TALAAT, M., WITTKOWSKI, K.M. (in press) In: BARLOW, R., BROWN, J.W.
(eds)
Reproductive health and infectious diseases in the Middle East. Aldershot,
UK: Ashgate
1) Medical Statistics and Computer Unit, Faculty of Medicine,
University of Cairo, Qasr El-Aini, El-Manial, Cairo, Egypt
2) Dept. Community Medicine, Theordor Bilharz Research Institute, Imbaba,
Cairo, Egypt
3) Dept. Med. Biometry,
Eberhard-Karls-University, D-72070
Tübingen, Germany; HIV
Center for Clinical and Behavioral Studies, New York, NY; Center
for Urban Epidemiological Studies, New
York Academy of Medicine, New York, NY
4) High Institute of Public Health, Alexandria, Egypt
Keywords: multivariate, ordinal, risk, rank, score, schistosomiasis
Exposure to schistosomiasis cercariae can be measured in terms of frequency of bathing, washing cloths, washing animals, cleaning canals, etc. The relative risk of these activities is unknown and difficult to access, because they are not independent (the relative proportion of these activities varies by age, sex, educa-tion, occupation, etc.), and randomised studies are neither practical nor would they be ethical. Therefore, univariate analyses are inappropriate, because they cannot reflect correlations between these activities. Furthermore, analyses based on simple sums of univariate scores are in-appropriate, because they are built on the assumption that the relative risks of these activities are known and constant over the whole range of (combined) risks.
The marginal likelihood principle (WITTKOWSKI 1992) provides a simple solution for this problem. For each record of (multivariate) observations a single marginal likelihood (MargL) score is computed as the average of the corresponding ranks among all rank vectors in accordance with the natural semi ordering among the multivariate observtions. A MargL weight is obtained from the variance of these ranks. These scores and weights can than be used with any univariate (unconditional) rank tests for weighted observations.
Twohundred-twentysix people (male and female, aged 13–62) from two villages (A and B) had been working in farming at least once in the past 12 months. Exposure related to farming is measured for two villages (A and B) in terms of irrigating fields, cleaning canals, and washing animals (HASAN et al. 1993). Univariate results were conflicting. After adjusting for multiple tests, people from village A had a higher exposure through washing animals (p<.407) while people from village B had a higher exposure through cleaning canals (p<.295), which might be interpreted at indicating that people in village B were at higher risk. Stratification, i.e. taking the differences in age and sex into account, and accounting for correlation between risk factors, reversed this result . Now farmers in village B seem to have a lower risk (p<0.590), although this observation should be interpreted with care, until confirmed by a study with a larger sample size..
The MrgL method proposed in WITTKOWSKI 1988 can be viewed as a generalisation of the WILCOXON-MANN-WHITNEY test (it adds stratification), the FRIEDMAN test (it adds replications), or the MANTEL-HAENSZEL test (it allows for more than two outcomes). Note, however, that the unconditional variance should be used (i.e. ‘correction’ for ties is inappropriate) when ties are due to rounding. Thus the commonly used test statistics are inappropriate for inexact (e.g. discretized or censored) data, because they do not take the precision of the data into account (WITTKOWSKI 1989, in press). This approach was originally criticized as being overly conservative. When observations from different groups are tied, however, using the marginal likelihood weights reduces the degree of conservativism, because less weight is given to the tied observations.
The proposed MrgL procedure provides a solution for a problem which frequently arises in the analysis of questionnaire data. When the parameter of interest (e.g. water contact) can only be measured indirectly (i.e. by several ordinal variables), it generates scores and weights for observations that can then be easily used with standard methods of statistical analysis. Recent extensions of the method (SUSSER et al., in press) would lead to improved results by adding data on the prevalence of eggs or blood in urine or stool.
HASAN, M.H., MILLER, F.D., EL SAYED, M.K., TALAAT, M., BADAWY, A. (1993) Schistosomiasis in Egypt: Sample design and data management. The SRP 1993 International Conference on Schistosomiasis, February 14–18, 1993, Cairo, Egypt. Abstract 203
SUSSER, E., DESVARIEUX, M., WITTKOWSKI, K.M. (im Druck / in press) Reporting sexual risk behavior for HIV: a practical risk index and a method for improving risk indices. Am J Public Health
WITTKOWSKI, K.M. (1988) Friedman-type statistics and consistent multiple comparisons for unbalanced designs. J American Statist Assoc 83: 1163-1170
WITTKOWSKI, K.M. (1989) An asymptotic UMP sign test for discretized data. The Statistician 38:93-6
WITTKOWSKI, K.M. (1992) An extension to Wittkowski. JASA 87:258
WITTKOWSKI, K.M. (im Druck / in press) Versions of the sign test in the presence of ties. Biometrics