Int. J. Pure Appl. Sci. Technol., 10(1) (2012), pp. 27-36

International Journal of Pure and Applied Sciences and Technology ISSN 2229 - 6107 Available online at www.ijopaasat.in Research Paper

Error Detection in Outpatients’ Age Data Using Demographic Techniques Yusuf Bello Department of Mathematics and Statistics, Hassan Usman Katsina, Polytechnic, Katsina, Nigeria Corresponding author, e-mail: ([email protected]) (Received: 23-3-12; Accepted: 12-5-12)

Abstract: Age is an important variable in epidemiological study and an invariable part of community base-study reports. Demographic data are usually classified by age and sex, where errors in age reporting are more frequent than errors in sex reporting. This research paper is purposely prepared to evaluate the accuracy of age reporting by the outpatients in General Hospital Dutsin-ma, Katsina state, Nigeria, in January 2012 using demographic techniques. The techniques include Whipple’s index which indicates the extent to which age data show systematic heaping on particular ages such as those ending with ‘0’ and ‘5’, Myer’s blended index that measures the extend of digit preference for all the digits and age-sex accuracy index that determine the accuracy of age reporting. The result of the work has shown very rough age data reporting for both male and female outpatients. For the Myer’s index, about 86 percent of male outpatients and 88 percent of female outpatients reported their ages with incorrect final digits. The most preferred final digits are ‘5’ and ‘0’, while the most avoided final digit by both sexes is ‘1’. Similarly, the Whipple’s index has also qualified the data as very rough by identifying a considerable heaping at ages ending with ‘5’ and ‘0’. Furthermore, the calculated age-sex accuracy index is 156.8 that qualified the age data highly inaccurate according to the United Nations scaling. The inaccuracy is more critical in female age data since the sum of the absolute deviation of the female age ratio from the unity (100) is almost twice that for male age ratio. Both sexes’ age data have fluctuations at the higher ages, although that for female age data is more noticeable. The evaluation of the outpatients’ age data using the demographic techniques has finally qualified the data inaccurate as the results of systematic age heaping and digit preference.

Keywords: Outpatient’s age data, Whipple’s index, Myer’s index, age-sex accuracy index.

1. Introduction: Age is an important study variable in demographic, epidemiological and clinical studies. Epidemiology has been described as the study of the distribution of health and diseases in groups of people and the study of the factors that influence this distribution (Smaller, 2004). From this, it is

