/
pcalc5.R
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pcalc5.R
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pcalc <- function(pars, dat, browse = F, compars = NULL, # compare lprob for true pars with other pars (fitted)
give.pis = F, # return individual pi values for couples (for outside mcmc)
sim = F, # just use this to simulate data given parameters? (outputs pser.a)
spar.log = F, # use sexual partner acquisition rate
heter = F, # individual heterogeneity; simulation only
## using global variables for these
# partner.arv = F, # ART coverage affects within-partnership transmission?
# low.coverage.arv = F, # if T, only 50% of those on ART are not infectious
survive = T, # account for survival in analysis
cond.sim = F, # only simulate individuals that will live
lrho.sd = 1/2, # sd on lrho prior
trace = T) # only do certain calculations when tracing parameters (i.e. for non-thinned versions)
{
if(browse) browser()
if(low.coverage.arv) # if assuming only 50% of those on ART are not-infectious
{
cov.scalar <- .5
}else{
cov.scalar <- 1
}
K <- nrow(dat)
if(!sim)
{
hh.log <- dat$ser==1
mm.log <- dat$ser==2
ff.log <- dat$ser==3
ss.log <- dat$ser==4
}
if(sum(pars[1:5]<0)>0) #if any parameters are <0 then the model must be rejected so we return logprob =-Inf
{
probs <- NA
lprob <- -Inf
pop.avs <- NA
proj12 <- NA
pser.a <- NA
pser <- NA
rrs <- NA
}else{
bmb <- as.numeric(pars["bmb"])
bfb <- as.numeric(pars["bfb"])
bme <- as.numeric(pars["bme"])
bfe <- as.numeric(pars["bfe"])
bmp <- as.numeric(pars["bmp"])
rho <- exp(as.numeric(pars["lrho"])) # feeding in log(rho)
bfp <- bmp * rho
# L stands for *L*ast iteration
s..L <- rep(1,K) # s: concordant negative
mb.L <- rep(0, K) # m: male positive
me.L <- rep(0, K)
f.bL <- rep(0, K) # f: female positive
f.eL <- rep(0, K)
hb1b2L <- rep(0, K) # h: concordant positive
hb2b1L <- rep(0, K) # b1b2 is both inf before, but female 1st, & vice versa
hbeL <- rep(0, K)
hebL <- rep(0, K) # 2nd & 3rd character give route of transmission for M & F, respectively
hbpL <- rep(0, K)
hpbL <- rep(0, K)
hepL <- rep(0, K)
hpeL <- rep(0, K)
he2e1L <- rep(0, K)
he1e2L <- rep(0, K)
## initiate vectors to update based on *L*ast state
s.. <- rep(1,K)
mb. <- rep(0, K)
me. <- rep(0, K)
f.b <- rep(0, K)
f.e <- rep(0, K)
hb1b2 <- rep(0, K)
hb2b1 <- rep(0, K)
hbe <- rep(0, K)
heb <- rep(0, K)
hbp <- rep(0, K)
hpb <- rep(0, K)
hep <- rep(0, K)
hpe <- rep(0, K)
he1e2 <- rep(0, K)
he2e1 <- rep(0, K)
# i.e., hbp is a ++ couple in which the male was inf *b*efore
# couple formation & the female by her *p*artner
if(survive)
{
# A stands for *A*live, i.e. joint probability of serostatus
# and both partners being alive at sampling
mb.AL <- rep(0, K)
me.AL <- rep(0, K)
f.bAL <- rep(0, K)
f.eAL <- rep(0, K)
hb1b2AL <- rep(0, K)
hb2b1AL <- rep(0, K)
hbeAL <- rep(0, K)
hebAL <- rep(0, K)
hbpAL <- rep(0, K)
hpbAL <- rep(0, K)
hepAL <- rep(0, K)
hpeAL <- rep(0, K)
he1e2AL <- rep(0, K)
he2e1AL <- rep(0, K)
## initiate vectors to update based on *L*ast state
mb.A <- rep(0, K)
me.A <- rep(0, K)
f.bA <- rep(0, K)
f.eA <- rep(0, K)
hb1b2A <- rep(0, K)
hb2b1A <- rep(0, K)
hbeA <- rep(0, K)
hebA <- rep(0, K)
hbpA <- rep(0, K)
hpbA <- rep(0, K)
hepA <- rep(0, K)
hpeA <- rep(0, K)
he1e2A <- rep(0, K)
he2e1A <- rep(0, K)
}
for(tt in 1:max(dat$bd))
{
## probabilities are non-zero only for times after started having sex and before couple formation
m.sex <- dat$tmar-dat$bd+tt-1 >= dat$tms & dat$tmar-dat$bd+tt-1 < dat$tmar
f.sex <- dat$tmar-dat$bd+tt-1 >= dat$tfs & dat$tmar-dat$bd+tt-1 < dat$tmar
e.sex <- m.sex|f.sex # either are active
## probability infected in month tt
p.m.bef <- rep(0,K)
p.f.bef <- rep(0,K)
## spar
if(spar.log)
{
m.spar <- rep(1, K)
f.spar <- rep(1, K)
}else{
m.spar <- rep(1, K)
f.spar <- rep(1, K)
}
if(heter)
{
m.het <- exp( rnorm(K, mean = 0, sd = 1) )
f.het <- exp( rnorm(K, mean = 0, sd = 1) )
}else{
m.het <- rep(1, K)
f.het <- rep(1, K)
}
p.m.bef[m.sex] <- (1 - exp(-bmb * m.spar[m.sex] * m.het[m.sex] *epicf[cbind(dat$tmar[m.sex]-dat$bd[m.sex]+tt-1, dat$epic.ind[m.sex])]))
p.f.bef[f.sex] <- (1 - exp(-bfb * f.spar[f.sex] * f.het[f.sex] *epicm[cbind(dat$tmar[f.sex]-dat$bd[f.sex]+tt-1, dat$epic.ind[f.sex])]))
## probability infected in month tt and alive at sampling
if(survive)
{
p.m.bef.a <- rep(0,K)
p.f.bef.a <- rep(0,K)
## csurv[time til interview, age in months in this month]
p.m.bef.a[m.sex] <- p.m.bef[m.sex] * csurv[cbind(dat$mage[m.sex]-dat$cd[m.sex]-dat$bd[m.sex]+tt-1, dat$cd[m.sex]+dat$bd[m.sex]-tt+1)]
p.f.bef.a[f.sex] <- p.f.bef[f.sex] * csurv[cbind(dat$fage[f.sex]-dat$cd[f.sex]-dat$bd[f.sex]+tt-1, dat$cd[f.sex]+dat$bd[f.sex]-tt+1)]
}
## iterate probabilities based on previous values for only cases where it needs updating
s..[e.sex] <- s..L[e.sex]*(1-p.m.bef[e.sex])*(1-p.f.bef[e.sex])
mb.[e.sex] <- mb.L[e.sex]*(1 - p.f.bef[e.sex]) + s..L[e.sex]*p.m.bef[e.sex]*(1-p.f.bef[e.sex])
f.b[e.sex] <- f.bL[e.sex]*(1 - p.m.bef[e.sex]) + s..L[e.sex]*p.f.bef[e.sex]*(1-p.m.bef[e.sex])
