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Sudden infant death syndrome
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Sudden infant death syndrome
Synonyms
Cot death, crib death
Safe to Sleep logo
Specialty
Pediatrics
Symptoms
Death of a child less than one year of age[1]
Usual onset
Sudden[1]
Causes
Unknown[1]
Risk factors
Sleeping on the stomach or side, overheating, exposure to tobacco smoke, bed sharing[2][3]
Diagnostic method
No cause found after an investigation and autopsy[4]
Similar conditions
Infections, genetic disorders, heart problems, child abuse[2]
Prevention
Putting newborns on their back to sleep, pacifier, breastfeeding, immunization[5][6][7]
Treatment
Support for families[2]
Frequency
1 in 1,000–10,000[2]
[edit on Wikidata]
Sudden infant death syndrome (SIDS), also known as cot death or crib death, is the sudden unexplained death of a child less than one year of age.[1] Diagnosis requires that the death remains unexplained even after a thorough autopsy and detailed death scene investigation.[4] SIDS usually occurs during sleep.[2] Typically death occurs between the hours of 00:00 and 09:00.[8] There is usually no evidence of struggle and no noise produced.[9]
The exact cause of SIDS is unknown.[3] The requirement of a combination of factors including a specific underlying susceptibility, a specific time in development, and an environmental stressor has been proposed.[2][3] These environmental stressors may include sleeping on the stomach or side, overheating, and exposure to tobacco smoke.[3] Accidental suffocation from bed sharing (also known as co-sleeping) or soft objects may also play a role.[2][10] Another risk factor is being born before 39 weeks of gestation.[7] SIDS makes up about 80% of sudden and unexpected infant deaths (SUIDs).[2] Other causes include infections, genetic disorders, and heart problems.[2] While child abuse in the form of intentional suffocation may be misdiagnosed as SIDS, this is believed to make up less than 5% of cases.[2]
The most effective method of reducing the risk of SIDS is putting a child less than one year old on their back to sleep.[7] Other measures include a firm mattress separate from but close to caregivers, no loose bedding, a relatively cool sleeping environment, using a pacifier, and avoiding exposure to tobacco smoke.[5] Breastfeeding and immunization may also be preventive.[5][6] Measures not shown to be useful include positioning devices and baby monitors.[5][6] Evidence is not sufficient for the use of fans.[5] Grief support for families affected by SIDS is important, as the death of the infant is sudden, without witnesses, and often associated with an investigation.[2]
Rates of SIDS vary nearly tenfold in developed countries from one in a thousand to one in ten thousand.[2] Globally it resulted in about 19,200 deaths in 2015 down from 22,000 deaths in 1990.[11][12] SIDS was the third leading cause of death in children less than one year old in the United States in 2011.[13] It is the most common cause of death between one month and one year of age.[7] About 90% of cases happen before six months of age, with it being most frequent between two months and four months of age.[2][7] It is more common in boys than girls.[7]
Play media
Video explanation
Contents
[hide]
1 Definition
1.1 Age
2 Risk factors
2.1 Tobacco smoke
2.2 Sleeping
2.3 Breastfeeding
2.4 Pregnancy and infant factors
2.5 Genetics
2.6 Alcohol
2.7 Other
3 Differential diagnosis
4 Prevention
4.1 Sleep positioning
4.2 Pacifiers
4.3 Bedding
4.4 Sleep sacks
4.5 Vaccination
5 Management
6 Epidemiology
6.1 Race
7 Society and culture
8 See also
9 References
10 Further reading
11 External links
Definition[edit]
SIDS is a diagnosis of exclusion and should be applied to only those cases in which an infant's death is sudden and unexpected, and remains unexplained after the performance of an adequate postmortem investigation, including:
an autopsy (by an experienced pediatric pathologist, if possible);
investigation of the death scene and circumstances of the death;
exploration of the medical history of the infant and family.
After investigation, some of these infant deaths are found to be caused by accidental suffocation, hyperthermia or hypothermia, neglect or some other defined cause.[14]
Australia and New Zealand are shifting to the term "sudden unexpected death in infancy" (SUDI) for professional, scientific, and coronial clarity.
The term SUDI is now often used instead of sudden infant death syndrome (SIDS) because some coroners prefer to use the term 'undetermined' for a death previously considered to be SIDS. This change is causing diagnostic shift in the mortality data.[15]
In addition, the U.S. Centers for Disease Control and Prevention (CDC) has recently proposed that such deaths be called "sudden unexpected infant deaths" (SUID) and that SIDS is a subset of SUID.[16]
Age[edit]
SIDS has a 4-parameter lognormal age distribution that spares infants shortly after birth — the time of maximal risk for almost all other causes of non-trauma infant death.
