The objective of this research is to propose and to validate two different statistical techniques to test the hypothesis of an association between surnames and pathologies, in a population participating in a screening procedure for a given pathology. We propose two statistical methods: a first technique is based on the rarefaction method, and second one is based on the principle of resampling, and it can be considered a special case of a randomisation test. Both the techniques are applied to a data set of babies screened for congenital hypothyroidism (CH), and they gave similar results. The large overlapping of the results seems to suggest a substantial validity of the proposed techniques

Marco B. L. Rocchi

ROCCHI, MARCO BRUNO LUIGI

Archivio istituzionale della ricerca - Università di Urbino

Surnames as markers of pathologies- Two statistical techniques and their applications

Hrčak - Portal of scientific journals of Croatia

Coll. Antropol. 30 (2006) 2: 383–385Original scientific paperSurnames as Markers of Pathologies – TwoStatistical Techniques and Their ApplicationsMarco B. L. RocchiInstitute of Biomathematics, Faculty of Pharmacy, University of Urbino »Carlo Bo«, Urbino, ItalyA B S T R A C TThe objective of this research is to propose and to validate two different statistical techniques to test the hypothesis ofan association between surnames and pathologies, in a population participating in a screening procedure for a given pa-thology. We propose two statistical methods: a first technique is based on the rarefaction method, and second one is basedon the principle of resampling, and it can be considered a special case of a randomisation test. Both the techniques areapplied to a data set of babies screened for congenital hypothyroidism (CH), and they gave similar results. The largeoverlapping of the results seems to suggest a substantial validity of the proposed techniques.Key words: screening, surnames, congenital hypothyroidismIntroductionIn societies where surnames pass from father to chil-dren, the Y chromosome is passed down in the same waythat a surname.Therefore, we can consider surnames as genetic char-acter linked to the Y chromosome1. The difference lies inthe fact that although all of the offspring get the sur-name, only half of them – the sons – get the Y chromo-some.Hence, surnames have been used effectively as mark-ers of biodiversity among different populations, ratherthan other biological markers that are more complicatedboth to obtain and to study, such as hypervariable regionof mtDNA2. There are already several applications forsurnames in anthropology and biodemography, while thepossible role of surnames in genetic analysis has only re-cently been discussed by Jobling3.A detailed review regarding the use of surnames inepidemiological research has been proposed by Cook etal.4. They considered two different applications for sur-names, both as indicators of ethnic or national origin,and as part of the identifying information needed for re-cord linkage or follow-up studies.More recently, several authors have used surnames asmarkers for pathologies5–10, but these authors based theirworks on different assumptions: (a) surnames are usefultools for the identification of ethnicity in multiethnicpopulations. In this case, surnames provide an easy andeffective means of subdivision for epidemiological pur-poses7; (b) the role of surnames as pathology markersmay be explained as a consequence of the founder effect,especially in the case of geographical (and also genetic)isolates; (c) from a broader standpoint, surnames can beconsidered »alleles« of a genetic locus that is associatedwith another genetic locus coding for a pathology. As anexample of the last consideration, a surname analysis ofover 40,000 Wisconsin cancer mortalities over the period1979–1985 was performed by Cleek8 to demonstrate thegenetic component associated with various major cancers(i.e. male and female leukaemia, and male lung cancer).In this paper, we propose two different statisticaltechniques to test