# Chapter 5 Analysis of TP53

## 5.1 Models

Each model adjusts for study site, reference age, and personal history of breast cancer. History of breast cancer is treated as a fixed effect, and the rest of the covariates’s coefficients are treated as normally distributed random effects.

$P(Y_{ij}=1| \beta^{site}_{ j}, \beta^{p53}_{j}, \beta^{age}_{j},\beta^{BC}) = \textsf{logit}^{-1}(\beta^{site}_{ j}+ \beta^{p53}_{j}*p53_{ij}+ \beta^{age}_{j}*age_{ij}+\beta^{BC}* BC_{ij})$

$\beta^{site}_{ j}|\mu_{site}, \sigma_{site}^{2}\sim \textsf{N}(\mu_{site}, \sigma_{site}^{2})$ $\beta^{age}_{j}|\mu_{age}, \sigma^{2}_{age}\sim \textsf{N}(\mu_{age}, \sigma^{2}_{age})$ $\beta^{\text{BC}}, \mu_{age},\mu_{site}\sim \textsf{N}(0,0.1)$ $\sigma_{age},\sigma_{site} \sim \textsf{invGamma}(1, 0.05)$

The p53 variable’s site-specific log OR priors were defined using the models described previously.

The fully Bayesian model was fit jointly as well as marginally. Since the results were very similar, the marginal models were used for computational efficiency and clarity of interpretation. Results from the joint analysis can be found in the supplement.

## 5.2 Results

The new models shrunk estimates towards 0 for all SNPs. The BF approximation model set all point estimates to zero, as did the fully Bayesian model with the exception of one. This is the same SNP (rs2287498n) that was detected as significant in the MISA analysis (Joellen M Schildkraut et al., 2010). However, the credible interval contains 0, so there is not enough evidence for association. Similarly, although the conditional likelihood model does not set any estimates to zero, all its credible intervals contain zero.

The original model has the longest credible intervals for all SNPs except rs2287498n, for which both the Bayesian and Bayes Factor models have large credible intervals, indicating more uncertainty than the original model.

These results are consistent with those from recent GWAS, specifically Phelan et al. (2017), which found no association between any of the TP53 SNPs and cancer.

Below are the full tables of OR by site and SNP.

