Comments On The 1998 Article by Plioplys

As noted in our letter to the editor of Seminars in Pediatric Neurology,1 the 1998 study by Plioplys et al.2 has a serious methodological error. This has resulted in gross overestimates of the probabilities of survival, and these estimates are contradicted by a large body of medical literature from around the world.3-18

The error in Dr. Plioplys' paper is most easily understood by an extreme example. Suppose that 100 children enter a study at birth, and 90 die prior to their first birthday. This is a mortality probability of 90% for age 0 to age 1. Now suppose that 5 of the 10 survivors at age 1.0 die in their second year. This is a mortality probability of 5/10 = 50% from age 1 to age 2. However, Dr. Plioplys’ method would erroneously compute the mortality probability to be 5/100 = 5%. The error is to assume that the denominator includes all the children in the study, instead of only those at risk at the age in question. This error is apparent in all 6 figures of his paper.

The situation is slightly more complicated in practice. Dr. Plioplys’ follow-up period was about 10 years, yet his Figures cover at least 34 years (from age 0 to age 34+). It was thus necessary for him to combine data from the various ages. The correct and standard method is to compute the age-specific mortality rates for each age x as the number of subjects who die at age x divided by the total number of persons in the study who were “exposed” at age x and thus could have died. The denominator would exclude, for example, all children who entered the study after age x and thus were not at risk of dying at age x in the study period. Again, Dr. Plioplys’ incorrect method would count such children in the denominator, and thus underestimate the true mortality rates.

For a specific example from the paper consider Figure 4, which applies to children in Group 4 (see the article for a definition of the groups). According to page 165 of the article, Group 4 had 11 patients with mean age 18.9. It is seen that 2 of the 11 died, at ages 4 and 20 (the curves drop at those ages). Consider just the curve for the group "age < 1".

  1. The curve begins at age 0 with 100% alive, then drops to 91% at age 4, and to 82% at age 20.

  2. The drops from 100% to 91% and 91% to 82% are both 9%, which is precisely equal to 1/11. From this alone it is clear that Dr. Plioplys has in effect assumed that all 11 people were alive both at age 4 and at age 20.

  3. It is impossible that all 11 people were at risk of death both at age 4 and at age 20. This is obvious for the following reasons:

    • His study period was only about 10 years. Thus, the same person could not have been both age 4 and age 20 during the 10-year period.

    • From the same Figure we see that 6 of the 11 persons were initially age 15 or over. This is clear because the curve for "age 15" drops from 100% to 83% (a drop of 17% or 1/6) at age 20.

    • Thus, at most 5 of the 11 were alive at age 4. [Note: This number, 5, could have been less if, for example, some persons entered the study at ages 4 to 15.]

  4. Assume that exactly 5 of the 11 were alive at age 4. It then follows that the correct probability of death at age 4 is 1/5 = 20%. The survival curve should thus drop from 100% to 80% at age 4.

  5. Similarly, if 6 of the 11 were alive at age 20 then the one death at age 20 gives a mortality rate of 1/6 = 17%. The curve should thus drop from 80% to 80%*(100% - 17%) = 66% at age 20.

Technically, one must use the same rule for counting exposure time (the number of persons alive and at risk of dying) as deaths (the number who died). Dr. Plioplys did not do so.

The error ensures that all of Dr. Plioplys’ survival probabilities are too high. This partly explains why he (page 170) "... obtained significantly better survival rates than those of Eyman et al." An additional reason is that the Eyman papers19,20 themselves have methodological errors that seriously biased their results downward – that is, in the opposite direction. We also noted this in our letter1 and have documented it in detail elsewhere.21,22

References

  1. Strauss DJ, Shavelle RM, Day SM (2004). Letter to the editor re: Plioplys article. Seminars in Pediatric Neurology, 11:236.

  2. Plioplys AV, Kasnicka I, Lewis S, Moller D (1998). Survival rates among children with severe neurologic disabilities. Southern Medical Journal, 91:161-172.

  3. Reid SM, Carlin JB, Reddihough DS (2012). Survival of individuals with cerebral palsy born in Victoria, Australia, between 1970 and 2004. Developmental Medicine & Child Neurology, 54:353–360.

  4. Brooks JC, Shavelle RM, Strauss DJ (2012). Survival in children with severe cerebral palsy: A further international comparison. Developmental Medicine & Child Neurology, 54:383-384. DOI: 10.1111/j.1469-8749.2012.04236.x.

  5. Strauss DJ, Shavelle RM, Rosenbloom L, Brooks JC (2008). Life expectancy in cerebral palsy: An update. Developmental Medicine & Child Neurology, 50:487-493.

  6. Hutton JL, Pharoah POD (2006). Life expectancy in severe cerebral palsy. Archives of Disease in Childhood, 91:254-258.

  7. Hemming K, Hutton JL, Pharoah PO (2006). Long-term survival for a cohort of adults with cerebral palsy. Developmental Medicine & Child Neurology, 48:90-95.

  8. Hemming K, Hutton J, Colver A, Platt MJ (2005). Regional variation in survival of people with cerebral palsy in the United Kingdom. Pediatrics, 116:1383-1390.

  9. Hutton JL, Pharoah POD (2002). Effects of cognitive, motor, and sensory disabilities on survival in cerebral palsy. Archives of Disease in Childhood, 86:84-89.

  10. Eyman RK, Grossman HJ (2001). Living with cerebral palsy and tube feeding [letter]. Journal of Pediatrics, 138:147.

  11. Shavelle RM, Strauss DJ, Day SM (2001). Comparison of survival in cerebral palsy between countries [letter]. Developmental Medicine & Child Neurology, 43:574.

  12. Blair E, Watson L, Badawi N, Stanley FJ (2001). Life expectancy among people with cerebral palsy in Western Australia. Developmental Medicine & Child Neurology, 43:508-515.

  13. Hutton JL, Colver AF, Mackie PC (2000). Effect of severity of disability on survival in north east England cerebral palsy cohort. Archives of Disease in Childhood, 83:468-474.

  14. Strauss DJ, Cable W, Shavelle RM (1999). Causes of excess mortality in persons with cerebral palsy. Developmental Medicine & Child Neurology 41:580-585.

  15. Strauss DJ, Shavelle RM, Anderson TW (1998). Life expectancy of children with cerebral palsy. Pediatric Neurology, 18:143-149.

  16. Strauss DJ, Shavelle RM (1998). Life expectancy of adults with cerebral palsy. Developmental Medicine & Child Neurology, 40:369-375.

  17. Crichton JU, Mackinnon M, White CP (1995). The life expectancy of persons with cerebral palsy. Developmental Medicine and Child Neurology, 37:567-576.

  18. Hutton JL, Cooke T, Pharoah POD (1994). Life expectancy in children with cerebral palsy. British Medical Journal, 309: 431-435.

  19. Eyman RK, Grossman HJ, Chaney RH, Call TL (1990). The life expectancy of profoundly handicapped people with mental retardation. New England Journal of Medicine, 323:584-589.

  20. Eyman RK, Grossman HJ, Chaney RH, Call TL (1993). Survival of profoundly handicapped people with severe mental retardation. American Journal of Diseases of Children, 147:329-336.

  21. Strauss DJ, Shavelle RM (1998). Survival estimates of severely disabled children [Letter]. Pediatric Neurology, 19:243-244.

  22. See, for example, this web page.