Crucial Areas Of Biostatistics

Measures of Association

Biostatistics is the application of statistical methods to biological sciences. This paper examines a number of crucial areas of biostatistics. These areas include hypothesis testing, measures of association and significance testing. These areas are examined through a series of questions. The three questions each covers one of the areas highlighted above. The first question covers measures of association, question two covers proportion and hypothesis testing and the third question covers significance testing. The paper answers these questions and gives a brief description of each area.

Measures of association are used to quantify the relationship between two or more variables. (Dicker, Coronado & Koo, 2006).  Several methods of analysis can be used to determine measures of associations. These include correlation analysis and regression analysis (Gaddis, 1990). Examples of such methods of analysis include Pearson’s correlation coefficient, Spearman order correlation coefficient, chi-square test, relative and odd ratio (Haung, 2016). To determine the association between alcohol and nicotine consumption we shall carry out a chi-square test on the data provided. A chi-square test is a measure of significance rather than a measure of the strength of the association.

1.Chi-square test

Null hypothesis: there is no association between alcohol and nicotine consumption.

H₀: X²=0

H₁: X²>0

Expected values = (row total x column total)/ grand total

X² statistic = (O-E) ² /E

ΣX² = 42.27

Degree of freedom = (r-1)(c-1)

= 2 x 2

= 4

Finding the critical value:

With P value of 0.05 and a d.f. of 4 the X²_critical = 2.78.

 From the above data, calculated X² is greater than the critical X², reject the H₀ hypothesis. There is, therefore, a strong association between alcohol and nicotine consumption.

Most measures of association have a scale such that they reach a value of 1 if the two variables have a perfect association with each other (Daniel, 2009). Methods used to measure the magnitude of association include Cramer’s V, Lambda, Phi, Kendall’s tau_b and Kendall’s tau_c (Cohen J, 2010). Chi-square does not show the strength of the association between the variables.

Proportion is the comparison of a part, a number or share in relation to the whole. It is a type of a ratio in which the numerator is part of the denominator. (Dicker, Coronado & Koo 2006). Proportion can be expressed as a decimal, fraction or a percentage.

Proportion is calculated by  

a.The proportion of the sample that underwent HIV testing: =

 = 0.4375

The proportion of those unemployed who underwent HIV testing

Proportion and Hypothesis Testing

=0.339The proportion of the employed who underwent HIV testing =

= 0.5254

To determine whether undergoing HIV testing is associated with employment status using the above proportions we have to calculate relative proportion and attributable proportion. Relative proportion compares the proportion of the employed who underwent HIV testing to the proportion of the unemployed who underwent HIV testing.  (Jorn, Murray& Ander, 2010) It shows how many times the employed underwent HIV testing compared to the unemployed

Relative proportion =

= 1.5471

From the calculation above the employed are 1.5471 times likely to attend HIV testing compared to the unemployed.  

Attributable proportion is the measure of the health impact of a causative factor (Dicker, Coronado & Koo, 2006). Attributable proportion shows what percentage of the HIV testing attendance is associated with employment status.

Attributable proportion =

 =

= 0.3540

= 0.3540 x100

= 35.40%

From the above calculation, only 35.40% of the HIV testing attendance is attributed to employment status. The remaining 64.60% is attributed to other factors. Therefore, undergoing HIV testing is not associated employment status.

A hypothesis is a statement about a characteristic of a population. It concerns itself with parameters of the population about which the hypothesis statement is made (Rosner, 2010). Hypothesis testing helps the researcher to reach a conclusion about the population by examining a sample from the population. (Rosner, 2010). A null hypothesis is a statement made so as to be put to test. An alternative hypothesis is a statement believed to be true if the testing done led to the rejection of the null hypothesis.