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clear that all the bio-statistical and epidemiological studies must require accurate age grouping of patients (Johannes and Polly, 1970). In clinical studies age is one of the most commonly assessed variables, and other parameters are often analyzed and results interpreted in relation to age. When study subjects are divided into different age groups, those who provide incorrect age could be put into a wrong age subgroup and this may affect results. In the decision-making process at the level of the physician–patient encounter, the correct age of the patient is important because many decisions are age-sensitive and misrepresentation of age may lead to inappropriate action. For example, a screening mammography is recommended to start at age 50 and patient’s inaccurate age may result in having either an unnecessary or delayed test (Denic et. al, 2003). Therefore, modern healthcare services must require accurate age-sex data for appropriate decisions, allocation of staff, disease surveillance and in the provision of required drugs and medications. The importance of accurate age-sex data in demographic analysis cannot be overemphasized. National development plans for the provision of such need as housing, food, education, health, employment, manpower, and etc, depend on the relevant socio-demographic statistics classified by age and sex. Most population analysis like fertility and mortality are either age-sex dependent or age sex selective (Lerche, 1983 and Kpedekpo, 1982). The quality of age data is important because age-sex distribution is not only an invariable part of the survey or interview report, but the bias introduced in studies can lead to wrong inferences. Demographic data are usually classified by age and sex, although, errors in age reporting are more frequent in age reporting than in sex reporting. In demographic studies, age misreporting is a common phenomenon (Shryock, 1976). The most common phenomenon among the irregularities is the age heaping. Age data frequently displays excess frequencies at round or attractive ages, such as even numbers and multiples of 5 leading to age heaping. Age heaping is considered to be a measure of data quality and consistency (Pardeshi, 2010). In developing countries, the deficiencies among other problems are as the results of individual ignorance about certain personal details and sometimes open hostility to some types of inquiry due to ignorance. In Nigeria, age heaping is one of the irregularities in census/survey reporting of age. In the United States inaccurately stated age by non-Hispanic whites was found in 5 per cent of the Medicare population (Kestenbaum, 1992). Among older African Americans, 37 per cent misrepresented their ages (Elo et al., 1996). Since age misreporting is a common phenomenon in demographic studies, while the quality of data in age-sex distribution is very important in medical studies, innovative methods in data collection along with demographic techniques for evaluation of the age and sex data should be applied to ensure accuracy of the age data. The demographic evaluation techniques are Whipple’s index, Myer’s index and age-sex accuracy index. The Whipple's index (index of concentration), invented by the American demographer George Chandler Whipple (1866–1924), indicates the extent to which age data show systematic heaping on certain ages as a result of digit preference or rounding. Typically the concern is for heaping on particular ages such as those ending with ‘0’ and ‘5’ (Wiki/Whipple, undated). Myer’s blended index of digit preference is used for evaluating single-year age-sex data by giving the extend of digit preference for all the digits 0, 1, 2, …,9 (Kpedekpo, 1982). Pardeshi (2010) has used Whipple’s index and identified a large age heaping at ages ending with terminal digits '0' and '5', on a data collected during a community survey in the Yavatmal district, Maharashtra, India. Shirley et al., (2004) have used Mye’s blended index and age-sex accuracy index to evaluate age and sex data from the Census population of Provinces and Territories of Canada. The result has shown no preference or avoidance of any year of birth, and the accuracy of the age-sex population data for almost all the provinces in Canada. The Quality of age data in patients from developing countries was evaluated using Whipple’s and Myer’s indices (Denic et. al, 2003). Despite the risk of misclassification of age data in medical studies, analysis on the prevalence and magnitude of age misreporting in medical studies is rarely available in Nigeria. This paper intends to apply the demographic techniques of Whipple’s index, Myer’s Blended Index of digit preference and age-sex accuracy index to evaluate the age and sex data of outpatients at General Hospital Dutsin-ma in Katsina State of Nigeria for the month of January 2012.

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2. Methodology: The age and sex data for the outpatients was collected from the Record Office of the General Hospital Dutsin-ma for the month of January 2012. The data is only for the outpatients, and do not include women clients on antenatal care consultations.

2.1 Method of Data Analysis The demographic methods used for measuring the extent of age heaping and digit preference are Whipple's index and Myers' blended index respectively. Age-sex accuracy index was also calculated.

2.2 Whipple’s Index Whipple’s index is applicable where age is reported in single-years. It gives the relative preference for digits ‘0’ and ‘5’ while reporting age in the interval 23 and 62 years (Kpedekpo, 1982). It is computed as

Whipple ' index =

∑ ( P + P + P + ... + P ) ×100 1 ∑ ( P + P + P + ... + P ) 5 25

30

23

35

24

60

25

1

62

To evaluate for ages ending with ‘0’, i.e. 30, 40, 50 and 60, the index is calculated as

Whipple ' s index =

∑(P 1 ∑(P 5

30

+ P40 + P50 + P60 )

23 + P24 + P25 + ... + P62 )

× 100

2

To evaluate for ages ending with ‘5’, i.e. 25, 35, 45 and 55, the index is calculated as

Whipple ' s index =

∑(P 1 ∑(P 5

25

+ P35 + P45 + P55 )

23 + P24 + P25 + ... + P62 )

× 100

3

If there is no heaping at age reporting ending with ‘0’ and ‘5’, the index will have a value of 100. If there is complete heaping, the index will have a value of 500. Between these extremes, the following scale for estimating the reliability of the data is used (Kpedekpo, 1982): Quality of Data Highly Accurate Fairly Accurate Approximate Rough Very Rough

Whipple’s Index Less than 105 105 – 109.5 110 – 124.5 125 – 174.9 175 +

2.3 Myer’s Blended Index This index is used for evaluating single-year age-sex data. It gives the extent of digit preference for all digits 0, 1, 2, 3,…, 9. It can be used to report errors for all ages 10 – 89 years (Kpedekpo, 1982). The underlined assumption of this method is that in the absence of systematic irregularities in the reporting of age, the blended sum at each terminal digit should be approximately equal to 10% of the total blended population. If the sum at any given digit exceeds 10% of the total blended population, it indicates over selection of ages ending in that digit (digit preference). On the other hand, a negative