By definition, SIDS deaths occur under the age of one year, with the peak incidence occurring when the infant is at 2 to 4 months of age. This is considered a critical period because the infant's ability to rouse from sleep is not yet mature.[2]
Risk factors[edit]
The cause of SIDS is unknown. Although studies have identified risk factors for SIDS, such as putting infants to bed on their stomachs, there has been little understanding of the syndrome's biological process or its potential causes. The frequency of SIDS does appear to be influenced by social, economic, and cultural factors, such as maternal education, race or ethnicity, and poverty.[17] SIDS is believed to occur when an infant with an underlying biological vulnerability, who is at a critical development age, is exposed to an external trigger.[2] The following risk factors generally contribute either to the underlying biological vulnerability or represent an external trigger:
Tobacco smoke[edit]
SIDS rates are higher for infants of mothers who smoke during pregnancy.[18][19] SID correlates with levels of nicotine and derivatives in the infant.[20] Nicotine and derivatives cause significant alterations in fetal neurodevelopment.[21]
Sleeping[edit]
Placing an infant to sleep while lying on the stomach or the side increases the risk.[5] This increased risk is greatest at two to three months of age.[5] Elevated or reduced room temperature also increases the risk,[22] as does excessive bedding, clothing, soft sleep surfaces, and stuffed animals.[23] Bumper pads may increase the risk of SIDS due to the risk of suffocation. They are not recommended for children under one years of age as this risk of suffocation greatly outweighs the risk of head bumping or limbs getting stuck in the bars of the crib.[5]
Sharing a bed with parents or siblings increases the risk for SIDS.[24] This risk is greatest in the first three months of life, when the mattress is soft, when one or more persons share the infant's bed, especially when the bed partners are using drugs or alcohol or are smoking.[5] The risk remains, however, even in parents who do not smoke or use drugs.[25] The American Academy of Pediatrics thus recommends "room-sharing without bed-sharing", stating that such an arrangement can decrease the risk of SIDS by up to 50%. Furthermore, the Academy recommended against devices marketed to make bed-sharing "safe", such as in-bed co-sleepers.[26]
Breastfeeding[edit]
Breastfeeding is associated with a lower risk of SIDS.[27] It is not clear if co-sleeping among mothers who breastfeed without any other risk factors increased SIDS risk.[28]
Pregnancy and infant factors[edit]
SIDS rates decrease with increasing maternal age, with teenage mothers at greatest risk.[18] Delayed or inadequate prenatal care also increases risk.[18] Low birth weight is a significant risk factor. In the United States from 1995 to 1998, the SIDS death rate for infants weighing 1000–1499 g was 2.89/1000, while for a birth weight of 3500–3999 g, it was only 0.51/1000.[29][30] Premature birth increases the risk of SIDS death roughly fourfold.[18][29] From 1995 to 1998, the U.S. SIDS rate for births at 37–39 weeks of gestation was 0.73/1000, while the SIDS rate for births at 28–31 weeks of gestation was 2.39/1000.[29]
Anemia has also been linked to SIDS[31] (note, however, that per item 6 in the list of epidemiologic characteristics below, extent of anemia cannot be evaluated at autopsy because an infant's total hemoglobin can only be measured during life.[32]). SIDS incidence rises from zero at birth, is highest from two to four months of age, and declines toward zero after the infant's first year.[33] Baby boys have a ~50% higher risk of SIDS than girls.[34]
Genetics[edit]
Genetics plays a role, as SIDS is more prevalent in males.[35][36] There is a consistent 50% male excess in SIDS per 1000 live births of each sex. Given a 5% male excess birth rate, there appears to be 3.15 male SIDS cases per 2 female, for a male fraction of 0.61.[35][36] This value of 61% in the US is an average of 57% black male SIDS, 62.2% white male SIDS and 59.4% for all other races combined. Note that when multiracial parentage is involved, infant race is arbitrarily assigned to one category or the other; most often it is chosen by the mother. The X-linkage hypothesis for SIDS and the male excess in infant mortality have shown that the 50% male excess could be related to a dominant X-linked allele, occurring with a frequency of 1⁄3 that is protective of transient cerebral anoxia. An unprotected male would occur with a frequency of 2⁄3 and an unprotected female would occur with a frequency of 4⁄9.
About 10 to 20% of SIDS cases are believed to be due to channelopathies, which are inherited defects in the ion channels which play an important role in the contraction of the heart.[37]
Alcohol[edit]
Drinking of alcohol by parents is linked to SIDS.[38] One study found a positive correlation between the two during New Years celebrations and weekends.[39] Another found that alcohol use disorder was linked to a more than twofold risk.[40]
Other[edit]
There is a tentative link with Staphylococcus aureus and Escherichia coli.[41]
Vaccinations do not increase the risk of SIDS; contrarily, they are linked to a 50% lower risk of SIDS.[42][43]
A 1998 report found that antimony- and phosphorus-containing compounds used as fire retardants in PVC and other cot mattress materials are not a cause of SIDS.[44] The report also states that toxic gas can not be generated from antimony in mattresses and that babies suffered SIDS on mattresses that did not contain the compound.
A set of risk factors SIDS has been identified with: seasonality: winter maximum, summer minimum; increasing SIDS rate with live birth order; low increased risk of SIDS in subsequent siblings of SIDS; apparent life-threatening events (ALTE) are not a risk factor for subsequent SIDS; SIDS risk is greatest during sleep.[45][unreliable medical source?]
Differential diagnosis[edit]
Some conditions that are often undiagnosed and could be confused with or comorbid with SIDS include:
medium-chain acyl-coenzyme A dehydrogenase deficiency (MCAD deficiency);[46]
infant botulism;[47]
long QT syndrome (accounting for less than 2% of cases);[48]
Helicobacter pylori bacterial infections;[49]
shaken baby syndrome and other forms of child abuse;[50][51]
overlaying, child smothering during carer's sleep[52]
For example, an infant with MCAD deficiency could have died by "classical SIDS" if found swaddled and prone with head covered in an overheated room where parents were smoking. Genes indicating susceptibility to MCAD and Long QT syndrome do not protect an infant from dying of classical SIDS. Therefore, presence of a susceptibility gene, such as for MCAD, means the infant may have died either from SIDS or from MCAD deficiency. It is currently impossible for the pathologist to distinguish between them.
