# mcmc inference of causal models with all possible causal factors: G, G*G, G*E and E provides proportions of each causal factor of G, G*G, G*E and E based on relative concordance data ```r iter.mcmc(ppt,aj=2,n.iter,n.chains,thinning=5,init.cut,darray,x,n,model,mcmcrg=0.01) ``` ## Arguments - `ppt`: population lifetime incidence - `aj`: a constant for the stage of data collection - `n.iter`: number of mcmc iterations - `n.chains`: number of mcmc chain - `thinning`: mcmc thinning parameter (default=5) - `init.cut`: mcmc data cut - `darray`: indicating the array positions of available data among 9 relative pairs: 1:mzt,2:parent-offspring,3:dzt,4:sibling,5:2-direct(grandparent-grandchild),6:3rd(uncle-niece),7:3-direct(great-grandparent-great-grandchild),8:4th (causin),9:4d(great-great-grandparent-great-great-grandchild) - `x`: number of disease concordance of relative pairs - `n`: total number of relative pairs - `model`: an array, size of 4 (1: E component; 2: G component; 3: G*E component; 4: G*G component), indicating the existance of the causal component: 0: excluded; 1: included. - `mcmcrg`: parameter of the data collection stage (default=0.01) ## Returns a list of rejectionRate, result summary, Gelman-Rubin diagnostics (point est. & upper C.I.) for output variables: e[1]: proportion of environmental factor (E) g[2]: proportion of genetic factor (G) ge[3]: proportion of gene-environment interaction (G*E) gg[4]: proportion of gene interactions (G*G) gn[5]: number of recessive genes in G ppe[6]: population proportion of interacting environment in G*E ppg[7]: population proportion of interacting genetic factor in G*E fd[8]: frequency of dominant genes in G fdge[9]: frequency of dominant genes in G*E gnge[10]: number of recessive genes in G*E ppd[11]: population proportion of dominant genes in G*G ppr[12]: population proportion of recessive genes in G*G kd[13]: number of dominant genes in G*G kr[14]: number of recessive genes in G*G ## References L. Park, J. Kim, A novel approach for identifying causal models of complex disease from family data, Genetics, 2015 Apr; 199, 1007-1016. ## Examples ```r ### PLI=0.01. ppt<-0.01 ### a simple causal model with G and E components pg<-0.007 # the proportion of G component in total populations pgg<-0 # the proportion of G*G component in total populations pge<-0 # the proportion of G*E component in total populations e<-1-(1-ppt)/(1-pg) # the proportion of E component in total populations fd<-0.001 # one dominant gene tt<-3 # the number of recessive genes temp<-sqrt(1-((1-pg)/(1-fd)^2)^(1/tt)) fr<-c(array(0,length(fd)),array(temp,tt)) fd<-c(fd,array(0,tt)) rp<-drgegggne(fd,fr,c(0,0),c(0,0),c(0,0),c(0,0),0,e) sdata<-rp[,3]/(rp[,2]+rp[,3]) #sdata<-round(sdata*500) darray<-c(1:2,4:6) ## available data= MZT, P-O, sibs, grandparent-grandchild, avuncular pair n<-array(1000,length(darray)) x<-array() for(i in 1:length(darray)){ x[i]<-rbinom(1,n[i],sdata[darray[i]]) } model<-c(1,1,0,0) ## remove # from the following lines to test examples. #iter.mcmc(ppt,2,15,2,1,1,darray,x,n,model) # provide a running test #iter.mcmc(ppt,2,2000,2,10,500,darray,x,n,model) # provide a proper result ```

iter.mcmc function