## A second course in statistics regression analysis pdf

While linkage studies can only use family data, association studies a second course in statistics regression analysis pdf be family or population based. Perhaps a more important reason is to refine already known or constantly emerging associations in the light of expanded knowledge of the HLA genetic map.

This review is on the basic principles of traditional HLA association studies in terms of statistical interpretation with the ultimate aim of providing an insight to the modern methods of association data analysis. A CI contains the result of a significance test, but a significance test cannot provide the confidence limit. The statistical tests are essentially a test of whether the confidence limits include unity. A test statistics generally relies on the comparison with the observed distribution of what is expected if the null hypothesis is true. The choice of the test to do this statistics depends on what is being compared. The usual tests used in HLA association studies and also in population genetic analysis of the HLA system are briefly described later.

If the probability of getting the right result is 0. Thus, the probability of getting it wrong is 1 – 0. This is to say that, for 20 comparisons and the significance level of 0. 05, the probability of getting at least one erroneous result is 0. To avoid a type I error, when independent multiple comparisons are carried out, and all genotypes examined have the same chance of being increased or decreased, a statistical safeguard should be applied. There is no definite limit for the number of comparisons that makes this necessary but it is a must if it is greater than 20. P is the uncorrected P value, and n is the number of comparisons 7.

For P values of less than 0. There has always been a debate about what number to use in the multiplication. In contrast to the most common practice, this is not supposed to be just the number of alleles in the locus analyzed 9. If the allele frequencies are compared between patients and controls, the number of alleles is important as well as the number of comparisons in terms of age groups, sex groups, clinical subgroups, etc. 05 as in the first study, then the second study has confirmed the results of the preliminary study. The second study is said to be done with a specific hypothesis, therefore, an expected association would not be regarded as an artifact of multiple comparisons. This means that some genuine finding may be ruled out as a chance finding where it is worth pursuing.

Murray has proposed another method for the design of the study, which would preserve the sensitivity while avoiding a high, risk of type I error 12. This method may be most useful for HLA association studies. This is to set down a priori a hierarchy of comparisons of interest. In their discussion of the statistical analysis of retrospective studies 13, Mantel and Haenszel state that “if the purpose of the retrospective study is to uncover leads for fuller investigation, it becomes clear there is no real multiple significance testing problem. A single retrospective study does not yield conclusions, only leads. A specific example for the application of Murray’s proposition in the light of Mantel and Haenszel’s view to the HLA field would be something like that: a study can be designed to investigate the relevance of homozygosity for an HLA class II supertype in childhood leukaemias as the same genotype has been found to be increased in two adult leukaemias.

More recently, Klitz suggested that if a G-test is applied to the overall distribution of genotype frequencies between patients and controls and if this yields a significant result, the individual associations cannot be taken as the result of multiple comparisons 14. A significant deviation in this analysis justifies further scrutiny of the data to single out the main association. Klitz also suggests grouping of very rare alleles in one category to increase the sensitivity of the test. Confusion may occasionally arise through wrong usage of the terms allele, gene, or marker in an association study. Some investigators state that they compare allele or haplotype frequencies, but only count each individual once. Population stratification can be thought of as confounding by ethnicity.

If ethnicity of cases and controls are reliably known, a stratified analysis would eliminate this problem. However, it is the unknown stratification within the population that causes this undesirable effect. In case-control studies, ideally there should be at least one control per case. If the number of cases is limited and cannot be increased easily, it may be an idea to increase the number of control to increase statistical confidence. A higher control to case ratio will not provide further benefit and may even result in type I errors.

Were the groups similar apart from the exposure under question? Were the data on outcomes collected identically in both groups? How strong is the association and how precise is the estimate? When two groups are to be compared in a case-control study, it is necessary to have a 2×2 contingency table cross-tabulating the frequencies. For a multiallelic locus like the HLA loci, however, the number of genotype categories is large. This is why originally the comparisons based on the presence or absence of an allele were thought to be more parsimonious and was established as the standard approach for HLA association studies 5. The number in each cell is a count, i.

Each subject must appear in one, and only in one, cell. In the table, switching rows and columns will not alter the result. 22, although there are also strong arguments against this 15. 2×2 table- may be 4 or 5 but not 4. With degrees of freedom greater than 1 and with expected frequencies of at least 5 in each cell, this is not a problem as the difference between the statistics and the true sampling distribution is so small. The Yates’s correction helps make the discrete data generated by the test statistics more closely approximate to the continuous Chi-squared distribution.

This is achieved by changing the above formula to . By doing so, the discrete data distribution and continuous data distribution are approximated better. In relatively large samples, this would not make an important difference. In the study of biological variations, a P value of less than 0. 05 is generally considered to be statistically significant.

In HLA association studies, because of the nature of the HLA system and random variations in gene frequencies, it is not infrequent that a P value of this magnitude is obtained. A RR may be more than 1. 0 or even greater, especially in small groups, but without statistical significance it is meaningless. In one report, a RR similar to the one reported for an HLA association in Hodgkin’s disease can be found even for comparisons between two control groups of the same study 28. Statistics does not prove the truth of anything, it just provides more or less evidence for its validity. 05 does not necessarily mean the null hypothesis is correct.