A 2010 study looked at 554 autopsies of infants in North Carolina that listed SIDS as the cause of death, and suggested that many of these deaths may have been due to accidental suffocation. The study found that 69% of autopsies listed other possible risk factors that could have led to death, such as unsafe bedding or sleeping with adults.[53]
Several instances of infanticide have been uncovered where the diagnosis was originally SIDS.[54][55] Estimate of the percentage of SIDS deaths that are actually infanticide vary from less than 1% to up to 5% of cases.[56]
Some have underestimated the risk of two SIDS deaths occurring in the same family and the Royal Statistical Society issued a media release refuting this expert testimony in one UK case in which the conviction was subsequently overturned.[57]
Prevention[edit]
A number of measures have been found to be effective in preventing SIDS including changing the sleeping position, breastfeeding, limiting soft bedding, immunizing the infant and using pacifiers.[5] The use of electronic monitors has not been found to be useful as a preventative strategy.[5] The effect that fans might have on the risk of SIDS has not been studied well enough to make any recommendation about them.[5] Evidence regarding swaddling is unclear regarding SIDS.[5] A 2016 review found tentative evidence that swaddling increases risk of SIDS, especially among babies placed on their stomachs or side while sleeping.[58]
Sleep positioning[edit]
SIDS]] rate from 1988 to 2006
Sleeping on the back has been found to reduce the risk of SIDS.[59] It is thus recommended by the American Academy of Pediatrics and promoted as a best practice by the US National Institute of Child Health and Human Development (NICHD) "Safe to Sleep" campaign. The incidence of SIDS has fallen in a number of countries in which this recommendation has been widely adopted.[60] Sleeping on the back does not appear to increase the risk of choking even in those with gastroesophageal reflux disease.[5] While infants in this position may sleep more lightly this is not harmful.[5] Sharing the same room as one's parents but in a different bed may decrease the risk by half.[5]
Pacifiers[edit]
The use of pacifiers appears to decrease the risk of SIDS although the reason is unclear.[5] The American Academy of Pediatrics considers pacifier use to prevent SIDS to be reasonable.[5] Pacifiers do not appear to affect breastfeeding in the first four months, even though this is a common misconception.[61]
Bedding[edit]
Product safety experts advise against using pillows, overly soft mattresses, sleep positioners, bumper pads (crib bumpers), stuffed animals, or fluffy bedding in the crib and recommend instead dressing the child warmly and keeping the crib "naked."[62]
Blankets or other clothing should not be placed over a baby's head.[63]
Sleep sacks[edit]
In colder environments where bedding is required to maintain a baby's body temperature, the use of a "baby sleep bag" or "sleep sack" is becoming more popular. This is a soft bag with holes for the baby's arms and head. A zipper allows the bag to be closed around the baby. A study published in the European Journal of Pediatrics in August 1998[64] has shown the protective effects of a sleep sack as reducing the incidence of turning from back to front during sleep, reinforcing putting a baby to sleep on its back for placement into the sleep sack and preventing bedding from coming up over the face which leads to increased temperature and carbon dioxide rebreathing. They conclude in their study, "The use of a sleeping-sack should be particularly promoted for infants with a low birth weight." The American Academy of Pediatrics also recommends them as a type of bedding that warms the baby without covering its head.[65]
Vaccination[edit]
A large investigation into diphtheria-tetanus-pertussis vaccination and potential SIDS association by Berlin School of Public Health, Charité – Universitätsmedizin Berlin concluded: "Increased DTP immunisation coverage is associated with decreased SIDS mortality. Current recommendations on timely DTP immunisation should be emphasised to prevent not only specific infectious diseases but also potentially SIDS."[66]
Many other studies have also reached conclusions that vaccinations reduce the risk of SIDS. Studies generally show that SIDS risk is approximately halved by vaccinations.[67][68][69][70][71]
Management[edit]
Families who are impacted by SIDS should be offered emotional support and grief counseling.[72] The experience and manifestation of grief at the loss of an infant are impacted by cultural and individual differences.[73]
Epidemiology[edit]
Globally SIDS resulted in about 22,000 deaths as of 2010, down from 30,000 deaths in 1990.[74] Rates vary significantly by population from 0.05 per 1000 in Hong Kong to 6.7 per 1000 in American Indians.[75]
SIDS was responsible for 0.54 deaths per 1,000 live births in the US in 2005.[29] It is responsible for far fewer deaths than congenital disorders and disorders related to short gestation, though it is the leading cause of death in healthy infants after one month of age.
SIDS deaths in the US decreased from 4,895 in 1992 to 2,247 in 2004.[76] But, during a similar time period, 1989 to 2004, SIDS being listed as the cause of death for sudden infant death (SID) decreased from 80% to 55%.[76] According to John Kattwinkel, chairman of the Centers for Disease Control and Prevention (CDC) Special Task Force on SIDS "A lot of us are concerned that the rate (of SIDS) isn't decreasing significantly, but that a lot of it is just code shifting".[76]
Race[edit]
Rates of SIDS by race/ethnicity in the U.S., 2009, CDC, 2013
In 2013, there are persistent disparities in SIDS deaths among racial and ethnic groups in the U.S. In 2009, the rates of death range from 20.3 per 100,000 live births for Asian/Pacific Islander to 119.2 per 100,000 live births for American Indians/Alaska Native. African American infants have a 24% greater risk of having a SIDS related death [77] and experience a 2.5 greater incidence of SIDS than in Caucasian infants.[78] Rates are per 100,000 live births and enable more accurate comparison across groups of different total population size.
Research suggests that factors which contribute more directly to SIDS risk—maternal age, exposure to smoking, safe sleep practices, etc.—vary by racial and ethnic group and therefore risk exposure also varies by these groups.[2] Risk factors associated with prone sleeping patterns of African American families include mother’s age, household poverty index, rural/urban status of residence, and infant’s age. More than 50% of African American infants were placed in non-recommended sleeping positions according to a study completed in South Carolina.[79] Cultural factors can be protective as well as problematic.[80]
The rate per 1000 births varies in different areas of the world:[22][81] Central Americans and South Americans - 0.20 Asian/Pacific Islanders - 0.28 Mexicans - 0.24 Puerto Ricans - 0.53 Whites - 0.51 African Americans - 1.08 American Indian - 1.24
Society and culture[edit]
Much of the media portrayal of infants shows them in non-recommended sleeping positions.[5]
See also[edit]
Newborn care and safety
Sudden unexpected death syndrome
Sudden unexplained death in childhood
References[edit]
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Jump up ^ Bajanowski T, Vennemann M, Bohnert M, Rauch E, Brinkmann B, Mitchell EA (July 2005). "Unnatural causes of sudden unexpected deaths initially thought to be sudden infant death syndrome". Int. J. Legal Med. 119 (4): 213–6. doi:10.1007/s00414-005-0538-8. PMID 15830244.
Jump up ^ Du Chesne A, Bajanowski T, Brinkmann B (1997). "[Homicides without clues in children]". Arch Kriminol (in German). 199 (1–2): 21–6. PMID 9157833.
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Jump up ^ "Archived copy". Archived from the original on 2011-08-11. Retrieved 2011-07-20.
Jump up ^ Glatt, John (2000). Cradle of Death: A Shocking True Story of a Mother, Multiple Murder, and SIDS. Macmillan. ISBN 0-312-97302-0.
Jump up ^ Havill, Adrian (2002). While Innocents Slept: A Story of Revenge, Murder, and SIDS. Macmillan. ISBN 0-312-97517-1.
