This was a research work done at the KATH (hospital) in Ghana.

1. The Beauty of Mathematics 1 x 9 + 2 = 1112 x 9 + 3 = 111123 x 9 + 4 = 11111 234 x 9 + 5 = 1111112345 x 9 + 6 = 111111123456 x 9 + 7 = 11111111234567 x 9 + 8 = 1111111112345678 x 9 + 9 = 111111111123456789 x 9 +10= 1111111111 1 x 8 + 1 = 912 x 8 + 2 = 98123 x 8 + 3 = 9871234 x 8 + 4 = 987612345 x 8 + 5 = 98765123456 x 8 + 6 = 9876541234567 x 8 + 7 = 987654312345678 x 8 + 8 = 98765432123456789 x 8 + 9 = 987654321 9 x 9 + 7 = 8898 x 9 + 6 = 888987 x 9 + 5 = 88889876 x 9 + 4 = 8888898765 x 9 + 3 = 888888987654 x 9 + 2 = 88888889876543 x 9 + 1 = 8888888898765432 x 9 + 0 = 888888888

2. And look at this symmetry: 1 x 1 = 111 x 11 = 121111 x 111 = 123211111 x 1111 = 123432111111 x 11111 = 123454321111111 x 111111 = 1234565432111111 11 x 1111111 = 123456765432111111111 x 11111111 = 123456787654321111111111 x 111111111=12345678987654321

3. PROJECT TITLE Estimation Of The Age Distribution Of Patients Operated And Effect Of Salmonella Typhi On The Incidence Of Typhoid Complications At The Main Surgical Theatre Supervisor Mr. S. K. Appiah

8. What category of surgery is high?

9. What proportion of the patients were females?

10. What are the major complications?

12. Most typhoid patients undergo surgery

14. Typhoid fever in patients is highest in adolescents and young adults

16. To estimate the average age of patients and age range who visit the department

17. To determine the ratio of males to females

18. To determine the ratioof general surgery to pediatric surgery

20. To seek sex-relation

21. Whether the environment or location of patients influence the number of cases.

22. Does the age of persons have anything to do with the complication?

25. SPSS

27. TYPHOID FEVER is also known as ENTERIC FEVER

28. ENDEMIC Developing Countries AFRICA & South America

29. CAUSE bacterium Salmonella Typhi

30. TRANSMISSION WATERBORNE OR FOODBORNE

32. Headache

33. Sore throat

34. Constipation

35. Joint pain

36. Abdominal pain

37. Loss of appetite

38. Fatigue

41. Peritonitis

42. Encephalopathy

43. Intestinal hemorrhage

44. Hepatosplenomegaly

48. LARGEST in the northern sector

50. A REFERRAL HOSPITAL having POLYCLINIC as well

51. THEIR VISION To become a medical centre of excellence offering Clinical and Non-Clinical services of the highest quality standards comparable to any international standards within 5 years (2003-2008)

52. THEIR MISSION “to provide quality services to meet the needs and expectations of all clients. This will be achieved through well-motivated and committed staff applying best practices and innovation”.

54. A1 Theatre

56. Urology

57. Neurosurgery

58. ENT, Eye

59. Paediatric Surgery

60. Plastic Surgery

64. Used to test the claim about the average age obtained in stratification and the average age obtained by the random sample generated by minitab

65. (Null hypothesis)

67. The use of P-values in hypothesis testing :-

68. P-value as the smallest level at which the data is significant.

70. In many engineering and industrial experiments, the experimenter already knows that the means µ1differ µ2, consequently, the hypothesis testing on is of little interest.

71. The experimenter would usually be more interested in a confidence interval on the difference in means . The interval is called a percent confidence interval for the parameter.

72. CORRELATION ANALYSIS 6/9/2008 37 CONCERNED WITH THE STRENGTH OF ASSOCIATION BETWEEN THE VARIABLE OF INTEREST AND THE OTHERS An error term which caters for the errors due to chance and neglected factors which we assume are not important

74. Spearman’s Rank Correlation Coefficient

79. ANALYSIS OF VARIANCE IN REGRESSION MODEL 6/9/2008 44 The application of analysis of variance (ANOVA) in regression analysis is based on the partitioning of the total variation and its degree of freedom into components.

