Correlation and Regression analyses are commonly used for analyzing association between continuous variables. You may also find these articles relevant -

https://www.biostat.wisc.edu/~page/liu_thesis.pdf

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwi91u-CzerVAhWH1xQKHY29CpEQFggrMAA&url=http%3A%2F%2Fwww.nature.com%2Fnrg%2Fjournal%2Fv7%2Fn10%2Ffull%2Fnrg1916.html&usg=AFQjCNFZ7F2pbgkPlAN1YxgFbeYshZYHFQ

https://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwi91u-CzerVAhWH1xQKHY29CpEQFgg1MAE&url=http%3A%2F%2Fwww.nature.com%2Fnrg%2Fjournal%2Fv11%2Fn11%2Ffull%2Fnrg2867.html&usg=AFQjCNHZUo6jLrQVObmYIZq_FosP3ErSAA

Regards.

Upendra 

You may choose a statistical model by dada attribute, such as continuous data and discrete data, and also sample size. For example, both phenotype data and genotype data are categorical data,  if small samples (eg: not more than 30),  then you can choose Fisher‘s exact test; but if big samples, then you can choose Chi-Squared test. However, when the rows or/and the columns are ordinal, you can choose Wilcoxon or Mann-Whitney test (Tables of size is 2*J) and Cochran-Armitage trend test (Tables of size is I*2).

There are a few method and it depend of the phenotype (binary or quantitative) and study system ( there are method specialized  for Humans and in plants).

The simplest method it would be a linear regression or a nonparametric test such as Wilcoxon rank sum test. The disadvantage of this methods is that they do not correct for population structure and you may end up with a lot of false positives.

The best methods are linear mixed models that account for population structure and cryptic relatedness :

1- •Yu, J., Pressoir, G., Briggs, W. H., Vroh Bi, I., Yamasaki, M., et al. (2006) A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nat Genet.

There are several variations of the linear mixed models :

Approximate methods

Zhang, Z, Ersoz, E, et al. (2010) Mixed linear model approach adapted for genome-wide association studies. Nat Genet.

Kang, H. M., et al. (2010) Variance component model to account for sample structure in genome-wide association studies. Nat Genet.

Exact methods (Better than approximate)

Lippert, C., Listgarten, J., et al. (2011) FaST linear mixed models for genome-wide association studies. Nat Meth.

Advanced linear mixed model

MLMM: 1-Help to resolve genetic heterogeneity and get an impression of the genetic architecture of the trait. 

Segura, V., Vilhjálmsson, B. J., et al. (2012) An efficient multilocus mixed-model approach for genome-wide association studies in structured populations. Nat Genet.

MTMM: Help you to find pleiotrophy between correlated traits or detect GxE

Korte, A., Vilhjálmsson, B. J., Segura, V., et al. (2012) A mixed model approach for genome-wide association studies of

correlated traits in structured populations. Nat Genet.

Increase in power to normal linear mixed model by avoiding proximal contamination (You test a SNP and use a Kinship that do not contain the SNP being tested. FaSTLMM has a efficient implementation of this method)

Rincent, R., Moreau, L., Monod, H., Kuhn, E., et al. (2014). Recovering power in association mapping panels with variable levels of linkage disequilibrium. Genetics.

To summarize

1- The most advance methods are linear mixed models and there are specialized version of the linear mixed models if you are interested in Pleiotrophy or GxE

2- I would recommend to use FaST LMM (See Lippert et al 2011). Because is fast, allow you also to avoid proximal contamination and it is an exact method.

Hope it helps!

The approach of population-based association mapping involving linkage disequilibrium (LD) between markers and genes underlying complex traits leads to more accurate and finer mapping of genes. The key idea is that a trait mutation assumed to have arisen once on the ancestral haplotype of a single chromosome in the past history of the population of interest has had many thousands of recombination events and is therefore passed on from generation to generation together with the markers at tightly linked loci resulting in LD. DNA markers close enough (< 2 cM) remain associated with the trait ‘gene’ for many generations.

The most usual model is to regress phenotypic values on one of the several markers at a time, repeat the process for all the markers and correct for multiple testing. By using this simple regression model however linkage information between the markers is lost needing the use of a multiple regression model where phenotypic values are regressed on the set of markers taken together. But this approach breaks down when some of the markers are highly correlated amongst themselves leading to problem of multi-collinearity. Ridge regression is then the most useful approach to adopt.This is what was done in a study relating to analysis of CEPH family gene expression data involving 26 SNPs genotyped on 57 unrelated individuals from the International HapMap Project database for studying association within the CH3L2 gene region (Am J Hum Genet, 82, 375-85, 2008). Three methods were used to analyze the data and compare their performance: (a) single locus analysis–simple regression analysis with a single SNP as the predictor, (b) a standard multiple-linear regression model, and (c) a ridge regression model. The case (b) was found to fit only 11 out of the 26 SNPs with several missing regression coefficients. In (a) 14 out of 26 analyses were significant. In (c) the performance was better than those in (a) and (b). It gave 8 SNPs as significant at an overall 5 % level with a Bonferroni correction for multiple testing. 11 SNPs in (a) and 5 SNPs in (c) were found to be significant in one method and not the other. Accounting for LD among the SNPs radically changed which of the SNPs is likely to be causally associated with the CH3L2 phenotype.

Hope this information will help you in deciding the best course of action.  

Thank you so much for such a detailed explanation by every one.  I have started going through the materials mentioned here. I am sure these are going to be quite  helpful to understand and choose the model for my study.