the hypothesis that some surnamesare linked to certain pathologies.Obviously, this approach doesn’t take into account thefactor that probably is the most important in case of ge-netic disorders of recessive inheritance: the risk of thedisease is high in familiar groups with high degree of con-sanguinity, where individuals are sharing the same sur-names. Nevertheless, the approaches presented in thisstudy should actually be interpreted as an exploratorytool to detect the association between surnames and pa-thologies, without taking into consideration the patho-logical model of the disease.Moreover, we only consider the case of pathologiesthat are screened for.383Received for publication April 19, 2004Materials and MethodsThe first statistical technique that we propose isbased on the rarefaction method, developed by San-ders10, and corrected and modified by Simberloff11. Thistechnique is usually applied in biodiversity analysis.The second statistical technique is an adjustment of aresampling method (i.e. a randomisation test).The rarefaction methodThis technique is based on the assumption that weknow the surname distribution of the population partici-pating in the screening procedure. More specifically, weknow:N – number of screened people;S – number of surnames in the screened population;n – number of subjects that test positive in thescreening (n<N);x – number of surnames in the set of positivesubjects (xn);Ni – number of subjects in the population, with thei-th surname (i=1,2,…,S), so that: N NiiS 1.Both the expected value E(x) and the variance Var(x)of x can be obtained using the rarefaction method:E xN NnNniiS( ) 11Var xNnN NnN NniiSi( )111 !!"!!## NnN N Nni j2 N NnN NnNni jj #$%!!&!!iSiS111Note that E(x) can be interpreted as the number ofsurnames expected in a sample of size n, randomly ex-tracted from the known distribution of surnames.Once the E(x) and Var(x) are known, we can easilyperform a z-test; if the observed value of x is significantlysmaller than the expected value of x, then we can rejectthe null hypothesis.The statistics zx E xVar x ( )( )is approximately distrib-uted as a standard normal distribution under the nullhypothesis. The test can be performed as a one-tailedtest, because it is reasonable to fix the alternative hy-pothesis unidirectionally.The decision rule (at a 5% significance level) is: ifz<–1.645 we can reject the null hypothesis and we canconclude that there is an association between surnamesand the given pathology.The randomisation methodOnce the surname distribution in the population ofsubjects participating in the screening is known, we canrandomly extract a high number of samples (at least1,000) having the same size as the subpopulation thattest positive in the screening (this procedure is namedresampling).For each sample the number of observed surnames iscounted. We can then arrange all the samples accordingto the number of recorded surnames. Among these sam-ples, we record the position occupied by the positivesubpopulation. The decision rule is then applied, i.e.: ifthe positive subpopulation occupies a position within the5-th percentile (one-tailed test) we can reject the null hy-pothesis and conclude that there is an association be-tween surnames and the pathology. The detailed algo-rithm for this randomisation test is the following:• step 1: compute the number of surnames in the posi-tive subpopulation (denote this number with the sym-bol x* and the size of the positive subpopulation withn);• step 2: randomly extract k samples (with k=1,000) ofsize n from the population (of size N>n);• step 3: for each of the k samples, compute the numberof observed surnames (denote this number with thesymbol xk);• step 4: arrange the (k+1) results (i.e., the x* and all thexk) in an increasing order, and denote the ordered xkwith the symbol x(k));• step 5: note the position r of x*;• step 6: if r<k×0.05 we can reject the null hypothesis;• step 7: compute the p-value as p=r/k.ResultsData setWe have considered the complete database of neonatalscreening for