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deviation (or sum that is less than 10% of the total blended population) indicates under-selection of the ages ending in that digits (digit avoidance). If age heaping is non-existent, the index would be approximately 0 (Kpedekpo, 1982). The procedure for computation is as follows: 1) 2) 3) 4) 5) 6) 7) 8)

Sum all the population ending in each terminal digit over the whole range for the ages 10 – 89. Sum all the population ending in each terminal digit over the whole range for the ages 20 – 89. Multiply the sums of ages at each terminal digit in (1) above by co-efficient, 1,2,3,4,5,6,7,8,9,10. Multiply the sums of ages at each terminal digit in (2) above by co-efficient 9,8,7,6,5,4,3,2,1,0. Add the product of (3) and (4) above to obtain the blended sum at each terminal digit. Add up the blended sum in (5) above. Find the percentage of the blended sum at each terminal digit to the total of the blended sum. Find the deviation of the percentage distribution from 10.

2.4 Ages-Sex Accuracy Index (Joint Score) This index measures the level of quality of age-sex population data. It employs the age ratios and the sex ratios simultaneously (Kpedekpo, 1982), and computed as: Joint score = 3 × (sex ratio score) + (male and female age ratio scores)

4

The United Nation (UN) scaling for estimating the reliability of the data is: Under 20 is accurate, 20 to 40 is inaccurate, and over 40 is highly inaccurate (Shirley et al., 2004).

Age Ratios Age ratio is usually defined as the ratio of the population in the given age group to one half of the population in the two adjacent groups. Mathematically, Let 5 PX be the age group from age X to age X + 5 , 5 PX −5 and 5 PX +5 be the preceding and the following age groups respectively, then,

Age ratio =

5

1

PX

P + P 2 ( 5 X −5 5 X +5 )

×100

5

The computed age ratio is then compared with the expected value, which is usually 100.. The discrepancy at each age group is a measure of net age misreporting. An overall measure of the accuracy of an age distribution, called an age accuracy index, is derived by taking the average deviation (regardless of the sign) from 100.0 of the age ratios and summing over all the age groups. The lower this index the more adequate the census data on age. The age ratios are usually calculated for males and females separately and can be calculated for each age group (except the youngest and the oldest) provided the intervals are equal. An age ratio under 100 implies either that members of the age group were selectively under enumerated or that errors in age reporting resulted in misclassifying persons who belong to the age group. A ratio of more than 100 suggests the opposite of one or the other or both of these conditions. Generally, age ratios should be studied for a series of age groups, preferably for the entire span of age for which they can be calculated (Kpedekpo, 1982).

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Sex Ratios The sex ratios or age specific sex ratios (number of males per 100 females in each age group) is defined as the ratio of the population of males in the given age group to the population of females in that given age group. Mathematically, Let 5 PXm stands for male aged X to age X + 5 , and 5 PXf stands for female aged X to age X + 5

Age specific sex ratio =

PXm × 100 f P 5 X

5

6

Sum over the successive differences between one age group and the next one (irrespective of the sign), and then take the average of the summation which is the sex accuracy index ( Kpedekpo, 1982).

3. Results and Discussion: The data consisting of the age and sex distribution of outpatients in General Hospital (GH) Dutsin-ma for January 2012 collected from the Record Office of the hospital is presented in table 1. Various demographic techniques would be employed to evaluate the accuracy of the age and sex data. Table 1. Age and Sex Distributions of Outpatients in General Hospital Dutsinma in January 2012 NUMBER OF NUMBER OF AGE (years) MALES FEMALES 0–4 422 260 5–9 114 99 10 – 14 78 82 15 – 19 90 265 20 – 24 126 384 25 – 29 132 319 30 – 34 109 260 35 – 39 92 111 40 – 44 78 112 45 – 49 46 33 50 – 54 62 60 55 – 59 33 24 60 – 64 50 31 65 + 57 48 TOTAL 1489 2088

3.1 Whipple’s Index Whipple’s Index (WI) is applied to measure the level of heaping at ages ending with ‘0’ and ‘5’. Table 2 presents the age distributions between 23 to 62 years for the male and female outpatients that attended GH Dutsin-ma in January 2012. The WI for heaping at male ages ending with ‘5’ and ‘0’ is 336.6, and the quality of the age data is considered to be very rough. The WI for each of the digit (‘0’ and ‘5’) is then calculated separately to determine the magnitude for each one of them. The WI for ages ending with ‘0’ is 188.4 that qualified the age data still very rough. Although very high again, the WI for ages ending with ‘5’ is 148.2 that improved the quality of the age data from very rough to rough data.

