Question

Problem 1 [9 points]. Sickle cell disease (SCD) is a classification of disorders that affect red blood cells such that they distort them into the shape of a crescent or sickle shape. Data was collected on age and prevalence of sickle cell disease of children, which we will use to examine any potential association between age and disease prevalance. The probabilities of each category can be estimated from the data by taking the relative frequency. For example, the probability that a child is 1-2 years old and is positive for sickle cell disease from this population is estimated to be 8/225, where 225 is the total number of children observed The two-way contingency table of counts is displayed below Age (Years) Positive for SCD Negative for SCD 17 76 45 19 36 16 3-4 5-6 Causing lPathogens Isolated from Febrile Children with and without Sickle Cell Disease in Kano, Nigeria, Feb. 2018 available here. a) (3 points) Represent the information appropriately in a tree diagram with the first set of branches representing age groups and secondary set of branches representing chance of sickle cell disease

Answer 1

a)

Age(Years)	Positive for SCD	likelihood	Negative for SCD	likelihood
<1	8	0.035	17	0.075
1-2	36	0.160	76	0.337
3-4	16	0.071	45	0.200
5-6	8	0.035	19	0.084
TOTAL	68	0.301	157	0.696

TREE 1-2 3-4 5-6 0.075 0.035 0.337 0.160 0.200 0.071 0.084 0.035

b) by using the law of total likelihood from above tree diagram the prevalence of sickle cell disease(SCD) Iin the 225 children observed in the study

from above table

total likelihood for positive = 0.301

number of childrens = 225

prevalence of sickle cell disease(SCD) =  total likelihood for positive x number of childrens

= 0.301 x 225 = 67.725 i.e 68

from tree diagram

the total likelihood for positive = 0.035+0.160+0.071+0.035 = 0.301

number of childrens = 225

prevalence of sickle cell disease(SCD) =  total likelihood for positive x number of childrens

= 0.301 x 225 = 67.725 i.e 68

c)

	Positive for SCD	Positive for SCD	Negative for SCD	Total
<1	watched	8	17	25
	anticipated	7.56	17.44	25.00
	(O – E)	0.44	-0.44	0.00
	(O – E)^2 / E	0.03	0.01	0.04
	% of chisquare	3.7%	1.6%	5.4%

	Positive for SCD	Positive for SCD	Negative for SCD	Total
1-2	watched	36	76	112
	anticipated	33.85	78.15	112.00
	(O – E)	2.15	-2.15	0.00
	(O – E)^2 / E	0.14	0.06	0.20
	% of chi square	19.6%	8.5%	28.0%

	Positive for SCD	Positive for SCD	Negative for SCD	Total
3-4	watched	16	45	61
	anticipated	18.44	42.56	61.00
	(O – E)	-2.44	2.44	0.00
	(O – E)^2 / E	0.32	0.14	0.46
	% of chi square	46.0%	19.9%	66.0%

	Positive for SCD	Positive for SCD	Negative for SCD	Total
5-6	watched	8	19	27
	anticipated	8.16	18.84	27.00
	(O – E)	-0.16	0.16	0.00
	(O – E)^2 / E	0.00	0.00	0.00
	% of chi square	0.4%	0.2%	0.6%

	Positive for SCD	Positive for SCD	Negative for SCD	Total
TOTAL	watched	68	157	225
	anticipated	68.00	18.84	27.00
	(O – E)	0.00	0.00	0.00
	(O – E)^2 / E	0.49	0.21	0.70
	% of chi square	69.8%	30.2%	100%

Hence chi-square = 0.70

degrees of freedom = 3

p-esteem = 0.8734

Since the p-esteem > 0.05, it gives the idea that age and predominance of Sickle cell disease are not independent.