Cycle-specific logistic regression of haplo-type effects with known haplo-type probabilities. Given observed genotype G and unobserved haplotypes H we here mix out over the possible haplotypes using that \(P(H|G)\) is given as input.
\[\begin{align*} S(t|x,G) & = E( S(t|x,H) | G) = \sum_{h \in G} P(h|G) S(t|z,h) \end{align*}\] so survival can be computed by mixing out over possible h given g.
Survival is based on logistic regression for the discrete hazard function of the form \[\begin{align*} \mbox{logit}(P(T=t| T >= t, x,h)) & = \alpha_t + x(h) beta \end{align*}\] where x(h) is a regression design of x and haplotypes \(h=(h_1,h_2)\)
For standard errors we assume that haplotype probabilities are known.
We are particularly interested in the types haplotypes:
types <- c("DCGCGCTCACG","DTCCGCTGACG","ITCAGTTGACG","ITCCGCTGAGG")
## some haplotypes frequencies for simulations
data(hapfreqs)
print(hapfreqs)
#> index haplotype freq
#> DCGAGCTCACG 1 DCGAGCTCACG 0.010681
#> DCGCGCTCACG 2 DCGCGCTCACG 0.138387
#> DTGAGCTCACG 3 DTGAGCTCACG 0.000310
#> DTGAGCTCACA 4 DTGAGCTCACA 0.006800
#> DTGAGCTCGCG 5 DTGAGCTCGCG 0.034517
#> DTGACCTCACG 6 DTGACCTCACG 0.001336
#> DTGCGCTCACG 7 DTGCGCTCACG 0.009969
#> DTGCGCTCACA 8 DTGCGCTCACA 0.011833
#> DTGCGCTCGCG 9 DTGCGCTCGCG 0.302389
#> DTGCGCCCGCG 10 DTGCGCCCGCG 0.001604
#> DTGCCCTCACG 11 DTGCCCTCACG 0.003912
#> DTCAGCTGACG 12 DTCAGCTGACG 0.001855
#> DTCCGCTGACG 13 DTCCGCTGACG 0.103394
#> DTCCCCTGACG 14 DTCCCCTGACG 0.000310
#> ITCAGTTGACG 15 ITCAGTTGACG 0.048124
#> ITCCGCTGAGG 16 ITCCGCTGAGG 0.291273
#> ITCCGTTGACG 17 ITCCGTTGACG 0.031089
#> ITCCGTCGACG 18 ITCCGTCGACG 0.001502
#> ITCCCCTGAGG 19 ITCCCCTGAGG 0.000653Among the types of interest we look up the frequencies and choose a baseline
www <-which(hapfreqs$haplotype %in% types)
hapfreqs$freq[www]
#> [1] 0.138387 0.103394 0.048124 0.291273
baseline=hapfreqs$haplotype[9]
baseline
#> [1] "DTGCGCTCGCG"We have cycle specific data with \(id\) and outcome \(y\)
data(haploX)
dlist(haploX,.~id|id %in% c(1,4,7))
#> id: 1
#> y X1 X2 X3 X4 times lbnr__id Count1
#> 1 0 0 0 0 0 1 1 0
#> 2 0 0 0 0 0 2 2 0
#> 3 0 0 0 0 0 3 3 0
#> 4 0 0 0 0 0 4 4 0
#> 5 0 0 0 0 0 5 5 0
#> 6 0 0 0 0 0 6 6 0
#> attr(,"class")
#> [1] matrix array
#> ------------------------------------------------------------
#> id: 4
#> y X1 X2 X3 X4 times lbnr__id Count1
#> 19 1 0 0 0 0 1 1 0
#> attr(,"class")
#> [1] matrix array
#> ------------------------------------------------------------
#> id: 7
#> y X1 X2 X3 X4 times lbnr__id Count1
#> 37 0 1 0 0 0 1 1 0
#> 38 0 1 0 0 0 2 2 0
#> 39 1 1 0 0 0 3 3 0
#> attr(,"class")
#> [1] matrix arrayand a list of possible haplo-types for each id and how likely they are \(p\) (the sum of within each id is 1):
data(hHaplos) ## loads ghaplos
head(ghaplos)
#> id haplo1 haplo2 p
#> 1 1 DTGCGCTCGCG DTGAGCTCGCG 1.00000000
#> 19 2 ITCCGTTGACG DTGAGCTCGCG 0.06867716
#> 21 2 ITCAGTTGACG DTGCGCTCGCG 0.93132284
#> 51 3 ITCCGTTGACG DTGAGCTCGCG 0.06867716
#> 53 3 ITCAGTTGACG DTGCGCTCGCG 0.93132284
#> 66 4 DTGCGCTCGCG DTGCGCTCGCG 1.00000000The first id=1 has the haplotype fully observed, but id=2 has two possible haplotypes consistent with the observed genotype for this id, the probabiblities are 7% and 93%, respectively.
