidence from 1975-2003 (from the 2005 data submission), which foundjoinpoints in 1988, 1992, and 1995. (This model is fit under the default joinpoint parameters). The AAPC over any fixed interval is a weighted average of the slope coefficients of the underlying joinpoint regression line with the weights equal to the length of each segment over the interval. The final step of the calculation transforms the weighted average of slope coefficients to an annualpercent change. If we denote bis as the slope coefficients for each segment in the desired range of years, and the wis as the length of each segment runs in the range of years, then:
APCi = { (Exp(bi) − 1) } × 100
and
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In the prostate cancer example, to compute the AAPC from 1994 to 2003, we first note that an APC of −10.7 runs for 1 year (with a slope coefficient of −0.113), while an...