Jump up ^ Hymel KP (July 2006). "Distinguishing sudden infant death syndrome from child abuse fatalities". Pediatrics. 118 (1): 421–7. doi:10.1542/peds.2006-1245. PMID 16818592.
Jump up ^ "About Statistics and the Law" Archived 2007-09-02 at the Wayback Machine. (Website). Royal Statistical Society. (2001-10-23) Retrieved on 2007-09-22
Jump up ^ Pease, AS; Fleming, PJ; Hauck, FR; Moon, RY; Horne, RS; L'Hoir, MP; Ponsonby, AL; Blair, PS (June 2016). "Swaddling and the Risk of Sudden Infant Death Syndrome: A Meta-analysis". Pediatrics. 137 (6): e20153275. doi:10.1542/peds.2015-3275. PMID 27244847. Limited evidence suggested swaddling risk increased with infant age and was associated with a twofold risk for infants aged >6 months.
Jump up ^ Mitchell EA (November 2009). "SIDS: past, present and future". Acta paediatrica (Oslo, Norway : 1992). 98 (11): 1712–9. doi:10.1111/j.1651-2227.2009.01503.x. PMID 19807704.
Jump up ^ Mitchell EA, Hutchison L, Stewart AW (July 2007). "The continuing decline in SIDS mortality". Arch Dis Child. 92 (7): 625–6. doi:10.1136/adc.2007.116194. PMC 2083749  . PMID 17405855.
Jump up ^ Jaafar, Sharifah Halimah; Ho, Jacqueline J.; Jahanfar, Shayesteh; Angolkar, Mubashir (2016-08-30). "Effect of restricted pacifier use in breastfeeding term infants for increasing duration of breastfeeding". The Cochrane Database of Systematic Reviews (8): CD007202. doi:10.1002/14651858.CD007202.pub4. ISSN 1469-493X. PMID 27572944. Archived from the original on 2017-02-08.
Jump up ^ "What Can Be Done?". American SIDS Institute. Archived from the original on 2003-06-21.
Jump up ^ Syndrome, Task Force on Sudden Infant Death (24 October 2016). "SIDS and Other Sleep-Related Infant Deaths: Updated 2016 Recommendations for a Safe Infant Sleeping Environment". Pediatrics. 138: e20162938. doi:10.1542/peds.2016-2938. ISSN 0031-4005. Archived from the original on 25 October 2016.
Jump up ^ L'Hoir MP, Engelberts AC, van Well GT, McClelland S, Westers P, Dandachli T, Mellenbergh GJ, Wolters WH, Huber J (1998). "Risk and preventive factors for cot death in The Netherlands, a low-incidence country". Eur. J. Pediatr. 157 (8): 681–8. doi:10.1007/s004310050911. PMID 9727856.
Jump up ^ "The Changing Concept of Sudden Infant Death Syndrome: Diagnostic Coding Shifts, Controversies Regarding the Sleeping Environment, and New Variables to Consider in Reducing Risk". American Academy of Pediatrics. Archived from the original on 2008-12-03. Retrieved 2008-11-06.
Jump up ^ Müller-Nordhorn, Jacqueline; Hettler-Chen, Chih-Mei; Keil, Thomas; Muckelbauer, Rebecca (28 January 2015). "Association between sudden infant death syndrome and diphtheria-tetanus-pertussis immunisation: an ecological study". BMC Pediatrics. 15 (1). doi:10.1186/s12887-015-0318-7.
Jump up ^ Mitchell, E A; Stewart, A W; Clements, M (1 December 1995). "Immunisation and the sudden infant death syndrome. New Zealand Cot Death Study Group". Archives of Disease in Childhood. 73 (6): 498–501. doi:10.1136/adc.73.6.498.
Jump up ^ Fleming, P. J (7 April 2001). "The UK accelerated immunisation programme and sudden unexpected death in infancy: case-control study". BMJ. 322 (7290): 822–822. doi:10.1136/bmj.322.7290.822.
Jump up ^ Vennemann, M.M.T.; Höffgen, M.; Bajanowski, T.; Hense, H.-W.; Mitchell, E.A. (2007). "Do immunisations reduce the risk for SIDS? A meta-analysis". Vaccine. 25 (26): 4875–9. doi:10.1016/j.vaccine.2007.02.077. PMID 17400342.
Jump up ^ Hoffman, HJ; Hunter, JC; Damus, K; Pakter, J; Peterson, DR; van Belle, G; Hasselmeyer, EG (April 1987). "Diphtheria-tetanus-pertussis immunization and sudden infant death: results of the National Institute of Child Health and Human Development Cooperative Epidemiological Study of Sudden Infant Death Syndrome risk factors". Pediatrics. 79 (4): 598–611. PMID 3493477.
Jump up ^ Carvajal, A; Caro-Patón, T; Martín de Diego, I; Martín Arias, LH; Alvarez Requejo, A; Lobato, A (4 May 1996). "[DTP vaccine and infant sudden death syndrome. Meta-analysis]". Medicina clinica. 106 (17): 649–52. PMID 8691909.
Jump up ^ Adams SM, Good MW, Defranco GM (2009). "Sudden infant death syndrome". Am Fam Physician. 79 (10): 870–4. PMID 19496386.
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Jump up ^ Lozano R, Naghavi M, Foreman K, Lim S, Shibuya K, Aboyans V, Abraham J, Adair T, Aggarwal R, Ahn SY, et al. (Dec 15, 2012). "Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010". Lancet. 380 (9859): 2095–128. doi:10.1016/S0140-6736(12)61728-0. PMID 23245604.
Jump up ^ Sharma BR (March 2007). "Sudden infant death syndrome: a subject of medicolegal research". The American Journal of Forensic Medicine and Pathology. 28 (1): 69–72. doi:10.1097/01.paf.0000220934.18700.ef. PMID 17325469.
^ Jump up to: a b c Bowman L, Hargrove T. Exposing Sudden Infant Death In America. Scripps Howard News Service. "Archived copy". Archived from the original on 2009-02-26. Retrieved 2008-09-30.
Jump up ^ Powers, D. A.; Song, S. (2009). "Absolute change in cause-specific infant mortality for blacks and whites in the US: 1983–2002". tion Research and Policy Review. 28 (6): 817–851. doi:10.1007/s11113-009-9130-0.