## for individuals infected in the same month, assign
## the order of infection based on competing risks
## formula, but if the denominator is 0, replace both
## with 0 to avoid errors.
p.mfirst <- p.m.bef[e.sex] / (p.m.bef[e.sex]+p.f.bef[e.sex])
p.ffirst <- 1-p.mfirst
p.mfirst[is.na(p.mfirst)] <- 0
p.ffirst[is.na(p.ffirst)] <- 0
hb1b2[e.sex] <- hb1b2L[e.sex] + p.mfirst * s..L[e.sex]*p.m.bef[e.sex]*p.f.bef[e.sex] +
mb.L[e.sex]*p.f.bef[e.sex]
hb2b1[e.sex] <- hb2b1L[e.sex] + p.ffirst * s..L[e.sex]*p.m.bef[e.sex]*p.f.bef[e.sex] +
f.bL[e.sex]*p.m.bef[e.sex]
## iterate joint probabilities with survival
if(survive)
{
mb.A[e.sex] <- mb.AL[e.sex]*(1 - p.f.bef[e.sex]) + s..L[e.sex]*p.m.bef.a[e.sex]*(1-p.f.bef[e.sex])
f.bA[e.sex] <- f.bAL[e.sex]*(1 - p.m.bef[e.sex]) + s..L[e.sex]*p.f.bef.a[e.sex]*(1-p.m.bef[e.sex])
## for individuals infected in the same month, assign
## the order of infection based on competing risks
## formula, but if the denominator is 0, replace both
## with 0 to avoid errors.
p.mfirst.a <- p.m.bef.a[e.sex] / (p.m.bef.a[e.sex]+p.f.bef.a[e.sex])
p.ffirst.a <- 1-p.mfirst.a
p.mfirst.a[is.na(p.mfirst.a)] <- 0
p.ffirst.a[is.na(p.ffirst.a)] <- 0
hb1b2A[e.sex] <- hb1b2AL[e.sex] + p.mfirst.a * s..L[e.sex]*p.m.bef.a[e.sex]*p.f.bef.a[e.sex] +
mb.AL[e.sex] * p.f.bef.a[e.sex]
hb2b1A[e.sex] <- hb2b1AL[e.sex] + p.ffirst.a * s..L[e.sex]*p.m.bef.a[e.sex]*p.f.bef.a[e.sex] +
f.bAL[e.sex] * p.m.bef.a[e.sex]
## Update *A*live *L*ast states
mb.AL[e.sex] <- mb.A[e.sex]
f.bAL[e.sex] <- f.bA[e.sex]
hb1b2AL[e.sex] <- hb1b2A[e.sex]
hb2b1AL[e.sex] <- hb2b1A[e.sex]
}
## Update other *L*ast states
s..L[e.sex] <- s..[e.sex]
mb.L[e.sex] <- mb.[e.sex]
f.bL[e.sex] <- f.b[e.sex]
hb1b2L[e.sex] <- hb1b2[e.sex]
hb2b1L[e.sex] <- hb2b1[e.sex]
}
## probability of being infected by partner (constant, used inside loop)
p.m.part <- 1 - exp(-bmp)
p.f.part <- 1 - exp(-bfp)
## Now loop through marriage
for(tt in 1:max(dat$cd-1))
