Liver metastases seen on CT scan. Built-in ruler makes measurement of metastatic lesions easy for subsequent growth calculations.
A 55 year old man complains of rectal bleeding to his family doctor. He is treated for hemorrhoids without further evaluation. Two years later his rectal cancer is discovered; two years after that he develops liver metastases. Could his cancer have been the cause of the rectal bleeding? If so, could it have been discovered had he been evaluated? Did his liver have microscopic metastases present at the time of the original complaint? All of these questions are terribly relevant to developing a proximate cause argument. Can Doubling Time analysis help? Is it science or junk science?
Crucial to an understanding of Doubling Time is Gompertzian Kinetics (see graph). This shows a tumor growing quickly as it starts out, then slowing down as it gets bigger. The growth rate changes, slows down, over time. When you measure a tumor at two moments in time (i.e., when the diagnosis was missed and made) you are looking at the right side of that curve. The life span of the tumor is much shorter than would be predicted using only that growth rate as an indicator of tumor growth during its entire existence. This is especially relevant when attempting to calculate backwards how long the liver metastases in the case above have been present. In most cases liver metastases have been present for less than two years when first observed. Using a constant growth rate that number would be closer to ten years. As to the size of the primary tumor at the earlier moment, colon cancer grows so slowly that it takes about three years for it to double in diameter; before that it would likely have been present as a polyp. Unless the interval from negligence to diagnosis is very long it is difficult to say the tumor was not visible.
The actual performance of growth calculations using the Gompertzian equations is complex because the growth rate is constantly changing, requiring the use of higher order equations. Dr. Stark and his son Brian (Ph.D, Electrical Engineering, University of Michigan) have developed software which makes the mathematics much easier (The Cancer Data Calculator, 1996) When the mathematics is understood and the calculations are performed properly there is a role for the use of doubling time in causation arguments. This is not junk.