Jump up ^ Pollack, H. A.; Frohna, J. G. (2001). "A competing risk model of sudden infant death syndrome incidence in two US birth cohorts". The Journal of Pediatrics. 138 (5): 661–667. doi:10.1067/mpd.2001.112248. PMID 11343040.
Jump up ^ Smith, M. G.; Liu, J.; Helms, K. H.; Wilkerson, K. L. (2012). "Racial differences in trends and predictors of infant sleep positioning in south carolina, 1996–2007". Maternal and Child Health Journal. 15 (1): 72–82. doi:10.1007/s10995-010-0718-0.
Jump up ^ Brathwaite-Fisher, T, Bronheim, S. Cultural Competence and Sudden Infant Death Syndrome and Other Infant Death: A Review of the Literature from 1990–2000. National Center for Cultural Competence, Georgetown University Center for Child and Human Development 2001. DOI: "Archived copy". Archived from the original on 2013-12-17. Retrieved 2013-09-29.
Jump up ^ Burnett, Lynn Barkley. "Sudden Infant Death Syndrom". Medscape. Archived from the original on 2016-08-01.
Further reading[edit]
Ottaviani, G. (2014). Crib death – Sudden infant Death Syndrome (SIDS). Sudden infant and perinatal unexplained death: the pathologist's viewpoint. Berlin Heidelberg, Germany: Springer. ISBN 978-3-319-08346-9.
Joan Hodgman; Toke Hoppenbrouwers (2004). SIDS. Calabasas, Calif: Monte Nido Press. ISBN 0-9742663-0-2.
Lewak N. "Book Review: SIDS". Arch Pediatr Adolesc Med. 158 (4): 405. doi:10.1001/archpedi.158.4.405.
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ICD-10: R95
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OMIM: 272120
MeSH: D013398
DiseasesDB: 12633
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Coefficient of determination
From Wikipedia, the free encyclopedia
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Not to be confused with Coefficient of variation or Coefficient of correlation.
Ordinary least squares regression of Okun's law. Since the regression line does not miss any of the points by very much, the R2 of the regression is relatively high.
Comparison of the Theil–Sen estimator (black) and simple linear regression (blue) for a set of points with outliers. Because of the many outliers, neither of the regression lines fits the data well, as measured by the fact that neither gives a very high R2.
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).[1]
It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.[2][3][4]
There are several definitions of R2 that are only sometimes equivalent. One class of such cases includes that of simple linear regression where r2 is used instead of R2. When an intercept is included, then r2 is simply the square of the sample correlation coefficient (i.e., r) between the observed outcomes and the observed predictor values.[5] If additional regressors are included, R2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination ranges from 0 to 1.
Important cases where the computational definition of R2 can yield negative values, depending on the definition used, arise where the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data, and where linear regression is conducted without including an intercept. Additionally, negative values of R2 may occur when fitting non-linear functions to data.[6] In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion.[7]
Contents
[hide]
1 Definitions
1.1 Relation to unexplained variance
1.2 As explained variance
1.3 As squared correlation coefficient
2 Interpretation
2.1 In a non-simple linear model
2.2 Inflation of R2
2.3 Caveats
3 Extensions
3.1 Adjusted R2
3.2 Coefficient of partial determination
3.3 Generalized R2
4 Comparison with norm of residuals
5 See also
6 Notes
7 References
Definitions[edit]
R 2 = 1 − S S res S S tot {\displaystyle R^{2}=1-{\frac {\color {blue}{SS_{\text{res}}}}{\color {red}{SS_{\text{tot}}}}}}
The better the linear regression (on the right) fits the data in comparison to the simple average (on the left graph), the closer the value of R 2 {\displaystyle R^{2}} is to 1. The areas of the blue squares represent the squared residuals with respect to the linear regression. The areas of the red squares represent the squared residuals with respect to the average value.
A data set has n values marked y1,...,yn (collectively known as yi or as a vector y = [y1,...,yn]T), each associated with a predicted (or modeled) value f1,...,fn (known as fi, or sometimes ŷi, as a vector f).
Define the residuals as ei = yi − fi (forming a vector e).
If y ¯ {\displaystyle {\bar {y}}} is the mean of the observed data:
y ¯ = 1 n ∑ i = 1 n y i {\displaystyle {\bar {y}}={\frac {1}{n}}\sum _{i=1}^{n}y_{i}}
then the variability of the data set can be measured using three sums of squares formulas:
The total sum of squares (proportional to the variance of the data):
S S tot = ∑ i ( y i − y ¯ ) 2 , {\displaystyle SS_{\text{tot}}=\sum _{i}(y_{i}-{\bar {y}})^{2},}
The regression sum of squares, also called the explained sum of squares:
S S reg = ∑ i ( f i − y ¯ ) 2 , {\displaystyle SS_{\text{reg}}=\sum _{i}(f_{i}-{\bar {y}})^{2},}
The sum of squares of residuals, also called the residual sum of squares:
S S res = ∑ i ( y i − f i ) 2 = ∑ i e i 2 {\displaystyle SS_{\text{res}}=\sum _{i}(y_{i}-f_{i})^{2}=\sum _{i}e_{i}^{2}\,}
The most general definition of the coefficient of determination is
R 2 ≡ 1 − S S r e s S S t o t . {\displaystyle R^{2}\equiv 1-{SS_{\rm {res}} \over SS_{\rm {tot}}}.\,}
Relation to unexplained variance[edit]
Main article: Fraction of variance unexplained
In a general form, R2 can be seen to be related to the fraction of variance unexplained (FVU), since the second term compares the unexplained variance (variance of the model's errors) with the total variance (of the data):
R 2 = 1 − FVU {\displaystyle {\begin{aligned}R^{2}=1-{\text{FVU}}\end{aligned}}}
As explained variance[edit]
Suppose r = 0.7, meaning r2 = 0.49. This implies that 49% of the variability between the two variables has been accounted for, and the remaining 51% of the variability is still unaccounted for. In some cases the total sum of squares equals the sum of the two other sums of squares defined above,
S S res + S S reg = S S tot . {\displaystyle SS_{\text{res}}+SS_{\text{reg}}=SS_{\text{tot}}.\,}
See partitioning in the general OLS model for a derivation of this result for one case where the relation holds. When this relation does hold, the above definition of R2 is equivalent to
R 2 = S S reg S S tot = S S reg / n S S tot / n . {\displaystyle R^{2}={\frac {SS_{\text{reg}}}{SS_{\text{tot}}}}={\frac {SS_{\text{reg}}/n}{SS_{\text{tot}}/n}}.}
In this form R2 is expressed as the ratio of the explained variance (variance of the model's predictions, which is SSreg / n) to the total variance (sample variance of the dependent variable, which is SStot / n).