{
## are partners formed in a couple?
fmd <- dat$cd >= tt
######################################################################
## everything below is automatically sum(fmd) length except p.m/f.part which are length 1
## probability infected extracouply in the ttc-th month of couple
p.m.exc <- (1 - exp(-bme * m.spar[fmd] * m.het[fmd] *epicf[cbind(dat$tmar[fmd]+(tt-1), dat$epic.ind[fmd])]))
p.f.exc <- (1 - exp(-bfe * f.spar[fmd] * f.het[fmd] *epicm[cbind(dat$tmar[fmd]+(tt-1), dat$epic.ind[fmd])]))
## adjust probability of being infected by partner by probability partner is infectious (i.e. not on ART)
if(partner.arv)
{
p.m.part <- 1 - exp(-bmp * (1 - cov.scalar * art.prev[cbind(dat$tmar[fmd]+(tt-1), dat$epic.ind[fmd])]))
p.f.part <- 1 - exp(-bfp * (1 - cov.scalar * art.prev[cbind(dat$tmar[fmd]+(tt-1), dat$epic.ind[fmd])]))
}
if(survive)
{
## Survival probabilities
s.p.m <- csurv[cbind(dat$mage[fmd]-dat$cd[fmd]+tt-1, dat$tint[fmd] - (dat$tmar[fmd] + tt - 1))]
s.p.f <- csurv[cbind(dat$fage[fmd]-dat$cd[fmd]+tt-1, dat$tint[fmd] - (dat$tmar[fmd] + tt - 1))]
## Transmission probabilities from partner (jointly with survival)
p.m.part.a <- p.m.part * s.p.m
p.f.part.a <- p.f.part * s.p.f
p.m.exc.a <- p.m.exc * s.p.m
p.f.exc.a <- p.f.exc * s.p.f
}
######################################################################
## iterate probabilities
s..[fmd] <- s..L[fmd]*(1-p.m.exc)*(1-p.f.exc)
mb.[fmd] <- mb.L[fmd]*(1-p.f.exc)*(1-p.f.part)
me.[fmd] <- me.L[fmd]*(1-p.f.exc)*(1-p.f.part) + s..L[fmd]*p.m.exc*(1-p.f.exc)
f.b[fmd] <- f.bL[fmd]*(1-p.m.exc)*(1-p.m.part)
f.e[fmd] <- f.eL[fmd]*(1-p.m.exc)*(1-p.m.part) + s..L[fmd]*p.f.exc*(1-p.m.exc)
## hb1b2[fmd] <- hb1b2L[fmd] # Doesn't change during couple duration
## hb2b1[fmd] <- hb2b1L[fmd] # Doesn't change during couple duration
hbe[fmd] <- hbeL[fmd] + mb.L[fmd]*(1-p.f.part)*p.f.exc
heb[fmd] <- hebL[fmd] + f.bL[fmd]*(1-p.m.part)*p.m.exc
hbp[fmd] <- hbpL[fmd] + mb.L[fmd]*p.f.part
hpb[fmd] <- hpbL[fmd] + f.bL[fmd]*p.m.part
hep[fmd] <- hepL[fmd] + me.L[fmd]*p.f.part
hpe[fmd] <- hpeL[fmd] + f.eL[fmd]*p.m.part
## for individuals infected in the same month, assign
## the order of infection based on competing risks
## formula, but if the denominator is 0, replace both
## with 0 to avoid errors.
p.mfirst <- p.m.exc / (p.m.exc+p.f.exc)
p.ffirst <- 1-p.mfirst
p.mfirst[is.na(p.mfirst)] <- 0
p.ffirst[is.na(p.ffirst)] <- 0
he1e2[fmd] <- he1e2L[fmd] + p.mfirst * s..L[fmd]*p.m.exc*p.f.exc +
me.L[fmd]*(1-p.f.part)*p.f.exc
he2e1[fmd] <- he2e1L[fmd] + p.ffirst * s..L[fmd]*p.m.exc*p.f.exc +
f.eL[fmd]*(1-p.m.part)*p.m.exc
######################################################################
## Iterate probabilities jointly with survival until survey.
## Note for probabilities of not being infected, we don't
## use the joint probability with being alive at sampling.
if(survive)
{
mb.A[fmd] <- mb.AL[fmd]*(1-p.f.exc)*(1-p.f.part)
me.A[fmd] <- me.AL[fmd]*(1-p.f.exc)*(1-p.f.part) + s..L[fmd]*p.m.exc.a*(1-p.f.exc)
f.bA[fmd] <- f.bAL[fmd]*(1-p.m.exc)*(1-p.m.part)
f.eA[fmd] <- f.eAL[fmd]*(1-p.m.exc)*(1-p.m.part) + s..L[fmd]*p.f.exc.a*(1-p.m.exc)
## hb1b2A[fmd] <- hb1b2AL[fmd] # Doesn't change during couple duration
## hb2b1A[fmd] <- hb2b1AL[fmd] # Doesn't change during couple duration
hbeA[fmd] <- hbeAL[fmd] + mb.AL[fmd]*(1-p.f.part)*p.f.exc.a
hebA[fmd] <- hebAL[fmd] + f.bAL[fmd]*(1-p.m.part)*p.m.exc.a
hbpA[fmd] <- hbpAL[fmd] + mb.AL[fmd]*p.f.part.a
hpbA[fmd] <- hpbAL[fmd] + f.bAL[fmd]*p.m.part.a
hepA[fmd] <- hepAL[fmd] + me.AL[fmd]*p.f.part.a
hpeA[fmd] <- hpeAL[fmd] + f.eAL[fmd]*p.m.part.a
## for individuals infected in the same month, assign
## the order of infection based on competing risks
## formula, but if the denominator is 0, replace both
## with 0 to avoid errors.
p.mfirst.a <- p.m.exc.a / (p.m.exc.a+p.f.exc.a)
p.ffirst.a <- 1-p.mfirst.a
p.mfirst.a[is.na(p.mfirst.a)] <- 0
p.ffirst.a[is.na(p.ffirst.a)] <- 0
he1e2A[fmd] <- he1e2AL[fmd] + p.mfirst.a * s..L[fmd]*p.m.exc.a*p.f.exc.a +
me.AL[fmd]*(1-p.f.part)*p.f.exc.a
he2e1A[fmd] <- he2e1AL[fmd] + p.ffirst.a * s..L[fmd]*p.m.exc.a*p.f.exc.a +
f.eAL[fmd]*(1-p.m.part)*p.m.exc.a
## update *L*ast month states for *A*live states
mb.AL[fmd] <- mb.A[fmd]
me.AL[fmd] <- me.A[fmd]
f.bAL[fmd] <- f.bA[fmd]
f.eAL[fmd] <- f.eA[fmd]
## hb1b2AL[fmd] <- hb1b2A[fmd]
## hb2b1AL[fmd] <- hb2b1A[fmd]
hbeAL[fmd] <- hbeA[fmd]
hebAL[fmd] <- hebA[fmd]
hbpAL[fmd] <- hbpA[fmd]
hpbAL[fmd] <- hpbA[fmd]
hepAL[fmd] <- hepA[fmd]
hpeAL[fmd] <- hpeA[fmd]
he1e2AL[fmd] <- he1e2A[fmd]
he2e1AL[fmd] <- he2e1A[fmd]
}
## update other *L*ast month states
s..L[fmd] <- s..[fmd]
mb.L[fmd] <- mb.[fmd]
me.L[fmd] <- me.[fmd]
f.bL[fmd] <- f.b[fmd]
f.eL[fmd] <- f.e[fmd]
## hb1b2L[fmd] <- hb1b2[fmd]
## hb2b1L[fmd] <- hb2b1[fmd]
hbeL[fmd] <- hbe[fmd]
hebL[fmd] <- heb[fmd]
hbpL[fmd] <- hbp[fmd]
hpbL[fmd] <- hpb[fmd]
hepL[fmd] <- hep[fmd]
hpeL[fmd] <- hpe[fmd]
he1e2L[fmd] <- he1e2[fmd]
he2e1L[fmd] <- he2e1[fmd]
}
allstates <- data.frame(s..,mb.,me.,f.b,f.e,hb1b2,hb2b1,hbe,heb,hbp,hpb,hep,hpe,he1e2,he2e1,
mb.A,me.A,f.bA,f.eA,hb1b2A,hb2b1A,hbeA,hebA,hbpA,hpbA,hepA,hpeA,he1e2A,he2e1A)
ss <- s..