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Table 2. (a) Age Distribution for Male Outpatients. (b) Age Distribution for Female Outpatients. Number of Number of Number of Number of Age Patients Age Patients Age Patients Age Patients 23 13 25 69 23 46 25 220 24 11 30 79 24 6 30 208 25 – 29 132 35 62 25 – 29 319 35 73 30 – 34 109 40 62 30 – 34 260 40 97 35 – 39 92 45 27 35 – 39 111 45 28 40 – 44 78 50 50 40 – 44 112 50 57 45 – 49 46 55 26 45 – 49 33 55 17 50 – 54 62 60 43 50 – 54 60 60 28 55 – 59 33 418 55 – 59 24 728 Total Total 60 43 60 28 61 0 61 0 62 2 62 1 621 1000 Total Total

The WI for heaping at female ages ending with ‘5’ and ‘0’ is 364.0, and the quality of the age data is also considered very rough. The WI for ages ending with ‘0’ is 195.0, which again qualified the age data very rough. The WI for ages ending with ‘5’ is 169.0, which is only a slight improvement that qualified the data from very rough to rough data. The result of the WI above can be justified using figure 1. The percentage of preference for digits ending with ‘0’ is almost multiple of preference for digits ending with ‘5’ and almost triple of the preferences for the remaining digits for both male and female populations. It also shows that female preference to digits ending with ‘0’ is higher than that for male except at age group 60 – 69 years. Again, from virtually examination, the trend shows that percentage of preferences for digits ending with ‘5’ and ‘0’ increases with the increase in age grouping.

40% 30%

67.9

66.9

56.1

65.1

20% 33.3 10% 0% 20 -- 29

30 -- 39

40 -- 49

50 -- 59

60 -- 69

Age group (years) Ending w ith '0' eEnding w ith '5' Ending w ith others

P e r c e n t a g e o f h e a p in g

P e r c e n t a g e o f h e a p in g

Fig. 1. Percentage of Heaping of digits ending with ‘5’ and ‘0’ a) Age Distribution for Female Outpatients b) Age Distribution for Male Outpatients 100% 100% 9.3 11.9 13.8 90% 15.3 90% 24.3 20.0 28.2 29.9 80%35.4 80% 20.2 25.6 11.9 19.3 46.9 70% 70% 19.7 27.4 60% 21.8 60% 30.8 50%31.3 50% 40%26.7

72.9

30% 20% 26.4 10% 0% 20 -- 29

39.3

30 -- 39

50.0

52.6

40 -- 49

50 -- 59

60 -- 69

Age group (years) Ending w ith '0' eEnding w ith '5' Ending w ith others

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3.2 Myer’s Blended Index Myer’s blended index of digit preference is used for evaluating single-year age-sex data by giving the extend of digit preference for all the digits 0, 1, 2, … , 9. The computation for Myer’s index for male outpatients in January 2012 in General Hospital Katsina is presented in Table 3.