This partition of the sum of squares holds for instance when the model values ƒi have been obtained by linear regression. A milder sufficient condition reads as follows: The model has the form
f i = α + β q i {\displaystyle f_{i}=\alpha +\beta q_{i}\,}
where the qi are arbitrary values that may or may not depend on i or on other free parameters (the common choice qi = xi is just one special case), and the coefficients α and β are obtained by minimizing the residual sum of squares.
This set of conditions is an important one and it has a number of implications for the properties of the fitted residuals and the modelled values. In particular, under these conditions:
f ¯ = y ¯ . {\displaystyle {\bar {f}}={\bar {y}}.\,}
As squared correlation coefficient[edit]
In linear least squares regression with an estimated intercept term, R2 equals the square of the Pearson correlation coefficient between the observed y {\displaystyle y} and modeled (predicted) f {\displaystyle f} data values of the dependent variable.
In a univariate linear least squares regression, this is also equal to the squared Pearson correlation coefficient of the dependent y {\displaystyle y} and explanatory x {\displaystyle x} variables.
Under more general modeling conditions, where the predicted values might be generated from a model different from linear least squares regression, an R2 value can be calculated as the square of the correlation coefficient between the original y {\displaystyle y} and modeled f {\displaystyle f} data values. In this case, the value is not directly a measure of how good the modeled values are, but rather a measure of how good a predictor might be constructed from the modeled values (by creating a revised predictor of the form α + βƒi).[citation needed] According to Everitt (p. 78),[8] this usage is specifically the definition of the term "coefficient of determination": the square of the correlation between two (general) variables.
Interpretation[edit]
R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data.
Values of R2 outside the range 0 to 1 can occur where it is used to measure the agreement between observed and modeled values and where the "modeled" values are not obtained by linear regression and depending on which formulation of R2 is used. If the first formula above is used, values can be less than zero. If the second expression is used, values can be greater than one. Neither formula is defined for the case where y 1 = … = y n = y ¯ {\displaystyle y_{1}=\ldots =y_{n}={\bar {y}}} .
In all instances where R2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SSres. In this case R2 increases as we increase the number of variables in the model (R2 is monotone increasing with the number of variables included—i.e., it will never decrease). This illustrates a drawback to one possible use of R2, where one might keep adding variables (Kitchen sink regression) to increase the R2 value. For example, if one is trying to predict the sales of a model of car from the car's gas mileage, price, and engine power, one can include such irrelevant factors as the first letter of the model's name or the height of the lead engineer designing the car because the R2 will never decrease as variables are added and will probably experience an increase due to chance alone.
This leads to the alternative approach of looking at the adjusted R2. The explanation of this statistic is almost the same as R2 but it penalizes the statistic as extra variables are included in the model. For cases other than fitting by ordinary least squares, the R2 statistic can be calculated as above and may still be a useful measure. If fitting is by weighted least squares or generalized least squares, alternative versions of R2 can be calculated appropriate to those statistical frameworks, while the "raw" R2 may still be useful if it is more easily interpreted. Values for R2 can be calculated for any type of predictive model, which need not have a statistical basis.
In a non-simple linear model[edit]
Consider a linear model with more than a single explanatory variable, of the form
Y i = β 0 + ∑ j = 1 p β j X i , j + ε i , {\displaystyle Y_{i}=\beta _{0}+\sum _{j=1}^{p}\beta _{j}X_{i,j}+\varepsilon _{i},}
where, for the ith case, Y i {\displaystyle {Y_{i}}} is the response variable, X i , 1 , … , X i , p {\displaystyle X_{i,1},\dots ,X_{i,p}} are p regressors, and ε i {\displaystyle \varepsilon _{i}} is a mean zero error term. The quantities β 0 , … , β p {\displaystyle \beta _{0},\dots ,\beta _{p}} are unknown coefficients, whose values are estimated by least squares. The coefficient of determination R2 is a measure of the global fit of the model. Specifically, R2 is an element of [0, 1] and represents the proportion of variability in Yi that may be attributed to some linear combination of the regressors (explanatory variables) in X.[9]
R2 is often interpreted as the proportion of response variation "explained" by the regressors in the model. Thus, R2 = 1 indicates that the fitted model explains all variability in y {\displaystyle y} , while R2 = 0 indicates no 'linear' relationship (for straight line regression, this means that the straight line model is a constant line (slope = 0, intercept = y ¯ {\displaystyle {\bar {y}}} ) between the response variable and regressors). An interior value such as R2 = 0.7 may be interpreted as follows: "Seventy percent of the variance in the response variable can be explained by the explanatory variables. The remaining thirty percent can be attributed to unknown, lurking variables or inherent variability."
A caution that applies to R2, as to other statistical descriptions of correlation and association is that "correlation does not imply causation." In other words, while correlations may sometimes provide valuable clues in uncovering causal relationships among variables, a non-zero estimated correlation between two variables is not, on its own, evidence that changing the value of one variable would result in changes in the values of other variables. For example, the practice of carrying matches (or a lighter) is correlated with incidence of lung cancer, but carrying matches does not cause cancer (in the standard sense of "cause").
In case of a single regressor, fitted by least squares, R2 is the square of the Pearson product-moment correlation coefficient relating the regressor and the response variable. More generally, R2 is the square of the correlation between the constructed predictor and the response variable. With more than one regressor, the R2 can be referred to as the coefficient of multiple determination.
Inflation of R2[edit]
In least squares regression, R2 is weakly increasing with increases in the number of regressors in the model. Because increases in the number of regressors increase the value of R2, R2 alone cannot be used as a meaningful comparison of models with very different numbers of independent variables. For a meaningful comparison between two models, an F-test can be performed on the residual sum of squares, similar to the F-tests in Granger causality, though this is not always appropriate. As a reminder of this, some authors denote R2 by Rp2, where p is the number of columns in X (the number of explanators including the constant).