mm <- mb. + me.
ff <- f.b + f.e
hh <- hb1b2 + hb2b1 + hbe + heb + hbp + hpb + hep + hpe + he1e2 + he2e1
## Calculate probability of data given parameters * priors of paramters
if(survive)
{
mmA <- mb.A + me.A
ffA <- f.bA + f.eA
hhA <- hb1b2A + hb2b1A + hbeA + hebA + hbpA + hpbA + hepA + hpeA + he1e2A + he2e1A
pser.a <- cbind(hhA, mmA, ffA, ss)
}
pser <- cbind(hh, mm, ff, ss)
if(trace & sim) # calculate expected route of transmission breakdowns for couples with unknown (or simulated serostatus)
{
######################################################################
## Route of transmission breakdowns for observed couples
## (conditional on survival)
######################################################################
## male breakdown amongst observed M+F- couples, partner *N*egative
pibNA <- mean(mb.A / mmA, na.rm = T)
pieNA <- mean(me.A / mmA, na.rm = T)
## female breakdown amongst observed M-F+ couples, partner *N*egative
piNbA <- mean(f.bA / ffA, na.rm = T)
piNeA <- mean(f.eA / ffA, na.rm = T)
## male breakdown amongst observed M+F+ couples, partner *P*ositive
pibPA <- mean((hb1b2A + hb2b1A + hbeA + hbpA) / hhA, na.rm = T)
piePA <- mean((hebA + hepA + he1e2A + he2e1A) / hhA, na.rm = T)
pipPA <- mean((hpbA + hpeA) / hhA, na.rm = T)
## female breakdown amongst observed M+F+ couples, partner *P*ositive
piPbA <- mean((hb1b2A + hb2b1A + hebA + hpbA) / hhA, na.rm = T)
piPeA <- mean((hbeA + hpeA + he1e2A + he2e1A) / hhA, na.rm = T)
piPpA <- mean((hbpA + hepA) / hhA, na.rm = T)
## male breakdown amongst infected males in any observed couples, partner *U*nknown (bc could be either)
pibUA <- mean((mb.A + hb1b2A + hb2b1A + hbeA + hbpA) / (mmA + hhA), na.rm = T)
pieUA <- mean((me.A + hebA + hepA + he1e2A + he2e1A) / (mmA + hhA), na.rm = T)
pipUA <- mean((hpbA + hpeA) / (mmA + hhA), na.rm = T)
## female breakdown amongst infected females in any observed couples, partner *U*nknown (bc could be either)
piUbA <- mean((f.bA + hb1b2A + hb2b1A + hebA + hpbA) / (ffA + hhA), na.rm = T)
piUeA <- mean((f.eA + hbeA + hpeA + he1e2A + he2e1A) / (ffA + hhA), na.rm = T)
piUpA <- mean((hbpA + hepA) / (ffA + hhA), na.rm = T)
######################################################################
pop.avs <- data.frame(
## conditional on survival
pibNA, pieNA, # b/e in +- given A
piNbA, piNeA, # b/e in -+ given A
pibPA, piePA, pipPA, # b/e/p in male in ++ given A
piPbA, piPeA, piPpA, # b/e/p in female in ++ given A
pibUA, pieUA, pipUA, # b/e/p in male in any given A
piUbA, piUeA, piUpA) # b/e/p in female in any given A
}
if(trace & !sim)
{
######################################################################
## Route of transmission breakdowns for observed couples
## (conditional on survival)
######################################################################
## male breakdown amongst observed M+F- couples, partner *N*egative
pibNA <- sum(mb.A[mm.log] / mmA[mm.log]) / sum(mm.log)
pieNA <- sum(me.A[mm.log] / mmA[mm.log]) / sum(mm.log)
## female breakdown amongst observed M-F+ couples, partner *N*egative
piNbA <- sum(f.bA[ff.log] / ffA[ff.log]) / sum(ff.log)
piNeA <- sum(f.eA[ff.log] / ffA[ff.log]) / sum(ff.log)
## male breakdown amongst observed M+F+ couples, partner *P*ositive
pibPA <- sum((hb1b2A[hh.log] + hb2b1A[hh.log] + hbeA[hh.log] + hbpA[hh.log]) / hhA[hh.log]) / sum(hh.log)
piePA <- sum((hebA[hh.log] + hepA[hh.log] + he1e2A[hh.log] + he2e1A[hh.log]) / hhA[hh.log]) / sum(hh.log)
pipPA <- sum((hpbA[hh.log] + hpeA[hh.log]) / hhA[hh.log]) / sum(hh.log)
## female breakdown amongst observed M+F+ couples, partner *P*ositive
piPbA <- sum((hb1b2A[hh.log] + hb2b1A[hh.log] + hebA[hh.log] + hpbA[hh.log]) / hhA[hh.log]) / sum(hh.log)
piPeA <- sum((hbeA[hh.log] + hpeA[hh.log] + he1e2A[hh.log] + he2e1A[hh.log]) / hhA[hh.log]) / sum(hh.log)
piPpA <- sum((hbpA[hh.log] + hepA[hh.log]) / hhA[hh.log]) / sum(hh.log)
## male breakdown amongst infected males in any observed couples, partner *U*nknown (bc could be either)
pibUA <- (pibNA*sum(mm.log) + pibPA*sum(hh.log)) / (sum(mm.log) + sum(hh.log))
pieUA <- (pieNA*sum(mm.log) + piePA*sum(hh.log)) / (sum(mm.log) + sum(hh.log))
pipUA <- (pipPA*sum(hh.log)) / (sum(mm.log) + sum(hh.log))