Congenital Hypothyroidism (CH) in theMarche region (Italy) in the 16-year period 1981–1996.In this period, N=186,690 newborns participated inthe screening and n=92 tested positive.Results of rarefaction methodWe observed x=88 different surnames in the set of n=92 babies testing positive for CH.The expected number of surnames under the null hy-pothesis (i.e., no association between surname and pa-thology) was E(x)=89.9, and the variance of x was Var(x)=1.83.The test statistics z results z  88 89 91 831 404... .According to the decision rule, we cannot reject thenull hypothesis, and the observed value of probabilityM. B. L. Rocchi: Surnames as Markers of Pathologies, Coll. Antropol. 30 (2006) 2: 383–385384(p-value) resulting from the statistical table of the nor-mal gaussian distribution is p=0.0808.Results of randomisation methodWe denoted with x*=88 the number of different sur-names out of n=92 babies testing positive for CH.We performed k=10,000 resampling and for eachsample we computed the number of surnames (xk). Wethen rearranged the samples in increasing order (x(k)).The position of x* among the x(k) values coming from theresampling procedure was r=714.Since 714 is greater than 500 (=10,000×0.05), wecannot reject the null hypothesis, and the observed valueof probability (p-value) was: p=0.0714.Discussion and ConclusionIn this paper we proposed and analysed two differentstatistical techniques able to detect an association be-tween surnames and pathologies, in the particular caseof diseases for which a screening program is developed.The first technique is based on the rarefaction me-thod, while the second one can be considered a specialcase of the randomisation test.When these techniques were applied to a data set ofbabies participating in a regional screening for congeni-tal hypothyroidism (CH) the results appeared largelyoverlapping. Hence, the proposed methods appear to besubstantially valid.However, it should be emphasized that, in order to ap-ply these techniques, the knowledge of the surname dis-tribution in the screened population is necessary.AcknowledgementsThe author wishes to thank the anonymous refereefor his helpful suggestions in improving the quality ofthe paper.R E F E R E N C E S1. CHEN, K. H., L. L. CAVALLI-SFORZA, Hum. Biol., 55 (1983) 367.— 2. STENICO, M., L. NIGRO, G. BERTORELLE, F. CALAFELL, M. CA-PITANIO, C. CORRAIN, G. BARBUJANI, Am. J. Hum. Genet., 59 (1996)1363. — 3. JOBLING, M. A., Trends Genet., 17 (2001) 353. — 4. COOK,D., D. HEWITT, J. MILNER, Am. J. Epidemiol., 95 (1972) 38. — 5. RU-DAN, I., G. N. RANZANI, M. STRNAD, A. VORKO-JOVIC, V. JOHN, J.UNUSIC, D. IVANKOVIC, R. STEVANOVIC, S. VULETIC, P. RUDAN,Coll. Antropol., 23 (1999) 557. — 6. DE SILVESTRI, A., C. R. GUGLIEL-MINO, Hum. Biol., 72 (2000) 573. — 7. TORRINGTON, M., P. A. BRINK,S. Afr. Med. J., 77 (1990) 289. — 8. CLEEK, R. K., Hum. Biol., 61 (1989)195. — 9. GARZA-CHAPA, R., M. DE LOS ANGELES ROJAS-ALVARA-DO, R. M. CERDA-FLORES, Am. J. Hum. Biol., 12 (2000) 721. — 10. RU-DAN, I., Hum. Biol., 73 (2001) 871. — 11. SANDERS, H. L., Am. Nat., 102(1968) 243. — 12. SIMBERLOFF, D. S., Am. Nat., 106 (1972) 414.M. B. L. RocchiInstitute of Biomathematics, Faculty of Pharmacy, University of Urbino »Carlo Bo«, Loc. Crocicchia, 61029 Urbino, Italye-mail: m.rocchi@uniurb.itPREZIMENA KAO BILJEZI BOLESTI – DVIJE STATISTI^KE METODE I NJIHOVA PRIMJENAS A @ E T A KCilj ovog istra`ivanja je predlo`iti i procijeniti dvije razli~ite statisti~ke metode za testiranje hipoteze povezanostiprezimena i bolesti u populaciji testiranoj za odre|enu bolest. Mi predla`emo dvije statisti~ke metode: prva metoda setemelji na rarefakcijskoj metodi a druga na ponovljenom odabiranju uzoraka i mo`e se smatrati posebnim slu~ajemtesta nasumi~nog odabira. Obje metode primijenjene su na podacima o dojen~adi testiranim na uro|eni hipotireoizam(CH) i dale su sli~ne rezultate. Velika podudarnost rezultata upu}uje na zna~ajnu preciznost predlo`enih metoda.M. B. L. Rocchi: Surnames as Markers of Pathologies, Coll. Antropol. 30 (2006) 2: 383–385385