To demonstrate this property, first recall that the objective of least squares linear regression is:
min b S S res ( b ) ⇒ min b ∑ i ( y i − X i b ) 2 {\displaystyle \min _{b}SS_{\text{res}}(b)\Rightarrow \min _{b}\sum _{i}(y_{i}-X_{i}b)^{2}\,}
The optimal value of the objective is weakly smaller as additional columns of X {\displaystyle X} are added, by the fact that less constrained minimization leads to an optimal cost which is weakly smaller than more constrained minimization does. Given the previous conclusion and noting that S S t o t {\displaystyle SS_{tot}} depends only on y, the non-decreasing property of R2 follows directly from the definition above.
The intuitive reason that using an additional explanatory variable cannot lower the R2 is this: Minimizing S S res {\displaystyle SS_{\text{res}}} is equivalent to maximizing R2. When the extra variable is included, the data always have the option of giving it an estimated coefficient of zero, leaving the predicted values and the R2 unchanged. The only way that the optimization problem will give a non-zero coefficient is if doing so improves the R2.
Caveats[edit]
R2 does not indicate whether:
the independent variables are a cause of the changes in the dependent variable;
omitted-variable bias exists;
the correct regression was used;
the most appropriate set of independent variables has been chosen;
there is collinearity present in the data on the explanatory variables;
the model might be improved by using transformed versions of the existing set of independent variables;
there are enough data points to make a solid conclusion.
Extensions[edit]
Adjusted R2[edit]
See also: Effect size § Omega-squared (ω2)
The use of an adjusted R2 (one common notation is R ¯ 2 {\displaystyle {\bar {R}}^{2}} , pronounced "R bar squared"; another is R adj 2 {\displaystyle R_{\text{adj}}^{2}} ) is an attempt to take account of the phenomenon of the R2 automatically and spuriously increasing when extra explanatory variables are added to the model. It is a modification due to Henri Theil of R2 that adjusts for the number of explanatory terms in a model relative to the number of data points.[10] The adjusted R2 can be negative, and its value will always be less than or equal to that of R2. Unlike R2, the adjusted R2 increases only when the increase in R2 (due to the inclusion of a new explanatory variable) is more than one would expect to see by chance. If a set of explanatory variables with a predetermined hierarchy of importance are introduced into a regression one at a time, with the adjusted R2 computed each time, the level at which adjusted R2 reaches a maximum, and decreases afterward, would be the regression with the ideal combination of having the best fit without excess/unnecessary terms. The adjusted R2 is defined as
R ¯ 2 = 1 − ( 1 − R 2 ) n − 1 n − p − 1 = R 2 − ( 1 − R 2 ) p n − p − 1 {\displaystyle {\bar {R}}^{2}={1-(1-R^{2}){n-1 \over n-p-1}}={R^{2}-(1-R^{2}){p \over n-p-1}}}
where p is the total number of explanatory variables in the model (not including the constant term), and n is the sample size.
Adjusted R2 can also be written as
R ¯ 2 = 1 − S S res / df e S S tot / df t {\displaystyle {\bar {R}}^{2}={1-{SS_{\text{res}}/{\text{df}}_{e} \over SS_{\text{tot}}/{\text{df}}_{t}}}}
where dft is the degrees of freedom n– 1 of the estimate of the population variance of the dependent variable, and dfe is the degrees of freedom n – p – 1 of the estimate of the underlying population error variance.
The principle behind the adjusted R2 statistic can be seen by rewriting the ordinary R2 as
R 2 = 1 − VAR res VAR tot {\displaystyle R^{2}={1-{{\textit {VAR}}_{\text{res}} \over {\textit {VAR}}_{\text{tot}}}}}
where VAR res = S S res / n {\displaystyle {\text{VAR}}_{\text{res}}=SS_{\text{res}}/n} and VAR tot = S S tot / n {\displaystyle {\text{VAR}}_{\text{tot}}=SS_{\text{tot}}/n} are the sample variances of the estimated residuals and the dependent variable respectively, which can be seen as biased estimates of the population variances of the errors and of the dependent variable. These estimates are replaced by statistically unbiased versions: VAR res = S S res / ( n − p − 1 ) {\displaystyle {\text{VAR}}_{\text{res}}=SS_{\text{res}}/(n-p-1)} and VAR tot = S S tot / ( n − 1 ) {\displaystyle {\text{VAR}}_{\text{tot}}=SS_{\text{tot}}/(n-1)} .
Adjusted R2 does not have the same interpretation as R2—while R2 is a measure of fit, adjusted R2 is instead a comparative measure of suitability of alternative nested sets of explanators.[citation needed] As such, care must be taken in interpreting and reporting this statistic. Adjusted R2 is particularly useful in the feature selection stage of model building.
Coefficient of partial determination[edit]
See also: Partial correlation
The coefficient of partial determination can be defined as the proportion of variation that cannot be explained in a reduced model, but can be explained by the predictors specified in a full(er) model.[11][12][13] This coefficient is used to provide insight into whether or not one or more additional predictors may be useful in a more fully specified regression model.
The calculation for the partial r2 is relatively straight forward after estimating two models and generating the ANOVA tables for them. The calculation for the partial r2 is:
S S E reduced − S S E full S S E reduced {\displaystyle {\frac {SSE_{\text{reduced}}-SSE_{\text{full}}}{SSE_{\text{reduced}}}}}
which is analogous to the usual coefficient of determination
S S T − S S E S S T . {\displaystyle {\frac {SST-SSE}{SST}}.}
Generalized R2[edit]
In the case of logistic regression, usually fit by maximum likelihood, there are several choices of Pseudo-R2.
One is the generalized R2 was originally proposed by Cox & Snell,[14] and independently by Magee:[15]
R 2 = 1 − ( L ( 0 ) L ( θ ^ ) ) 2 / n {\displaystyle R^{2}=1-\left({L(0) \over L({\hat {\theta }})}\right)^{2/n}}
where L(0) is the likelihood of the model with only the intercept, L ( θ ^ ) {\displaystyle {L({\hat {\theta }})}} is the likelihood of the estimated model (i.e., the model with a given set of parameter estimates) and n is the sample size.