Table 3. Myer’s Blended Index for Male Outpatients Terminal Digits

Sum of Ages 10 - 89

Coefficient

Ages 10 89 Coefficient Product

0

365

1

365

335

9

1

21

2

42

14

2

91

3

273

3

29

4

4

33

5

Sum of Ages 20 – 89

Ages 20 – 89 Coefficient Product

Blended sum

% Distribution

Deviation from 10

3015

3380

38.61

28.61

8

112

154

1.76

-8.24

72

7

504

777

8.87

-1.13

116

17

6

102

218

2.49

-7.51

5

165

23

5

115

280

3.20

-6.80

225

6

1350

199

4

796

2146

24.51

14.51

6

24

7

168

16

3

48

216

2.47

-7.53

7

48

8

384

37

2

74

458

5.23

-4.77

8

83

9

747

49

1

49

796

9.09

-0.91

9

33

10

330

22

0

0

330

3.77

-6.23

8755

100.00

86.24

Sum

952

Coefficient

784

The result has shown the over selection of ages ending with digits ‘0’ and ‘5’ with the respective preferences of 38.6 percent and 24.5 percent. However, the ages ending with ‘1’ have the highest avoidance, followed by ages ending with ‘3’ and ‘6’. Table 4 shows the computation of Myer’s index for female outpatients. The result has also shown the over selection of ages ending with digits ‘0’ and ‘5’ with the respective preferences of 40.4 percent and 23.5 percent. Similarly, the ages ending with ‘4’ have the highest avoidance, followed by ages ending with ‘1’ and ‘9’. Table 4. Myer’s Blended Index for Females Outpatients

Coefficient

Ages 10 – 89 Coefficient Product

Sum of Ages 20 – 89

Coefficient

672

1

672

654

9

1

30

2

60

23

2

140

3

420

3

83

4

4

34

5

Terminal Digits

Sum of Ages 10 - 89

0

Ages 20 89 Coefficient Product

Blended sum

% Distribution

Deviation from 10

5886

6558

40.36

30.36

8

184

244

1.50

-8.50

122

7

854

1274

7.84

-2.16

332

64

6

384

716

4.41

-5.59

5

170

14

5

70

240

1.48

-8.52

402

6

2412

352

4

1408

3820

23.51

13.51

6

63

7

441

35

3

105

546

3.36

-6.64

7

101

8

808

57

2

114

922

5.67

-4.33

8

158

9

1422

48

1

48

1470

9.05

-0.95

9

46

10

460

13

0

0

460

2.83

-7.17

16250

100.00

87.73

Sum

1729

1382

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The result has shown that, about 86 percent of male outpatients and 88 percent of female outpatients reported ages with incorrect final digits.

35 30 25 20 15 10 5 0 -5

0

1

2

3

4

5

6

7

8

-10 -15

9

Deviation of % blended population fron 10

Deviation of % blended population from 10

Fig. 2 a) Myer’s Blended Index For Male Outpatients

b) Myer’s Blended Index For Female Outpatients 35 30 25 20 15 10 5 0 -5

0

1

2

3

4

5

6

7

8

9

-10 -15

Te rm inal digit

Term inal digit

Figure 2 describes the deviations of the percentage of the blended population from 10 among each of the terminal digits. The most preferred terminal digits while reporting ages were ‘0’ and ‘5’ for both male and female population, although, male slightly inclined to ‘5’, while female slightly inclined to ‘0’.

3.3 Ages-Sex Accuracy Index (Joint Score) Table 5 shows computation of age-sex accuracy index for male and female outpatients. Table 5. Results of Age Ratios, Sex Ratios and Joint Score Age Group 0–4 5–9 10. -14 15 – 19 20 – 24 25 – 29 30 – 34 35 – 39 40 – 44 45 – 49 50 – 54 55 – 59 60 – 64

Male Number 422 114 78 90 126 132 109 92 78 46 62 33 50

Age Ratio

Deviation from 100

45.60 76.47 88.24 113.51 112.34 97.32 98.40 113.04 65.71 156.96 58.93 111.11

-54.40 -23.53 -11.76 13.51 12.34 -2.68 -1.60 13.04 -34.29 56.96 -41.07

57 228.00 65+ Total 1,489 Total (irrespective of sign) Mean

265.194 24.1085

Joint Score

156.837

Female Number 260 99 82 265 384 319 260 111 112 33 60 24 31

Age Ratio

Deviation from 100

57.89 45.05 113.73 131.51 99.07 120.93 59.68 155.56 38.37 210.53 52.75 86.11

-42.11 -54.95 13.73 31.51 -0.93 20.93 -40.32 55.56 -61.63 110.53 -47.25

48

309.68

Sex Ratio 162.31 115.15 95.12 33.96 32.81 41.38 41.92 82.88 69.64 139.39 103.33 137.50 161.29

First Difference 47.16 20.03 61.16 1.15 -8.57 -0.54 -40.96 13.24 -69.75 36.06 -34.17 -23.79