Surnames as Markers of Pathologies – Two Statistical Techniques and Their Applications

HRČAK - Portal of Croatian Scientific and Professional Journals

Coll. Antropol. 30 (2006) 2: 383–385Original scientific paperSurnames as Markers of Pathologies – TwoStatistical Techniques and Their ApplicationsMarco B. L. RocchiInstitute of Biomathematics, Faculty of Pharmacy, University of Urbino »Carlo Bo«, Urbino, ItalyA B S T R A C TThe objective of this research is to propose and to validate two different statistical techniques to test the hypothesis ofan association between surnames and pathologies, in a population participating in a screening procedure for a given pa-thology. We propose two statistical methods: a first technique is based on the rarefaction method, and second one is basedon the principle of resampling, and it can be considered a special case of a randomisation test. Both the techniques areapplied to a data set of babies screened for congenital hypothyroidism (CH), and they gave similar results. The largeoverlapping of the results seems to suggest a substantial validity of the proposed techniques.Key words: screening, surnames, congenital hypothyroidismIntroductionIn societies where surnames pass from father to chil-dren, the Y chromosome is passed down in the same waythat a surname.Therefore, we can consider surnames as genetic char-acter linked to the Y chromosome1. The difference lies inthe fact that although all of the offspring get the sur-name, only half of them – the sons – get the Y chromo-some.Hence, surnames have been used effectively as mark-ers of biodiversity among different populations, ratherthan other biological markers that are more complicatedboth to obtain and to study, such as hypervariable regionof mtDNA2. There are already several applications forsurnames in anthropology and biodemography, while thepossible role of surnames in genetic analysis has only re-cently been discussed by Jobling3.A detailed review regarding the use of surnames inepidemiological research has been proposed by Cook etal.4. They considered two different applications for sur-names, both as indicators of ethnic or national origin,and as part of the identifying information needed for re-cord linkage or follow-up studies.More recently, several authors have used surnames asmarkers for pathologies5–10, but these authors based theirworks on different assumptions: (a) surnames are usefultools for the identification of ethnicity in multiethnicpopulations. In this case, surnames provide an easy andeffective means of subdivision for epidemiological pur-poses7; (b) the role of surnames as pathology markersmay be explained as a consequence of the founder effect,especially in the case of geographical (and also genetic)isolates; (c) from a broader standpoint, surnames can beconsidered »alleles« of a genetic locus that is associatedwith another genetic locus coding for a pathology. As anexample of the last consideration, a surname analysis ofover 40,000 Wisconsin cancer mortalities over the period1979–1985 was performed by Cleek8 to demonstrate thegenetic component associated with various major cancers(i.e. male and female leukaemia, and male lung cancer).In this paper, we propose two different statisticaltechniques to test the hypothesis that some surnamesare linked to certain pathologies.Obviously, this approach doesn’t take into account thefactor that probably is the most important in case of ge-netic disorders of recessive inheritance: the risk of thedisease is high in familiar groups with high degree of con-sanguinity, where individuals are sharing the same sur-names. Nevertheless, the approaches presented in thisstudy should actually be interpreted as an exploratorytool to detect the association between surnames and pa-thologies, without taking into consideration the patho-logical model of the disease.Moreover, we only consider the case of pathologiesthat are screened for.383Received for publication April 19, 2004Materials and MethodsThe first statistical technique that we propose isbased on the rarefaction method, developed by San-ders10, and corrected and modified by Simberloff11. Thistechnique is usually applied in biodiversity analysis.The second statistical technique is an adjustment of aresampling method (i.e. a randomisation test).The rarefaction methodThis technique is based on the assumption that weknow the surname distribution of the population partici-pating in the screening procedure. More specifically, weknow:N – number of screened people;S – number of surnames in the screened population;n – number of subjects that test positive in thescreening (n<N);x – number of surnames in the set of positivesubjects (xn);Ni – number of subjects in the population, with thei-th surname (i=1,2,…,S), so that: N NiiS  1 .Both the expected value E(x) and the variance Var(x)of x can be obtained using the rarefaction method:E xN NnNniiS( )  11Var xNnN NnN NniiSi( ) 111 !!"!!## NnN N Nni j2 N NnN NnNni jj # $%!!