Nagelkerke[16] noted that it had the following properties:
It's consistent with the classical coefficient of determination when both can be computed;
Its value is maximised by the maximum likelihood estimation of a model;
It is asymptotically independent of the sample size;
The interpretation is the proportion of the variation explained by the model;
The values are between 0 and 1, with 0 denoting that model does not explain any variation and 1 denoting that it perfectly explains the observed variation;
It does not have any unit.
However, in the case of a logistic model, where L ( θ ^ ) {\displaystyle L({\hat {\theta }})} cannot be greater than 1, R1 is between 0 and R max 2 = 1 − ( L ( 0 ) ) 2 / n {\displaystyle R_{\max }^{2}=1-(L(0))^{2/n}} : thus, Nagelkerke suggested the possibility to define a scaled R2 as R²/R2max.[17]
Comparison with norm of residuals[edit]
Occasionally, the norm of residuals is used for indicating goodness of fit. This term is calculated as the square-root of the sum of squared residuals:
norm of residuals = S S res = ∥ e ∥ . {\displaystyle {\text{norm of residuals}}={\sqrt {SS_{\text{res}}}}=\|e\|.}
Both R2 and the norm of residuals have their relative merits. For least squares analysis R2 varies between 0 and 1, with larger numbers indicating better fits and 1 represents a perfect fit. Norm of residuals varies from 0 to infinity with smaller numbers indicating better fits and zero indicating a perfect fit. One advantage and disadvantage of R2 is the S S tot {\displaystyle SS_{\text{tot}}} term acts to normalize the value. If the yi values are all multiplied by a constant, the norm of residuals will also change by that constant but R2 will stay the same. As a basic example, for the linear least squares fit to the set of data:
x = 1 , 2 , 3 , 4 , 5 {\displaystyle x=1,\ 2,\ 3,\ 4,\ 5}
y = 1.9 , 3.7 , 5.8 , 8.0 , 9.6 {\displaystyle y=1.9,\ 3.7,\ 5.8,\ 8.0,\ 9.6}
R2 = 0.998, and norm of residuals = 0.302. If all values of y are multiplied by 1000 (for example, in an SI prefix change), then R2 remains the same, but norm of residuals = 302.
Another way to examine goodness of fit would be to examine residuals as a function of x. Other single parameter indicators include the standard deviation of the residuals, or the RMSE of the residuals. These would have values of 0.151 and 0.174 respectively for the above example given that the fit was linear with an unforced intercept.[18]
See also[edit]
Fraction of variance unexplained
Goodness of fit
Nash–Sutcliffe model efficiency coefficient (hydrological applications)
Pearson product-moment correlation coefficient
Proportional reduction in loss
Regression model validation
Root mean square deviation
t-test of H 0 : R 2 = 0. {\displaystyle H_{0}\colon R^{2}=0.}
Notes[edit]
Jump up ^ Coefficient of Determination definition, Statrek website
Jump up ^ Steel, R. G. D.; Torrie, J. H. (1960). Principles and Procedures of Statistics with Special Reference to the Biological Sciences. McGraw Hill.
Jump up ^ Glantz, Stanton A.; Slinker, B. K. (1990). Primer of Applied Regression and Analysis of Variance. McGraw-Hill. ISBN 0-07-023407-8.
Jump up ^ Draper, N. R.; Smith, H. (1998). Applied Regression Analysis. Wiley-Interscience. ISBN 0-471-17082-8.
Jump up ^ Devore, Jay L. (2011). Probability and Statistics for Engineering and the Sciences (8th ed.). Boston, MA: Cengage Learning. pp. 508–510. ISBN 0-538-73352-7.
Jump up ^ Colin Cameron, A.; Windmeijer, Frank A.G. (1997). "An R-squared measure of goodness of fit for some common nonlinear regression models". Journal of Econometrics. 77 (2): 1790–2. doi:10.1016/S0304-4076(96)01818-0.
Jump up ^ Imdadullah, Muhammad. "Coefficient of Determination". itfeature.com.
Jump up ^ Everitt, B. S. (2002). Cambridge Dictionary of Statistics (2nd ed.). CUP. ISBN 0-521-81099-X.
Jump up ^ Computing Adjusted R2 for Polynomial Regressions
Jump up ^ Theil, Henri (1961). Economic Forecasts and Policy. Holland, Amsterdam: North. [page needed]
Jump up ^ Richard Anderson-Sprecher, "Model Comparisons and R2", The American Statistician, Volume 48, Issue 2, 1994, pp. 113–117.
Jump up ^ (generalized to Maximum Likelihood) N. J. D. Nagelkerke, "A Note on a General Definition of the Coefficient of Determination", Biometrika, Vol. 78, No. 3. (Sep., 1991), pp. 691–692.
Jump up ^ "R implementation of coefficient of partial determination"
Jump up ^ Cox, D. D.; Snell, E. J. (1989). The Analysis of Binary Data (2nd ed.). Chapman and Hall.
Jump up ^ Magee, L. (1990). "R2 measures based on Wald and likelihood ratio joint significance tests". The American Statistician. 44. pp. 250–3. doi:10.1080/00031305.1990.10475731.
Jump up ^ Nagelkerke, Nico J. D. (1992). Maximum Likelihood Estimation of Functional Relationships, Pays-Bas. Lecture Notes in Statistics. 69. ISBN 0-387-97721-X.
Jump up ^ Nagelkerke, N. J. D. (1991). "A Note on a General Definition of the Coefficient of Determination". Biometrika. 78 (3): 691–2. JSTOR 2337038. doi:10.1093/biomet/78.3.691.
Jump up ^ OriginLab webpage, http://www.originlab.com/doc/Origin-Help/LR-Algorithm. Retrieved February 9, 2016.
References[edit]
Gujarati, Damodar N.; Porter, Dawn C. (2009). Basic Econometrics (Fifth ed.). New York: McGraw-Hill/Irwin. pp. 73–78. ISBN 978-0-07-337577-9.
Kmenta, Jan (1986). Elements of Econometrics (Second ed.). New York: Macmillan. pp. 240–243. ISBN 0-02-365070-2.
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