Table 5.1: rs9894946n
original estimate original CI bayesian estimate bayesian CI CL estimate CL CI BF estimate BF CI
AUS 0.969 0.74 - 1.219 1 1 - 1 0.983 0.744 - 1.194 1 0.902 - 1.08
HAW 0.935 0.423 - 1.469 1 1 - 1 0.982 0.539 - 1.356 1 0.811 - 1.148
MAY 0.952 0.672 - 1.215 1 1 - 1 0.973 0.728 - 1 , 1 - 1.203 1 0.898 - 1.083
POL 1.481 0.949 - 2.184 1 1 - 1 1.076 0.89 - 1 , 1 - 1.458 1 0.922 - 1.144 , 1.206 - 1.532
Overall 1.061 0.407 - 1 , 1 - 1.839 1 1 - 1 1.006 0.672 - 1.338 1 0.875 - 1.169
Table 5.1: rs12951053n
original estimate original CI bayesian estimate bayesian CI CL estimate CL CI BF estimate BF CI
AUS 1.234 1.031 - 1.512 1 0.942 - 1.082 1.132 0.973 - 1 , 1 - 1.396 1.215 0.956 - 1.596
HAW 1.177 0.855 - 1.481 1 0.948 - 1.06 1.095 0.872 - 1 , 1 - 1.337 1.158 0.84 - 1.526
MAL 1.184 0.957 - 1.447 1 0.96 - 1.064 1.107 0.925 - 1 , 1 - 1.343 1.176 0.897 - 1.516
MAY 1.203 0.951 - 1.504 1 0.94 - 1.079 1.109 0.942 - 1 , 1 - 1.353 1.183 0.918 - 1.542
NCO 1.251 1.034 - 1.607 1 0.987 - 1.099 1.072 0.8 - 1 , 1 - 1.286 1.112 0.726 - 1.422
NEC 1.189 0.963 - 1.457 1 0.958 - 1.066 1.073 0.871 - 1 , 1 - 1.252 1.108 0.81 - 1.396
NHS 1.139 0.78 - 1.428 1 0.955 - 1.049 1.099 0.908 - 1.345 1.171 0.883 - 1.535
POL 1.173 0.923 - 1.448 1 0.954 - 1.055 1.096 0.905 - 1.33 1.163 0.862 - 1.493
SEA 1.13 0.855 - 1 , 1 - 1.345 1 0.966 - 1.037 1.113 0.924 - 1 , 1 - 1.393 1.191 0.913 - 1.585
STA 1.182 0.914 - 1.464 1 0.955 - 1.064 1.114 0.944 - 1.369 1.186 0.922 - 1.54
UCI 1.175 0.919 - 1.44 1 0.95 - 1.058 1.079 0.941 - 1.243 1.188 0.902 - 1.548
UKO 1.2 0.939 - 1.494 1 0.952 - 1.055 1.097 0.96 - 1 , 1 - 1.287 1.236 0.959 - 1.632
USC 1.203 0.977 - 1 , 1.001 - 1.471 1 0.939 - 1.079 1.07 0.928 - 1 , 1 - 1.225 1.161 0.87 - 1.496
Overall 1.186 1.028 - 1.343 1 0.983 - 1.073 1.099 0.987 - 1 , 1 - 1.232 1.178 0.951 - 1.393
Table 5.1: rs1625895n
original estimate original CI bayesian estimate bayesian CI CL estimate CL CI BF estimate BF CI
AUS 1.007 0.804 - 1.207 1 1 - 1 1.002 0.816 - 1 , 1 - 1.17 1 1 - 1
HAW 1.017 0.674 - 1.276 1 1 - 1 1.006 0.749 - 1.226 1 1 - 1
MAL 1.051 0.846 - 1.306 1 1 - 1 1.029 0.855 - 1.242 1 1 - 1
MAY 1.043 0.838 - 1.283 1 1 - 1 1.023 0.863 - 1.238 1 1 - 1
NCO 0.997 0.801 - 1.19 1 1 - 1 0.994 0.817 - 1.158 1 1 - 1
POL 1.103 0.871 - 1.543 1 1 - 1 1.026 0.845 - 1.219 1 1 - 1
SEA 1.047 0.832 - 1.263 1 1 - 1 1.012 0.807 - 1.21 1 1 - 1
STA 1.025 0.796 - 1.273 1 1 - 1 1.035 0.898 - 1.22 1 1 - 1
Overall 1.035 0.877 - 1.215 1 1 - 1 1.016 0.883 - 1.163 1 1 - 1
Table 5.1: rs1042522n
original estimate original CI bayesian estimate bayesian CI CL estimate CL CI BF estimate BF CI
AUS 1.043 0.845 - 1.206 1 1 - 1 1.033 0.854 - 1.174 1 1 - 1
HAW 1.051 0.771 - 1.273 1 1 - 1 1.039 0.829 - 1 , 1 - 1.231 1 1 - 1
MAL 1.085 0.937 - 1.266 1 1 - 1 1.064 0.934 - 1.216 1 1 - 1
MAY 1.097 0.92 - 1.311 1 1 - 1 1.07 0.928 - 1.267 1 1 - 1
NCO 1.067 0.881 - 1.235 1 1 - 1 1.048 0.901 - 1 , 1 - 1.201 1 1 - 1
POL 1.117 0.947 - 1.398 1 1 - 1 1.045 0.904 - 1.196 1 1 - 1
SEA 1.061 0.895 - 1.242 1 1 - 1 1.048 0.885 - 1.215 1 1 - 1
STA 1.067 0.88 - 1 , 1 - 1.272 1 1 - 1 1.053 0.953 - 1.201 1 1 - 1
Overall 1.075 0.931 - 1.204 1 1 - 1 1.049 0.941 - 1.174 1 1 - 1
Table 5.1: rs2287498n
original estimate original CI bayesian estimate bayesian CI CL estimate CL CI BF estimate BF CI
HAW 1.288 0.88 - 1.691 1.254 0.875 - 1.667 1.132 0.873 - 1 , 1 - 1.436 1.293 0.874 - 1.665
MAL 1.269 0.995 - 1 , 1 - 1.535 1.238 0.924 - 1.59 1.141 0.958 - 1.39 1.281 0.998 - 1 , 1 - 1.543
MAY 1.35 1.025 - 1.802 1.32 0.96 - 1.817 1.121 0.912 - 1.355 1.251 0.929 - 1.503
NCO 1.352 1.07 - 1.709 1.328 0.972 - 1.771 1.138 0.916 - 1.445 1.299 0.96 - 1.646
POL 1.285 0.938 - 1.605 1.249 0.892 - 1.647 1.134 0.92 - 1.422 1.292 0.947 - 1 , 1 - 1.641
SEA 1.233 0.94 - 1.522 1.195 0.871 - 1.55 1.197 0.984 - 1 , 1.001 - 1.581 1.384 1.092 - 1.837
STA 1.287 0.937 - 1.62 1.259 0.909 - 1.698 1.122 0.949 - 1 , 1 - 1.365 1.365 1.029 - 1.783
UKO 1.287 0.942 - 1.604 1.252 0.897 - 1.663 1.121 0.964 - 1.352 1.361 1.09 - 1.714
USC 1.368 1.056 - 1.797 1.34 0.977 - 1.872 1.094 0.94 - 1.298 1.292 0.93 - 1 , 1 - 1.591
Overall 1.302 1.069 - 1.525 1.279 0.968 - 1.599 1.138 0.998 - 0.999 , 1 - 1.303 1.312 1.08 - 1.533