## female breakdown amongst infected females in any observed couples, partner *U*nknown (bc could be either)
piUbA <- (piNbA*sum(ff.log) + piPbA*sum(hh.log)) / (sum(ff.log) + sum(hh.log))
piUeA <- (piNeA*sum(ff.log) + piPeA*sum(hh.log)) / (sum(ff.log) + sum(hh.log))
piUpA <- (piPpA*sum(hh.log)) / (sum(ff.log) + sum(hh.log))
######################################################################
## Give pieNA, piNeA, piePA, piPeA, for each couple
if(give.pis)
{
## probability infection was extracouple given ser
piCe.A <- rep(NA, K)
piC.eA <- rep(NA, K)
piCe.A[mm.log] <- me.A[mm.log] / mmA[mm.log]
piCe.A[hh.log] <- (hebA[hh.log] + hepA[hh.log] + he1e2A[hh.log] + he2e1A[hh.log]) / hhA[hh.log]
piC.eA[ff.log] <- f.eA[ff.log] / ffA[ff.log]
piC.eA[hh.log] <- (hbeA[hh.log] + hpeA[hh.log] + he1e2A[hh.log] + he2e1A[hh.log]) / hhA[hh.log]
pis <- data.frame(piCe.A, piC.eA)
}
######################################################################
## Route of transmission breakdowns for inferred
## pseudopopulation (unconditional on survival)
######################################################################
######################################################################
## Index infections, do with estimators summing over all
## infected couples and over all couples
## version 1 - all infected couples
mb1. <- rowSums(allstates[!ss.log, c("mb.","hb1b2","hbe","hbp")])
me1. <- rowSums(allstates[!ss.log, c("me.","he1e2","hep")])
## female
f.b1 <- rowSums(allstates[!ss.log, c("f.b","hb2b1","heb","hpb")])
f.e1 <- rowSums(allstates[!ss.log, c("f.e","he2e1","hpe")])
all.infA <- rowSums(allstates[!ss.log,names(allstates)[(grepl("m", names(allstates)) | grepl("f", names(allstates)) | grepl("h", names(allstates))) & grepl("A", names(allstates))]])
## number of inflated male before-couple index infections (in any couple)
mb1.Infl <- sum( mb1. / all.infA)
## number of inflated male extra-couple index infections (in any couple)
me1.Infl <- sum( me1. / all.infA)
## nufber of inflated male before-couple index infections (in any couple)
f.b1Infl <- sum( f.b1 / all.infA)
## number of inflated male extra-couple index infections (in any couple)
f.e1Infl <- sum( f.e1 / all.infA)
## number of inflated index infections (1 in each couple with an infection)
IndInfl <- mb1.Infl + me1.Infl + f.b1Infl + f.e1Infl
######################################################################
## Proportion of index infections pooling across gender
piGb1.sumI <- mb1.Infl / IndInfl
piGe1.sumI <- me1.Infl / IndInfl
piG.b1sumI <- f.b1Infl / IndInfl
piG.e1sumI <- f.e1Infl / IndInfl
## ## version 2 - sum over all couples
mb1. <- rowSums(allstates[, c("mb.","hb1b2","hbe","hbp")])
me1. <- rowSums(allstates[, c("me.","he1e2","hep")])
## female
f.b1 <- rowSums(allstates[, c("f.b","hb2b1","heb","hpb")])
f.e1 <- rowSums(allstates[, c("f.e","he2e1","hpe")])
all.infA <- rowSums(allstates[,c("s..", names(allstates)[(grepl("m", names(allstates)) | grepl("f", names(allstates)) | grepl("h", names(allstates))) & grepl("A", names(allstates))])])
## number of inflated male before-couple index infections (in any couple)
mb1.Infl <- sum( mb1. / all.infA)
## number of inflated male extra-couple index infections (in any couple)
me1.Infl <- sum( me1. / all.infA)
## nufber of inflated male before-couple index infections (in any couple)
f.b1Infl <- sum( f.b1 / all.infA)
## number of inflated male extra-couple index infections (in any couple)
f.e1Infl <- sum( f.e1 / all.infA)
## number of inflated index infections (1 in each couple with an infection)
IndInfl <- mb1.Infl + me1.Infl + f.b1Infl + f.e1Infl
######################################################################
## Proportion of index infections pooling across gender
piGb1.sumIS <- mb1.Infl / IndInfl
piGe1.sumIS <- me1.Infl / IndInfl
piG.b1sumIS <- f.b1Infl / IndInfl
piG.e1sumIS <- f.e1Infl / IndInfl
## put them all in a dataframe
pop.avs <- data.frame(
## conditional on survival
pibNA, pieNA, # b/e in +- given A
piNbA, piNeA, # b/e in -+ given A
pibPA, piePA, pipPA, # b/e/p in male in ++ given A
piPbA, piPeA, piPpA, # b/e/p in female in ++ given A
pibUA, pieUA, pipUA, # b/e/p in male in any given A