118.75

2088 479.438 43.5853

356.574 29.715

The Index is extremely very high that rated the age data highly inaccurate according to the UN scaling. The inaccuracy is more critical in female age data since the sum of the absolute deviation of the female age ratio from the unity (100) is almost twice that for male age ratio. From Figure 3, while male age ratio is smoother than female age ratio at the lower ages, the female age ratio appeared to have serious fluctuation at the higher ages. The fluctuation indicates large differences between frequencies of populations in adjacent groups. The maximum positive deviations

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in females is 111% in the age group 50 – 54, which is almost twice that in males (57%) in the same age group. The maximum negative deviation is in the 5 – 9 years age group (54%) in males and in the 45 – 49 years age group (62%) in females. An age ratio under 100 implies either that members of the age group were selectively under enumerated or that errors in age reporting resulted in misclassifying persons who belong to the age group. A ratio of more than 100 suggests the opposite of one or the other or both of these conditions (Kpedekpo G.M.K. 1982). Fig. 3. Age Ratios by Sex for 5 years age group 250.0

Age ratios

200.0 150.0 100.0 50.0 0.0 5-9

10.-14

15-19

20-24

25-29

30-34

35-39

40-44

45-49

50-54

55-59

60-64

Age (years) Male

Female

4. Conclusion: The age data collected for the outpatients in General Hospital Dutsin-ma were very rough in quality for both male and female outpatients. There was age heaping at ages ending with terminal digits ‘0’ and ‘5’, indicating a preference in reporting such ages. The result has shown that, about 86 percent of male outpatients and 88 percent of female outpatients reported ages with incorrect final digits. The evaluation of the outpatients’ age data using the demographic techniques has finally qualified the data inaccurate as the results of systematic heaping and digit preference. To ensure the accuracy of the age data, innovative method of local time path calendar was proved to be useful. The interviewer took the respondent back in time using local time calendar and the memory of the respondent is triggered by relating events festivals and other landmarks in the lives of people, enabling them to reply their own time perspective (Haandrikman, 2004).

References [1] [2] [3] [4] [5] [6] [7]

B. Kestenbaum, A description of the extreme age population based on improved Medicare enrollment data, Demography, 29 (1992), 565–580. C. O. Lerche, Social and Economic Statistics for Africa, (2nd Edition), Longman group, London, 1983. G.S. Pardeshi, Age heaping and accuracy of age data collected during a community survey in the Yavatmal district, Maharashtra, Indian J Community Med, 35(3) (2010), 391-395. G.M.K. Kpedekpo, Essentials of Demographic Analysis for Africa, Hernerman Educational Books Inc., New Hemisphere, 1982. H.S. Shryock, J.S. Siegel and Associates, The Methods and Materials of Demography, Condensed edition by Edward G. Stockewell, Academic Press, New York, 1976. I. Johannes and F. Polly, Bancroft’s Introduction to Biostatistics, (2nd Edition), Harper and Row publishers, New-York, 1970. I.T. Elo, S.H. Preston, I. Rosenwaike, M. Hill and T.P. Cheney, Consistency of age reporting on death certificates and social security administration record among elderly AfricanAmericans, Soc Sci Res, 25(1996), 292–307.

Int. J. Pure Appl. Sci. Technol., 10(1) (2012), 27-36.

[8]

[9]

[10] [11] [12]

36

K. Haandrikman, Using a local time-path calendar to reduce heaping in durations of postpartum Amenorrhea, breastfeeding, postpartum Abstinence and contraceptive use, Time Soc, 13(2004), 339-62. L. Shirley, V. Ravi and M. Margaret, An evaluation of the age and sex data from the census population of Canada, provinces and territories, 1971 to 2001, Canadian Population Society Annual Meeting, Winnipeg, Manitoba, (2004). http://web.uvic.ca/~canpop/2004/Loh-VermaMichalowski-CPS04.ppt S. Denic, F. Khatib and H. Saadi, Quality of age data in patients from developing countries, Journal of Public Health, 26(2) (2003), 168–171. S.W. Smaller, Biostatistics and Epidemiology, (3rd Ed.), Sponger-Verlay, New York, (2004). Wiki/Whipple, (undated), Whipple index, http://en.wikipedia.org/wiki/Whipple's_index