With the baseline given above we can specify a regression design that gives an effect if a “type” is present (sm=0), or an additive effect of haplotypes (sm=1):
designftypes <- function(x,sm=0) {
hap1=x[1]
hap2=x[2]
if (sm==0) y <- 1*( (hap1==types) | (hap2==types))
if (sm==1) y <- 1*(hap1==types) + 1*(hap2==types)
return(y)
}To fit the model we start by constructing a time-design (named X) and takes the haplotype distributions for each id
haploX$time <- haploX$times
Xdes <- model.matrix(~factor(time),haploX)
colnames(Xdes) <- paste("X",1:ncol(Xdes),sep="")
X <- dkeep(haploX,~id+y+time)
X <- cbind(X,Xdes)
Haplos <- dkeep(ghaplos,~id+"haplo*"+p)
desnames=paste("X",1:6,sep="") # six X's related to 6 cycles
head(X)
#> id y time X1 X2 X3 X4 X5 X6
#> 1 1 0 1 1 0 0 0 0 0
#> 2 1 0 2 1 1 0 0 0 0
#> 3 1 0 3 1 0 1 0 0 0
#> 4 1 0 4 1 0 0 1 0 0
#> 5 1 0 5 1 0 0 0 1 0
#> 6 1 0 6 1 0 0 0 0 1Now we can fit the model with the design given by the designfunction
out <- haplo.surv.discrete(X=X,y="y",time.name="time",
Haplos=Haplos,desnames=desnames,designfunc=designftypes)
names(out$coef) <- c(desnames,types)
out$coef
#> X1 X2 X3 X4 X5 X6
#> -1.82153345 -0.61608261 -0.17143057 -1.27152045 -0.28635976 -0.19349091
#> DCGCGCTCACG DTCCGCTGACG ITCAGTTGACG ITCCGCTGAGG
#> 0.79753613 0.65747412 0.06119231 0.31666905
summary(out)
#> Estimate Std.Err 2.5% 97.5% P-value
#> X1 -1.82153 0.1619 -2.13892 -1.5041 2.355e-29
#> X2 -0.61608 0.1895 -0.98748 -0.2447 1.149e-03
#> X3 -0.17143 0.1799 -0.52398 0.1811 3.406e-01
#> X4 -1.27152 0.2631 -1.78719 -0.7559 1.346e-06
#> X5 -0.28636 0.2030 -0.68425 0.1115 1.584e-01
#> X6 -0.19349 0.2134 -0.61184 0.2249 3.647e-01
#> DCGCGCTCACG 0.79754 0.1494 0.50465 1.0904 9.445e-08
#> DTCCGCTGACG 0.65747 0.1621 0.33971 0.9752 5.007e-05
#> ITCAGTTGACG 0.06119 0.2145 -0.35931 0.4817 7.755e-01
#> ITCCGCTGAGG 0.31667 0.1361 0.04989 0.5834 1.999e-02Haplotypes “DCGCGCTCACG” “DTCCGCTGACG” gives increased hazard of pregnancy
The data was generated with these true coefficients
tcoef=c(-1.93110204,-0.47531630,-0.04118204,-1.57872602,-0.22176426,-0.13836416,
0.88830288,0.60756224,0.39802821,0.32706859)
cbind(out$coef,tcoef)
#> tcoef
#> X1 -1.82153345 -1.93110204
#> X2 -0.61608261 -0.47531630
#> X3 -0.17143057 -0.04118204
#> X4 -1.27152045 -1.57872602
#> X5 -0.28635976 -0.22176426
#> X6 -0.19349091 -0.13836416
#> DCGCGCTCACG 0.79753613 0.88830288
#> DTCCGCTGACG 0.65747412 0.60756224
#> ITCAGTTGACG 0.06119231 0.39802821
#> ITCCGCTGAGG 0.31666905 0.32706859The design fitted can be found in the output
head(out$X,10)
#> X1 X2 X3 X4 X5 X6 haplo1 haplo2 haplo3 haplo4
#> 1 1 0 0 0 0 0 0 0 0 0
#> 2 1 1 0 0 0 0 0 0 0 0
#> 3 1 0 1 0 0 0 0 0 0 0
#> 4 1 0 0 1 0 0 0 0 0 0
#> 5 1 0 0 0 1 0 0 0 0 0
#> 6 1 0 0 0 0 1 0 0 0 0
#> 8 1 0 0 0 0 0 0 0 1 0
#> 10 1 1 0 0 0 0 0 0 1 0
#> 12 1 0 1 0 0 0 0 0 1 0
#> 14 1 0 0 1 0 0 0 0 1 0sessionInfo()
#> R version 4.1.1 (2021-08-10)
#> Platform: x86_64-apple-darwin20.4.0 (64-bit)
#> Running under: macOS Big Sur 11.5.2
#>
#> Matrix products: default
#> BLAS: /usr/local/Cellar/openblas/0.3.17/lib/libopenblasp-r0.3.17.dylib
#> LAPACK: /usr/local/Cellar/r/4.1.1/lib/R/lib/libRlapack.dylib
#>
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] mets_1.2.9 lava_1.6.11 timereg_2.0.0 survival_3.2-13
#>
#> loaded via a namespace (and not attached):
#> [1] Rcpp_1.0.7 highr_0.9 bslib_0.2.5.1
#> [4] compiler_4.1.1 jquerylib_0.1.4 tools_4.1.1
#> [7] digest_0.6.27 jsonlite_1.7.2 evaluate_0.14
#> [10] lattice_0.20-44 ucminf_1.1-4 rlang_0.4.11
#> [13] Matrix_1.3-4 yaml_2.2.1 parallel_4.1.1
#> [16] mvtnorm_1.1-2 xfun_0.25 fastmap_1.1.0
#> [19] stringr_1.4.0 knitr_1.33 sass_0.4.0
#> [22] globals_0.14.0 grid_4.1.1 listenv_0.8.0
#> [25] R6_2.5.1 future.apply_1.8.1 parallelly_1.27.0
#> [28] rmarkdown_2.10 magrittr_2.0.1 codetools_0.2-18
#> [31] htmltools_0.5.2 splines_4.1.1 future_1.22.1
#> [34] numDeriv_2016.8-1.1 stringi_1.7.4