Risk to a child from Measles if not vaccinated until the age of 5:
Measles (also known as Rubeola or morbilli) is a viral infection of the respiratory system. It is classically characterized by initial fever followed by a rash that covers most of the body. Measles is highly infectious and is spread through aerosolized droplets from infected persons. It is contagious from 2-4 days prior to and 2-5 days after the onset of the rash. Prior to vaccination, 90% of the population in the US contracted measles by the time they turned 15. Although it is generally a mild illness, it can be accompanied by very serious complications (pneumonia, encephalitis, SSPE) or death in a small number of cases.  Measles can be very serious in immunocompromised persons.
The severity of the disease is hard to judge due to inconsistent documentation and conclusions by various authors worldwide. In a 1967 study by authors from the CDC they state: “For centuries the measles virus has maintained a remarkably stable ecological relationship with man. The clinical disease is a characteristic syndrome of notable constancy and only moderate severity. Complications are infrequent, and, with adequate medical care, fatality is rare. Susceptibility to the disease after the waning of maternal immunity is universal; immunity following recovery is solid and lifelong in duration.” In 2004, we find CDC authors telling a very different story about the exact same time period: “Nevertheless, in the late 1950s, serious complications due to measles remained frequent and costly. As a result of measles virus infections, an average of 150,000 patients had respiratory complications and 4000 patients had encephalitis each year; the latter was associated with a high risk of neurological sequelae and death. These complications and others resulted in an estimated 48,000 persons with measles being hospitalized every year.”(Orenstein). Following the reference chain, we see these estimates are mainly based on a study from cases between 1929-1953 . Miller performs a UK based study in 1964 and observes: “In the meantime it can be said that the results reflect complication rates under the present conditions of medical practice, and on these grounds measles can scarcely be regarded as a mere inconvenience.” A subsequent study from Denmark by Tidstrom (1968) makes the following observation: “Encephalitis is a rare complication in measles and, concerning mortality rate and sequelae, is not so severe as considered previously.” 
Factors Not Considered: There is considerable evidence that the risk from severe measles disease is highly variable depending on factors influenced by economic and living conditions. Morbidity and mortality due to measles is far higher in the developing world. In a study from the UK, Maclure found that the risk of hospitalization from measles in children living in deprived households was over 10 times higher than in areas where households were not deprived. For measles, overcrowding and unemployment were more correlated with measles hospitalization than vaccination rates. In the developing world, the majority of complications occur in the younger children. Gordon et al describe that in Guatemala, nutritional supplements reduced the annual mortality rate by 65% while medical care reduced it by almost 70% .
Case Fatality Rate: The CDC Pink book lists several causes of death from measles including: Death from pneumonia, acute encephalitis, and subacute sclerosing panencephalitis (SSPE).
Determining an accurate case fatality rate is very difficult given that reported incidence of measles is deemed unreliable and varies over time. During epidemics, it is assumed that more cases are reported. It was assumed prior to mass vaccination in 1963, only 1 in 10 cases were reported. (Bellini) Today, it is assumed that most cases are reported and these assumptions heavily affect the case fatality calculations. There is also evidence that during epidemics that many subclinical cases occur. [9,10]
The most recent study of the pre-vaccine era is the Tidstrom study from Denmark in 1968. Tidstrom is insightful because it analyses measles data over 15 years, and it separately analyzes two distinct periods where treatment of respiratory failure were fundamentally changed following a severe poliomyelitis epidemic in 1952. The study covers a 15 year period during which there were 298,700 births (estimated total child population of 577,477 children < 15) with 157,300 notifications (~27%) and a total of 4874 patient hospitalizations. This study provides a unique view into the effects of more modern medical protocols when treating measles encephalitis. The difference was quite striking. In the period prior to 1952, there were 5 deaths among 21 patients (24%) of encephalitis. In the period following 1952, there was only one death among 47 patients (2.1%) from encephalitis. Tidstrom notes that the latter rate of 2.1% was consistent with a Swedish publication showing one death among 38 patients (2.6%). Consistent with most other studies, pneumonia was the most frequent complication resulting 1,268 hospitalized cases (26%) and 12 deaths (0.9%). Unlike the case fatality rate from encephalitis, the case fatality rate from pneumonia was surprisingly consistent across the entire 15 year period of study. There were 4 other deaths (2%) of the 4874 hospitalizations from a variety of different complications and pre-existing conditions. Tidstrom notes that most of the numbers are consistent with other studies from that era, with the exception of a lower encephalitis rate. She explains this: “The frequency of encephalitis was 0.043% of the notified cases in the City and County of Copenhagen. The incidence of encephalitis as a complication in measles is reported to range from 0.1% to 0.25%. The variations may be caused by varying criteria for the diagnosis. Some authors classify every symptom from the central nervous system as due to encephalitis, which means that cases with secondary lymphocytic meningitis without other signs of central nervous disturbances than pleocytosis are included.”
In 1964, Miller published a study from a postal follow-up of ~53,000 notified measles cases in England and Wales. The Miller (1964) study was mainly focused on complications and notes a total number of 12 deaths (0.022 per 1000 notifications) which is higher but in a similar ballpark to the case fatality rate from Tidstrom (0.014 per 1000 notifications). However, Miller (1964) notes that there is evidence that half of the deaths occur in persons with serious or chronic disease or disability. So if you take that into consideration, the Tidstrom numbers based on healthy patients are higher. This analysis uses the case fatality data from Tidstrom (1968) with a heavier weighting of notifications to population based on the notifications percentages from ages 1-4 (measles vaccine doesn’t protect children < 1 year old) from Miller (1964).