81. The total sum of squares of deviation (SSyy, ) is a measure of dispersion of the total variation in the observed values, y.

82. The explained sum of squares, (SSR ), measures the amount of the total deviation in the observed values of y that is accounted for by the linear relationship between the observed values of x and y. This is also referred to as sum of squares due to the linear regression model.

83. The unexplained sum of squares is a measure of dispersion of the observed y values about the regression which is sometimes called the error residual sum of squares (SSE ).

84. COEFFICIENT OF DETERMINATION 6/9/2008 46 r2 is called the coefficient of determination which is explained variation expressed as fraction of total variation. It is also defined as a square of the correlation coefficient.

86. The analysis involves a large array of data system of equations which are conveniently and effectively performed in matrix

88. 6/9/2008 49

90. 6/9/2008 52

91. THE BEAUTY OF MATHEMATICS ANALYSIS OF DATA AND DISCUSSION 6/9/2008 53

93. Which class or nature of surgical equipments or devises that should not be limited in number.

95. 6/9/2008 56

96. 6/9/2008 57

97. 6/9/2008 58

98. 6/9/2008 59 Estimating frequency Distribution of age of Patients

99. 6/9/2008 60 The estimate for the mean age was 28.55549 with standard error 1.281085

100. 6/9/2008 61 The estimate for the mean age is 30.76648 with standard error 1.787193

101. 6/9/2008 62 STRATIFICATION OF PATIENTS BY COMPLICATIONS The estimate for the mean age is 29.352 years with standard error 1.133

102. 6/9/2008 63 The estimate for the mean age is 29.01362 years with standard error 0.3770333

103. The Claim! The Mean Age is 29 years 6/9/2008 64

104. STATISTICAL HYPOTHESIS TESTING Null Hypothesis: The Mean Age is 29 years 6/9/2008 65

105. 6/9/2008 66 Descriptive Statistics: factor, formulation1 Variable N Mean Median TrMean StDev SE Mean factor 750 3.0000 3.0000 3.0000 1.4152 0.0517 formulation 750 28.973 25.000 27.872 21.557 0.787 Variable Minimum Maximum Q1 Q3 factor 1.0000 5.0000 2.0000 4.0000 formulation 1.000 96.000 10.000 43.000

106. 6/9/2008 67

107. 6/9/2008 68

108. ` 6/9/2008 69

109. 6/9/2008 70

110. 6/9/2008 71 One-way ANOVA: formulation1 versus factor Analysis of Variance for formulation Source DF SS MS F P factor 4 842 210 0.45 0.771 Error 745 347210 466 Total 749 348051 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ----------+---------+---------+------ 1 150 27.53 19.68 (-----------*----------) 2 150 28.48 21.37 (-----------*----------) 3 150 28.70 21.90 (-----------*----------) 4 150 29.47 21.47 (----------*-----------) 5 150 30.69 23.36 (----------*-----------) ----------+---------+---------+------ Pooled StDev = 21.59 27.0 30.0 33.0