piUbA, piUeA, piUpA, # b/e/p in female in any given A
## unconditional on survival version 1
piGb1.sumI, piGe1.sumI, # b/e index in males amongst all infected
piG.b1sumI, piG.e1sumI, # b/e index in females amongst all infected
piGb1.sumIS, piGe1.sumIS, # b/e index in males amongst all infected
piG.b1sumIS, piG.e1sumIS) # b/e index in females amongst all infected
######################################################################
## Project incidence forward 12 months for each of the 3
## couple types (ss, mh, fh) for each country in the data
## set (because they have different population prevalences
num.country <- length(unique(dat$epic.ind))
cc.inds <- unique(dat$epic.ind)
## concordant negative
ss12.ssL <- rep(1, num.country)
mm12.ssL <- rep(0, num.country)
ff12.ssL <- rep(0, num.country)
hh12.ssL <- rep(0, num.country)
## male positive discordant
mm12.mmL <- rep(1, num.country)
hh12.mmL <- rep(0, num.country)
## female positive discordant
ff12.ffL <- rep(1, num.country)
hh12.ffL <- rep(0, num.country)
## initialize pis
pi.m.part12.ss <- 0
pi.f.part12.ss <- 0
pi.m.exc12.ss <- 0
pi.f.exc12.ss <- 0
pi.f.part12.mm <- 0
pi.f.exc12.mm <- 0
pi.m.part12.ff <- 0
pi.m.exc12.ff <- 0
for(tt in 1:12)
{
if(partner.arv)
{
p.m.part <- 1 - exp(-bmp * (1 - cov.scalar * art.prev[1332+tt-1, cc.inds]))
p.f.part <- 1 - exp(-bfp * (1 - cov.scalar * art.prev[1332+tt-1, cc.inds]))
}
######################################################################
## Transmission probabilities
## probability infected extracouply in various months of 2011
p.m.exc <- 1 - exp(-bme*epicf[1332+tt-1, cc.inds])
p.f.exc <- 1 - exp(-bfe*epicm[1332+tt-1, cc.inds])
## concordant negative couples
ss12.ss <- ss12.ssL*(1-p.m.exc)*(1-p.f.exc)
mm12.ss <- mm12.ssL*(1-p.f.exc)*(1-p.f.part) + ss12.ssL*p.m.exc*(1-p.f.exc)
ff12.ss <- ff12.ssL*(1-p.m.exc)*(1-p.m.part) + ss12.ssL*p.f.exc*(1-p.m.exc)
hh12.ss <- hh12.ssL + ss12.ssL* p.m.exc*p.f.exc +
mm12.ssL*(p.f.part + (1-p.f.part)*p.f.exc) +
ff12.ssL*(p.m.part + (1-p.m.part)*p.m.exc)
pi.m.part12.ss <- pi.m.part12.ss + ff12.ssL*p.m.part
pi.f.part12.ss <- pi.f.part12.ss + mm12.ssL*p.f.part
pi.m.exc12.ss <- pi.m.exc12.ss + (ss12.ssL + ff12.ssL*(1-p.m.part))*p.m.exc
pi.f.exc12.ss <- pi.f.exc12.ss + (ss12.ssL + mm12.ssL*(1-p.f.part))*p.f.exc
## male positive couples & female seroconversion
mm12.mm <- mm12.mmL*(1-p.f.exc)*(1-p.f.part)
hh12.mm <- hh12.mmL + mm12.mmL*(p.f.part + (1-p.f.part)*p.f.exc)
pi.f.part12.mm <- pi.f.part12.mm + mm12.mmL*p.f.part
pi.f.exc12.mm <- pi.f.exc12.mm + mm12.mmL*(1-p.f.part)*p.f.exc
## female positive couples & male seroconversion
ff12.ff <- ff12.ffL*(1-p.m.exc)*(1-p.m.part)
hh12.ff <- hh12.ffL + ff12.ffL*(p.m.part + (1-p.m.part)*p.m.exc)
pi.m.part12.ff <- pi.m.part12.ff + ff12.ffL*p.m.part
pi.m.exc12.ff <- pi.m.exc12.ff + ff12.ffL*(1-p.m.part)*p.m.exc
ss12.ssL <- ss12.ss
mm12.ssL <- mm12.ss
ff12.ssL <- ff12.ss
hh12.ssL <- hh12.ss
## male positive discordant
mm12.mmL <- mm12.mm
hh12.mmL <- hh12.mm
## female positive discordant
ff12.ffL <- ff12.ff
hh12.ffL <- hh12.ff
}
n.m.part.dc <- 0
n.m.part.cc <- 0
n.f.part.dc <- 0
n.f.part.cc <- 0
n.m.exc.dc <- 0
n.m.exc.cc <- 0
n.f.exc.dc <- 0
n.f.exc.cc <- 0
## add all the different countries incidence by scaling by serotype
for(cc in 1:num.country)
{
n.m.part.dc <- n.m.part.dc + pi.m.part12.ff[cc]*sum(ff.log & dat$epic.ind == cc.inds[cc])
n.f.part.dc <- n.f.part.dc + pi.f.part12.mm[cc]*sum(mm.log & dat$epic.ind == cc.inds[cc])
n.m.part.cc <- n.m.part.cc + pi.m.part12.ss[cc]*sum(ss.log & dat$epic.ind == cc.inds[cc])
n.f.part.cc <- n.f.part.cc + pi.f.part12.ss[cc]*sum(ss.log & dat$epic.ind == cc.inds[cc])
n.m.exc.dc <- n.m.exc.dc + pi.m.exc12.ff[cc]*sum(ff.log & dat$epic.ind == cc.inds[cc])
n.f.exc.dc <- n.f.exc.dc + pi.f.exc12.mm[cc]*sum(mm.log & dat$epic.ind == cc.inds[cc])
n.m.exc.cc <- n.m.exc.cc + pi.m.exc12.ss[cc]*sum(ss.log & dat$epic.ind == cc.inds[cc])
n.f.exc.cc <- n.f.exc.cc + pi.f.exc12.ss[cc]*sum(ss.log & dat$epic.ind == cc.inds[cc])
}
n.m.dc <- n.m.part.dc + n.m.exc.dc
n.f.dc <- n.f.part.dc + n.f.exc.dc
n.m.part.tot <- n.m.part.dc + n.m.part.cc
n.f.part.tot <- n.f.part.dc + n.f.part.cc
n.m.exc.tot <- n.m.exc.dc + n.m.exc.cc