SSPE is a progressive fatal disease caused by persistent measles infection. SSPE occurs an average 7-10 years post measles infection. The main risk factor for SSPE is the development of measles infection at an early age (before 2 years of age). Bellini et al did a rigorous SSPE follow-up case study after the large measles outbreak from the US in 1989-1991. They concluded that SSPE rates were traditionally underestimated and calculated a rate of 6.5-11 cases of SSPE per 100,000 cases of measles. This analysis needs to determine the individual risk that is vaccine preventable. Although Bellini et al concluded that vaccination prevents more cases of SSPE than previously thought, an examination of the cases shows that this protection is entirely due to herd immunity, not directly due to vaccination. In every case they document, the patient contracted the disease prior to vaccination, or post-vaccination (indicating vaccine failure in that individual). For the purposes of this analysis, the risk of SSPE is not considered directly vaccine preventable.
Rate of Long Term Sequelae: Miller (1964) discusses many complications of measles but notes that a subsequent study would have to follow-up the cases and determine the rates of long term sequelae. Tidstrom (1968) performs a follow-up of 95% of the hospitalized encephalitis cases (59 of 62) over the study period. Forty five patients were examined by Tidstrom and 14 answered questions by mail. Tidstrom notes that 68% had a complete recovery, 3 had serious defects and 16 had mild defects. Three of the 15 mild defects were classified as “dubious”. This analysis will use a long term sequelae rate of 16/59 or 27% of encephalitis cases.
Incremental Risk in Population with Low Rates of Vaccination (if a child does not vaccinate by age 5): As described above, this analysis calculates the risk of death and long term sequelae based on Tidstrom (1968) case rates, with adjusted weightings by age provided by the Miller (1964) study. This analysis uses a weighted notification rate of 54% (based on Tidstrom population weighted by Miller notifications). The cumulative fatality rate was 0.5284 per 10,000 or 1 in 18,924. The cumulative risk of long term sequelae was 0.6309 per 10,000 or 1 in 15,851.
Incremental Risk in Highly Vaccinated Population (if a child does not vaccinate by age 5): Calculations of vaccine preventable risk are very difficult in highly vaccinated populations due to the lack of good statistics regarding vaccinated population counts, and percentage of vaccinated incidence. As described above, in the case of measles, the reduction of risk is due to herd immunity. The CDC declared measles eradicated in the US around the year 2000. Statistics show that the measles cases have dropped to less than 0.1% of the rates pre-vaccination. Taking 0.1% of the risk from populations with low rates of vaccination, yields a fatality rate of 0.00053 per 10,000 or 1 in 18,923,686. The cumulative risk of long term sequelae was 0.00063 per 10,000 cases or 1 in 15,851,399.
 Centers for Disease Control and Prevention: Epidemiology and Prevention of Vaccine-Preventable Disease. Atkinson W, Wolfe S, Hamborsky J, McIntyre L. eds. 11th edition. Washington D.C.: Public Health Foundation, 2009.
 D. J. Sencer, H. B. Dull, and A. D. Langmuir. Epidemiologic basis for eradication of measles in 1967. Public Health Rep. 1967 March; 82(3): 253–256.
 Orenstein WA, Papania MJ, Wharton ME. Measles elimination in the United States. J Infect Dis. 2004 May 1;189 Suppl 1:S1-3.
 MILLER HG, STANTON JB., GIBBONS JL. Para-infectious encephalomyelitis and related syndromes; a critical review of the neurological complications of certain specific fevers. Q J Med. 1956 Oct;25(100):427-505.
 MILLER DL., FREQUENCY OF COMPLICATIONS OF MEASLES, 1963. REPORT ON A NATIONAL INQUIRY BY THE PUBLIC HEALTH LABORATORY SERVICE IN COLLABORATION WITH THE SOCIETY OF MEDICAL OFFICERS OF HEALTH. Br Med J. 1964 Jul 11;2(5401):75-8.
 Tidstrom B. Complications in measles with special reference to encephalitis. Acta Med Scand. 1968 Nov;184(5):411-5. Maclure A, Stewart GT. Admission of children to hospitals in Glasgow: relation to unemployment and other deprivation variables. Lancet 1984 Sep 22;2(8404):682-5.
 Maclure A, Stewart GT. Admission of children to hospitals in Glasgow: relation to unemployment and other deprivation variables. Lancet 1984 Sep 22;2(8404):682-5.
 GORDON JE, JANSEN AA, ASCOLI W. MEASLES IN RURAL GUATEMALA. J Pediatr. 1965 Apr;66:779-86.
 Bellini WJ, Rota JS, Lowe LE, Katz RS, Dyken PR, Zaki SR, Shieh WJ, Rota PA. Subacute sclerosing panencephalitis: more cases of this fatal disease are prevented by measles immunization than was previously recognized. J Infect Dis. 2005 Nov 15;192(10):1686-93. Epub 2005 Oct 12.
 Miller C, Andrews N, Rush M, Munro H, Jin L, Miller E. The epidemiology of subacute sclerosing panencephalitis in England and Wales 1990-2002. Arch Dis Child. 2004 Dec;89(12):1145-8.