111. 6/9/2008 72 Multiple Comparisons Dependent Variable: age formulation of patients Mean 95% Confidence Interval Difference (J) factor (I) factor (I-J) Std. Error Sig. Lower Bound Upper Bound 2.00 1.00 Tukey HSD -.9533 2.49280 .995 -7.7698 5.8631 3.00 -1.1733 2.49280 .990 -7.9898 5.6431 4.00 -1.9400 2.49280 .937 -8.7565 4.8765 5.00 -3.1667 2.49280 .710 -9.9831 3.6498 1.00 2.00 .9533 2.49280 .995 -5.8631 7.7698 3.00 -.2200 2.49280 1.000 -7.0365 6.5965 4.00 -.9867 2.49280 .995 -7.8031 5.8298 5.00 -2.2133 2.49280 .901 -9.0298 4.6031 1.00 3.00 1.1733 2.49280 .990 -5.6431 7.9898 2.00 .2200 2.49280 1.000 -6.5965 7.0365 4.00 -.7667 2.49280 .998 -7.5831 6.0498 5.00 -1.9933 2.49280 .931 -8.8098 4.8231 1.00 4.00 1.9400 2.49280 .937 -4.8765 8.7565 2.00 .9867 2.49280 .995 -5.8298 7.8031 3.00 .7667 2.49280 .998 -6.0498 7.5831 5.00 -1.2267 2.49280 .988 -8.0431 5.5898 1.00 5.00 3.1667 2.49280 .710 -3.6498 9.9831 2.00 2.2133 2.49280 .901 -4.6031 9.0298 3.00 1.9933 2.49280 .931 -4.8231 8.8098 4.00 1.2267 2.49280 .988 -5.5898 8.0431 2.00 1.00 LSD -.9533 2.49280 .702 -5.8471 3.9404 3.00 -1.1733 2.49280 .638 -6.0671 3.7204 4.00 -1.9400 2.49280 .437 -6.8337 2.9537 5.00 -3.1667 2.49280 .204 -8.0604 1.7271 1.00 2.00 .9533 2.49280 .702 -3.9404 5.8471 3.00 -.2200 2.49280 .930 -5.1137 4.6737 4.00 -.9867 2.49280 .692 -5.8804 3.9071 5.00 -2.2133 2.49280 .375 -7.1071 2.6804 1.00 3.00 1.1733 2.49280 .638 -3.7204 6.0671 2.00 .2200 2.49280 .930 -4.6737 5.1137 4.00 -.7667 2.49280 .759 -5.6604 4.1271 5.00 -1.9933 2.49280 .424 -6.8871 2.9004 1.00 4.00 1.9400 2.49280 .437 -2.9537 6.8337 2.00 .9867 2.49280 .692 -3.9071 5.8804 3.00 .7667 2.49280 .759 -4.1271 5.6604 5.00 -1.2267 2.49280 .623 -6.1204 3.6671 1.00 5.00 3.1667 2.49280 .204 -1.7271 8.0604 2.00 2.2133 2.49280 .375 -2.6804 7.1071 3.00 1.9933 2.49280 .424 -2.9004 6.8871 4.00 1.2267 2.49280 .623 -3.6671 6.1204

112. 6/9/2008 73 Each sample was used for the hypothesis testing of the claim that the mean age was 29 years. One-Sample Z: sample1 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 1 150 27.53 19.68 1.76 Variable 95.0% CI Z P Sample 1 ( 24.07, 30.98) -0.84 0.403 One-Sample Z: sample 2 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 2 150 28.48 21.37 1.76 Variable 95.0% CI Z P Sample 2 ( 25.02, 31.94) -0.29 0.768 One-Sample Z: sample 3 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 3 150 28.70 21.90 1.76 Variable 95.0% CI Z P Sample 3 ( 25.24, 32.16) -0.17 0.865 One-Sample Z: sample 4 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 4 150 29.47 21.47 1.76 Variable 95.0% CI Z P Sample 4 ( 26.01, 32.92) 0.26 0.791 One-Sample Z: sample 5 Test of mu = 29 vs mu not = 29 The assumed sigma = 21.6 Variable N Mean StDev SE Mean Sample 5 150 30.69 23.36 1.76 Variable 95.0% CI Z P Sample 5 ( 27.24, 34.15) 0.96 0.337

113. 6/9/2008 74

114. 6/9/2008 75 AGE AND TYPHOID STATISTICS

115. 6/9/2008 76 DATA FROM THE PEDIATRIC UNIT

116. 6/9/2008 77 Regression Analysis: patients versus zongo, age, female The regression equation is patients = 4.07 + 0.42 zongo + 0.824 age + 0.500 female Predictor Coef SE Coef T P Constant 4.068 5.642 0.72 0.494 zongo 0.420 1.003 0.42 0.688 age 0.8240 0.6766 1.22 0.263 female 0.5002 0.7478 0.67 0.525 S = 5.899 R-Sq = 84.0% R-Sq(adj) = 77.2% Analysis of Variance Source DF SS MS F P Regression 3 1282.58 427.53 12.29 0.004 Residual Error 7 243.60 34.80 Total 10 1526.18