n.f.exc.tot <- n.f.exc.dc + n.f.exc.cc
proj12 <- data.frame(n.m.part.dc, n.f.part.dc, # incidence per 1000
n.m.part.cc, n.f.part.cc,
n.m.exc.dc, n.f.exc.dc,
n.m.exc.cc, n.f.exc.cc,
n.m.part.tot, n.f.part.tot,
n.m.exc.tot, n.f.exc.tot) / sum(!hh.log) * 1000
prop.exc.m <- n.m.exc.tot / (n.m.exc.tot + n.m.part.tot)
prop.exc.f <- n.f.exc.tot / (n.f.exc.tot + n.f.part.tot)
prop.exc.m.dc <- n.m.exc.dc / n.m.dc
prop.exc.f.dc <- n.f.exc.dc / n.f.dc
proj12 <- data.frame(proj12, prop.exc.m, prop.exc.f, prop.exc.m.dc, prop.exc.f.dc)
## relative rate of transmission coefficient extracouply vs before relationship
rr.m.out <- bme/bmb
rr.f.out <- bfe/bfb
rr.m.in <- bmp/bme
rr.f.in <- bfp/bfe
rr.m.pbef <- bmp/bmb #partner to before
rr.f.pbef <- bfp/bfb
## relative rate of transmission coefficient extracouply and before relationship between males and females
rr.mf.bef <- bmb/bfb
rr.mf.exc <- bme/bfe
## rho is the last one
## relative rate of contact/risk paramter (i.e. accounting
## for difference in per coital act probability as estimated
## from within partnership transmission.
rr.mf.bef.cont <- rr.mf.bef * rho
rr.mf.exc.cont <- rr.mf.exc * rho
rrs <- data.frame(rr.m.out = rr.m.out, rr.f.out = rr.f.out,
rr.m.in = rr.m.in, rr.f.in = rr.f.in,
rr.m.pbef = rr.m.pbef, rr.f.pbef = rr.f.pbef,
rr.mf.bef = rr.mf.bef, rr.mf.exc = rr.mf.exc,
rr.mf.bef.cont = rr.mf.bef.cont, rr.mf.exc.cont = rr.mf.exc.cont)
}
if(sim) # if simulating data
{
probs <- NA
lprob <- NA
## create couple state probability *A*live & *D*ead
sim.probs <- data.frame(s..A = s..,
mb.A, mb.D = mb.- mb.A,
me.A, me.D = me. - me.A,
f.bA, f.bD = f.b - f.bA,
f.eA, f.eD = f.e - f.eA,
hb1b2A, hb1b2D = hb1b2 - hb1b2A, # note some of the dead cases were infected by dead partners, so can only use the index cases in any h couple
hb2b1A, hb2b1D = hb2b1 - hb2b1A,
hbeA, hbeD = hbe - hbeA,
hebA, hebD = heb - hebA,
hepA, hepD = hep - hepA,
hpeA, hpeD = hpe - hpeA,
hbpA, hbpD = hbp - hbpA,
hpbA, hpbD = hpb - hpbA,
he1e2A, he1e2D = he1e2 - he1e2A,
he2e1A, he2e1D = he2e1 - he2e1A)
for(ii in 1:nrow(dat))
{
dat$cat[ii] <- which(rmultinom(1, 1, sim.probs[ii,])==1)
}
dat$cat.nm <- names(sim.probs)[dat$cat]
dat$cat.nm <- factor(dat$cat.nm, levels = names(sim.probs))
K <- nrow(dat)
if(!survive) pser.a <- NA
}else{ ## if not simulating data calculate likelihood p(data|pars)
if(survive)
{ # must NORMALIZE probabilities to 1 for likelihood!
probs <- pser.a[cbind(1:K,dat$ser)] / rowSums(pser.a) # accounting for survival
}else{
probs <- pser[cbind(1:K,dat$ser)] # if not accounting for survival
pser.a <- NA
}
if(sum(probs==0)==0) # if non of the serotatuses occur with 0 probability in the current model
{
lprob <- sum(log(probs)) + dnorm(log(rho), log(trans.ratio), lrho.sd, log = T)
if(length(compars)>0) clprob <- sum(log(cprobs)) + dnorm(as.numeric(compars["lrho"]),
log(trans.ratio), lrho.sd, log = T)
}else{ # if some of the serostatuses are 0, then the current parameters have 0 probability
lprob <- -Inf
}
}
}
if(length(compars)==0)
{
clprob <- NA
cprobs <- NA
}
if(sim)
{
if(trace)
{
if(give.pis)
{
return(list(lprob = lprob,pop.avs = pop.avs, proj12 = proj12, sim.probs, allstates = allstates,
pser.a = pser.a, pser = pser, dat = dat, clprob = clprob, probs = probs, cprobs = cprobs, m.het = m.het, f.het = f.het))
}else{
return(list(lprob = lprob,pop.avs = pop.avs, rrs = rrs, proj12=proj12, sim.probs, allstates = allstates,
pser.a = pser.a, pser = pser, dat = dat, clprob = clprob, probs = probs, cprobs = cprobs, m.het = m.het, f.het = f.het))
}
}else{
return(list(lprob = lprob, pser.a = pser.a, pser = pser, dat = dat, sim.probs, allstates = allstates,
clprob = clprob, probs = probs, cprobs = cprobs, m.het = m.het, f.het = f.het))
}
}else{ # if not simulating
if(trace)
{
if(give.pis)
{
return(list(lprob = lprob,pop.avs = pop.avs, rrs = rrs, proj12=proj12, pis = pis, allstates = allstates,
pser.a = pser.a, pser = pser, probs = probs))
}else{
return(list(lprob = lprob,pop.avs = pop.avs, rrs = rrs, proj12=proj12,
pser.a = pser.a, pser = pser, probs = probs))
}
}else{
return(list(lprob = lprob, pser.a = pser.a, pser = pser))
}
}
}
init.fxn <- function(seed = 1)
{
set.seed(seed)
