Clustered data analysis and an application in health sciences

Aim: Clustered data structure can be confronted frequently in health field studies. The most important feature that distinguishes clustered data from other data is that the results from the same cluster are related to each other. Ignoring this correlation structure may lead to bias in statistical inference. The aim of this study is to introduce alternative methods that take into account the correlation structure for clustered data and demonstrate its application on a data in the field of health. Thus, it will be illustrated that the standard statistical analysis methods applied to the clustered datasets may yield biased results and valid findings can be obtained with the correct analysis method. Material and Method: For the comparison and illustration of the standard chi-square test and the adjusted tests a hypothetical health data was used. This data was analyzed with proposed methods for clustered categorical data which are Rosner (1982) adjusted chi-square (1), Dallal (1988) adjusted chi-square (2), Donner (1989) adjusted chi-square (3) and Rao and Scott (1992) adjusted chi-square (4) test and standard Pearson chi-square test. Results: The presence of cataract was assessed as the result of measurement on two eyes of each patient. It is aimed to compare the positivity rates according to age groups. The results of the test statistics were obtained as T = 9.04; p = 0.010 for Rosner adjusted chi-square test statistic, D = 8.27; p = 0.040 for Dallal adjusted chi-square test statistic, 〖X_A〗^2 = 9.12; p = 0.010 for Donner adjusted chi-square statistic and (X^2 ) ̃ = 8.9; p=0.011 for Rao and Scott adjusted chi-square test statistic. The other applied method standard Pearson chi-square test statistic was obtained as 𝑋2 = 9.2; p = 0.055. Conclusion: While the H0 hypothesis was rejected by the adjusted test statistics taking into account the clustered data structure, the H0 hypothesis was accepted by the standard chi-square test. Using statistical methods that are not suitable for data structure may lead to wrong results.