Null hypothesis: Undergoing HIV testing is not associated with employment status

H₀: p₁ = p₂

H₁: p₁p₂

P = (  x

= 0.2768 + 0.1607

= 0.4375

q = 0.5625

Z=

= 1. 979

From the z tables, P-value corresponding to Z = 1.979 is 0. 0478. This value is less than 0.05 and therefore we reject the null hypothesis. Therefore, there is an association between undergoing HIV testing and employment status.

Confidence Interval is a pair of numerical values that define an interval that include a certain parameter to a specific degree of confidence.

 C.I

= 0. 1858  1.96

= 0.1858  0.01657

  = 0.1692, 0.2024

Therefore, we are 95% confident that the true population difference between the proportion of employed men undergoing HIV testing and the unemployed men undergoing HIV testing lies between 0.1692 and 0.2024.

Significance Testing

2.b.The odds ratio for the association between HIV testing and being employed is 2.15. This implies that there is a 2.15 time more likely for an employed person to undergo HIV testing than an unemployed person.

2.c.The researcher needs to increase the sample size. This will authenticate the association between undergoing HIV testing and employment status. A larger sample can be used to generalize the conclusion to the entire target population. A small sample size may lead to bias or a false association between the variables. The researcher should also do more measures of association to ascertain the relationship between undergoing HIV testing and employment status. The P value obtained from the hypothesis testing was 0.0478. This denotes a weak association which may have come about by chance.

3.Significance testing

1. Methods that can be used to carry out significance test on the PASI score include unpaired t-test and analysis of variance, ANOVA. This is because the data provided by PASI score is numerical as opposed to categorical (Parikh & Hazra, 2010). The data provided by PASI score is also not paired. This is because it was taken at the end of the six weeks. If the data was paired, paired t-test and repeated measured ANOVA could have been used (Wang, Clayton & Bakhai, 2006). From the data given, we cannot determine a correlation association between the data hence Pearson’s coefficient and Spearman’s coefficient cannot be used (Petrie& Sabin, 2005).
2. Methods that can be used to carry out significance test on the self-assessment are chi-square test. This is because the data provided by the self-assessment is categorical as opposed to numerical (Barun & Hazra, 2011). The data provided is not paired hence McNemar’s test cannot be used (Wang, Clayton & Bakhai, 2006). If an association between the parameters are established then odd ratio/risk ratio might be used (Petrie & Sabin 2005)

Conclusion

Measures of associations quantify the relationship between two or more variables. They show whether the association between two or more variables exists and if so to what strength. Chi-square does not show the strength of the association between the variables. Proportion is a ratio in which the numerator is a subset of the denominator. The two methods by which conclusion can be made about a population from a sample is by finding the confidence interval and hypothesis testing. Deciding what method of significance testing to use involves severally steps. The steps include deciding whether the data given is numeral or categorical, paired or non-paired and whether or not there is an association between the variables                               

References

Bernard Rosner (2010). Fundamental of Biostatistics. Boston: Brooks/ Cole.

Cohen, J., & Nee, J. C. (2010). Estimators for two measures of association for set correlation. Educational and Psychological Measurement, 44(4), 907-917.

Dicker, R., Coronado, F., & Koo, D. (2006). Principles of Epidemiology in Public Health Practice: An introduction to applied epidemiology and biostatistics. Waldorf: PHF.

Olsen, J., Christensen, K., Murray, J., & Ekbom, A. (2010). An Introduction to Epidemiology for    Health Professionals. New York: Springer

Parikh, M., N., Hazra, A., Mukherjee, J., Gogtay, N. (2010). Research methodology simplified:                                                                                                                            Hypothesis testing and choice of statistical test. New Delhi: Jaypee brothers

Petrie, A., Sabin, C. (2005). Medical statistics at a glance. The theory of linear regression and performing a linear regression analysis. London: Blackwell Publishers.

Wang, D., Clayton, T., & Bakhai, A. (2006).  A practical guide to design, analysis, and reporting. London: Remedica.

Wayne, W., D. (2009). Biostatistics: A foundation for analysis in health sciences. Danvers: Wile

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