&!!iSiS111Note that E(x) can be interpreted as the number ofsurnames expected in a sample of size n, randomly ex-tracted from the known distribution of surnames.Once the E(x) and Var(x) are known, we can easilyperform a z-test; if the observed value of x is significantlysmaller than the expected value of x, then we can rejectthe null hypothesis.The statistics zx E xVar x  ( )( )is approximately distrib-uted as a standard normal distribution under the nullhypothesis. The test can be performed as a one-tailedtest, because it is reasonable to fix the alternative hy-pothesis unidirectionally.The decision rule (at a 5% significance level) is: ifz<–1.645 we can reject the null hypothesis and we canconclude that there is an association between surnamesand the given pathology.The randomisation methodOnce the surname distribution in the population ofsubjects participating in the screening is known, we canrandomly extract a high number of samples (at least1,000) having the same size as the subpopulation thattest positive in the screening (this procedure is namedresampling).For each sample the number of observed surnames iscounted. We can then arrange all the samples accordingto the number of recorded surnames. Among these sam-ples, we record the position occupied by the positivesubpopulation. The decision rule is then applied, i.e.: ifthe positive subpopulation occupies a position within the5-th percentile (one-tailed test) we can reject the null hy-pothesis and conclude that there is an association be-tween surnames and the pathology. The detailed algo-rithm for this randomisation test is the following:• step 1: compute the number of surnames in the posi-tive subpopulation (denote this number with the sym-bol x* and the size of the positive subpopulation withn);• step 2: randomly extract k samples (with k=1,000) ofsize n from the population (of size N>n);• step 3: for each of the k samples, compute the numberof observed surnames (denote this number with thesymbol xk);• step 4: arrange the (k+1) results (i.e., the x* and all thexk) in an increasing order, and denote the ordered xkwith the symbol x(k));• step 5: note the position r of x*;• step 6: if r<k×0.05 we can reject the null hypothesis;• step 7: compute the p-value as p=r/k.ResultsData setWe have considered the complete database of neonatalscreening for Congenital Hypothyroidism (CH) in theMarche region (Italy) in the 16-year period 1981–1996.In this period, N=186,690 newborns participated inthe screening and n=92 tested positive.Results of rarefaction methodWe observed x=88 different surnames in the set of n=92 babies testing positive for CH.The expected number of surnames under the null hy-pothesis (i.e., no association between surname and pa-thology) was E(x)=89.9, and the variance of x was Var(x)=1.83.The test statistics z results z    88 89 91 831 404... .According to the decision rule, we cannot reject thenull hypothesis, and the observed value of probabilityM. B. L. Rocchi: Surnames as Markers of Pathologies, Coll. Antropol. 30 (2006) 2: 383–385384(p-value) resulting from the statistical table of the nor-mal gaussian distribution is p=0.0808.Results of randomisation methodWe denoted with x*=88 the number of different sur-names out of n=92 babies testing positive for CH.We performed k=10,000 resampling and for eachsample we computed the number of surnames (xk). Wethen rearranged the samples in increasing order (x(k)).The position of x* among the x(k) values coming from theresampling procedure was r=714.Since 714 is greater than 500 (=10,000×0.05), wecannot reject the null hypothesis, and the observed valueof probability (p-value) was: p=0.0714.Discussion and ConclusionIn this paper we proposed and analysed two differentstatistical techniques able to detect an association be-tween surnames and pathologies, in the particular caseof diseases for which a screening program is developed.The first technique is based on the rarefaction me-thod, while the second one can be considered a specialcase of the randomisation test.When these techniques were applied to a data set ofbabies participating in a regional screening for congeni-tal hypothyroidism (CH) the results appeared largelyoverlapping. Hence, the proposed methods appear to besubstantially valid.However, it should be emphasized that, in order to ap-ply these techniques, the knowledge of the surname dis-tribution in the screened population is necessary.AcknowledgementsThe author wishes to thank the anonymous refereefor his helpful suggestions in improving the quality ofthe paper.R E F E R E N C E S1. CHEN, K. H., L. L. CAVALLI-SFORZA, Hum. Biol., 55 (1983) 367.— 2. STENICO, M., L. NIGRO, G. BERTORELLE, F. CALAFELL, M. CA-PITANIO, C. CORRAIN, G. BARBUJANI, Am. J. Hum. Genet., 59 (1996)1363. — 3. JOBLING, M. A., Trends Genet., 17 (2001) 353. — 4. COOK,D., D. HEWITT, J. MILNER, Am. J. Epidemiol., 95 (1972) 38. — 5. RU-DAN, I., G. N. RANZANI, M. STRNAD, A. VORKO-JOVIC, V. JOHN, J.UNUSIC, D. IVANKOVIC, R. STEVANOVIC, S. VULETIC, P. RUDAN,Coll. Antropol., 23 (1999) 557. — 6. DE SILVESTRI, A., C. R. GUGLIEL-MINO, Hum. Biol., 72 (2000) 573. — 7. TORRINGTON, M., P. A. BRINK,S. Afr. Med. J., 77 (1990) 289. — 8. CLEEK, R. K., Hum. Biol., 61 (1989)195. — 9. GARZA-CHAPA, R., M. DE LOS ANGELES ROJAS-ALVARA-DO, R. M. CERDA-FLORES, Am. J. Hum. Biol., 12 (2000) 721. — 10. RU-DAN, I., Hum. Biol., 73 (2001) 871. — 11. SANDERS, H. L., Am. Nat., 102(1968) 243. — 12. SIMBERLOFF, D. S., Am. Nat., 106 (1972) 414.M. B. L. RocchiInstitute of Biomathematics, Faculty of Pharmacy, University of Urbino »Carlo Bo«, Loc. Crocicchia, 61029 Urbino, Italye-mail: m.rocchi@uniurb.itPREZIMENA KAO BILJEZI BOLESTI – DVIJE STATISTI^KE METODE I NJIHOVA PRIMJENAS A @ E T A KCilj ovog istra`ivanja je predlo`iti i procijeniti dvije razli~ite statisti~ke metode za testiranje hipoteze povezanostiprezimena i bolesti u populaciji testiranoj za odre|enu bolest. Mi predla`emo dvije statisti~ke metode: prva metoda setemelji na rarefakcijskoj metodi a druga na ponovljenom odabiranju uzoraka i mo`e se smatrati posebnim slu~ajemtesta nasumi~nog odabira. Obje metode primijenjene su na podacima o dojen~adi testiranim na uro|eni hipotireoizam(CH) i dale su sli~ne rezultate. Velika podudarnost rezultata upu}uje na zna~ajnu preciznost predlo`enih metoda.M. B. L. Rocchi: Surnames as Markers of Pathologies, Coll. Antropol. 30 (2006) 2: 383–385385

Surnames as Markers of Pathologies – Two Statistical Techniques and Their Applications

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