117. 6/9/2008 78

118. 6/9/2008 79 Correlations: patients, zongo, age, female patients zongo age zongo 0.832 0.001 age 0.909 0.886 0.000 0.000 female 0.865 0.791 0.905 0.001 0.004 0.000 Cell Contents: Pearson correlation P-Value

119. A NEED FOR MODEL MODIFICATION 6/9/2008 80

120. 6/9/2008 81 THE PRODUCT TRANSFORMATION Regression Analysis: patients versus zonagefem This modification considers the product of the predictor factors as a single variable. The regression equation is patients = 24.3 + 0.00230 zonagefem Predictor Coef SE Coef T P Constant 24.293 4.256 5.71 0.000 zonagefe 0.0022960 0.0008795 2.61 0.028 S = 9.824 R-Sq = 43.1% R-Sq(adj) = 36.8% Analysis of Variance Source DF SS MS F P Regression 1 657.66 657.66 6.82 0.028 Residual Error 9 868.52 96.50 Total 10 1526.18

121. 6/9/2008 82 THE SQUARE ROOT TRANSFORMATION Regression Analysis: patients versus sqrt (zonagefem) This modification considers the square root of the product of the predictor factors as a single variable. The regression equation is patients = 14.1 + 0.353 sqrt(zonagefem) Predictor Coef SE Coef T P Constant 14.079 4.162 3.38 0.008 sqrt(zon 0.35299 0.07059 5.00 0.001 S = 6.700 R-Sq = 73.5% R-Sq(adj) = 70.6% Analysis of Variance Source DF SS MS F P Regression 1 1122.2 1122.2 25.00 0.001 Residual Error 9 404.0 44.9 Total 10 1526.2

122. 6/9/2008 83 THE NATURAL LOG TRANSFORMATION The regression equation is patients = - 18.5 + 6.87 Ln(zonagefem) Predictor Coef SE Coef T P Constant -18.480 5.142 -3.59 0.006 Ln(zonag 6.8658 0.6790 10.11 0.000 S = 3.704 R-Sq = 91.9% R-Sq(adj) = 91.0% Analysis of Variance Source DF SS MS F P Regression 1 1402.7 1402.7 102.24 0.000 Residual Error 9 123.5 13.7 Total 10 1526.2

123. 6/9/2008 84

124. 6/9/2008 85

125. 6/9/2008 86 The regression equation is patients = - 18.5 + 6.87 Ln(zonagefem) where patients represents the number of patient admitted with typhoid at the Pediatric Unit; zonagefem represents the product of the environment, age below six years and number of females. The Ln is the natural logarithm function.

126. MAJOR FINDINGS AND IMPLICATIONS 6/9/2008 87

128. The age range which had more surgical complications was 0-9 years.

129. The percentage of cases were relatively high for males. It was realized that about that 62.64 of the cases worked on were males. The ratio of males to femaleswas 1.7:1

130. The complete data indicates that out of a total of 1831patients 27.1%and 22.17% suffered from hernia and typhoid complications6/9/2008 88

132. It was also observed that 39.9% of the children with typhoid complication were aged below 16years.In other words, approximately 8.84% of the cases handled by the theatre were children below 16 years with typhoid fever.

133. The ratio of the male to female was nearly 1:1 respectively

134. The known dirty environs (“Zongo”) did not contribute a high percentage in the case of typhoid.6/9/2008 89

136. Nature of the water they drink or use in cooking

137. Poor keeping of the kitchen and toilet facilities

138. Poor personal hygiene

139. Parent Inadequate education of nursing children 6/9/2008 90

141. The hospital administrators should provide more equipments and surgical devices to accommodated patients especially those with age less 16 years.

142. The public should be informed as to the risk of complications of people aged in interval 0-10 years so as to minimize these cases.

143. Counseling on ways to minimize some of these related complications should be carried out.6/9/2008 91

145. The Ministry of Health can help create animations (Cartoons) on our visual media stations so as to educate the children faster.

146. Rural Water Projects should be encouraged in way to enhance proper distribution of water to various locations.6/9/2008 92

148. This survey has revealed to as certain conditions at the main theatre of the KATH. The recommendations outlined, based on the survey, above should be considered so as to ensure that the health of all are stabilize6/9/2008 93

149. 6/9/2008 94 Thank you