## sample uniform dispersed on log scale
lpars <- c(bmb = runif(1, -6, -3),
bfb = runif(1, -6, -3),
bme = runif(1, -6, -3),
bfe = runif(1, -6, -3),
bmp = runif(1, -6, -3))
pars <- c(exp(lpars), lrho = runif(1, -1, 1))
return(pars)
}
## MCMC SAMPLER
sampler <- function(sd.props = sd.props, inits,
multiv = F, covar = NULL, # if multiv, sample from multivariate distribution (calculated during adaptive phase)
verbose = T, tell = 100, seed = 1, lrho.sd,
niter = 6*1000, survive,
nthin = 5,
nburn = 1000, browse=F)
{
if(browse) browser()
set.seed(seed)
pars <- inits
vv <- 2
accept <- 0 #track each parameters acceptance individually
cur <- pcalc(pars, dat = dat, trace = T, survive = survive) #calculate first log probability
lprob.cur <- cur$lprob
out <- t(data.frame(c(pars, bfp = as.numeric(pars["bmp"]*exp(pars["lrho"])),
cur$pop.avs, cur$rrs, cur$proj12)))
last.it <- 0
start <- Sys.time()
while(vv < niter + 1)
{
if(verbose & vv%%tell+1==1) print(paste("on iteration",vv,"of",last.it + niter + 1))
pars.prop <- pars #initialize proposal parameterr vector
## propose new parameter vector
if(multiv)
{
pars.prop <- pars.prop + rmnorm(1, mean = 0, varcov = covar)
pars.prop <- as.vector(pars.prop) #otherwise is a matrix
names(pars.prop) <- parnames
}else{
pars.prop <- pars.prop + rnorm(length(pars), mean = 0, sd = sd.props)
}
## trace = T if in non-thinned iteration, or the previous one (in case of rejection)
## calculate proposal par log probability
prop <- pcalc(pars.prop, dat = dat, survive = survive, trace = vv%%nthin + 1 %in% c(nthin,1))
lprob.prop <- prop$lprob
lmh <- lprob.prop - lprob.cur # log Metropolis-Hastings ratio
## if MHR >= 1 or a uniform random # in [0,1] is <= MHR, accept otherwise reject
if(lmh >= 0 | runif(1,0,1) <= exp(lmh))
{
pars <- pars.prop
if(vv>nburn) accept <- accept + 1 #only track acceptance after burn-in
lprob.cur <- lprob.prop
cur <- prop
}
if(vv%%nthin + 1 ==1)
{
out <- cbind(out,t(data.frame(c(pars, bfp = as.numeric(pars["bmp"]*exp(pars["lrho"])),
cur$pop.avs, cur$rrs, cur$proj12))))
}
vv <- vv+1
}
if(verbose) print(paste("took", difftime(Sys.time(),start, units = "mins"),"mins"))
aratio <- accept/((vv-nburn))
return(list(out = out[,1:ncol(out)>(nburn+1)/nthin], aratio = aratio, inits = inits))
}
## plot trajectory for selected couples
ctraj <- function(pars, dat, browse = F, width = 11, height = 8.5, last.year = 2012,
plot.cpls = NULL, ylab = "probability in couple serostatus / pop prevalence",
surv = T, # show curves joint with survival
nsurv = F, # show curves not joint with survival
survive = T, # show point on surv curve
dead = T, # show curve for prob of couple dying
cprob = T, # show conditional probabilities
cols = c("orange", "darkgreen", "purple","gray"),
col.dead = "black",
lty.surv = 1, lty.dead = 1,
lty.nsurv = 2, blob = T, blob.cex = 3, show.susc = T, cex.leg = 1,
show.age = F, do.leg = T, drp = 1, x.ticks = T, t.lwd = 1,
do.pdf = T, pdf.name = "surv traj.pdf")
{
if(browse) browser()
K <- nrow(dat)
if(do.pdf)
{
pdf(pdf.name, width = width, height = height)
par(mar=c(0,4,.5,2))
}
for(cpl in plot.cpls)
{
temp <- dat[cpl,]
xlim <- c(80*12, (last.year-1900)*12)
if(show.susc)
{
ylim <- c(-.3,1)
}else{
ylim <- c(-.3,.5)
}
plot(0,0, type = "n", xlim = xlim, axes = F,
ylim = ylim, xlab = "", ylab = ylab, bty = "n")
lines(xlim[1]:xlim[2], epicm[xlim[1]:xlim[2],temp$epic.ind], col = "red", lty = 2, lwd = 3)
lines(xlim[1]:xlim[2], epicf[xlim[1]:xlim[2],temp$epic.ind], col = "red", lty = 3, lwd = 3)
if(surv & !nsurv & dead & do.leg) legend("topleft", c("M+F+ & alive", "M+F- & alive","M-F+ & alive","M-F- & alive", "dead before DHS sampling"),
col = c(cols,col.dead), lwd = 3,
lty = c(rep(lty.surv,3),1,lty.dead), bty = "n", cex = cex.leg)
if(surv & nsurv & do.leg) legend("topleft", c("M+F+","M+F-","M-F+","M+F+ & alive",
"M+F- & alive","M-F+ & alive","M-F-"),
col = c(cols[1:3],cols), lwd = 3,
lty = c(rep(lty.nsurv,3),rep(lty.surv,3),1), bty = "n", cex = cex.leg)
if(surv & !nsurv & do.leg & !dead) legend("topleft", c("M+F+ & alive", "M+F- & alive","M-F+ & alive","M-F-"),
col = cols, lwd = 3,
lty = c(rep(lty.surv,3),1), bty = "n", cex = cex.leg)
if(!surv & nsurv & do.leg) legend("topleft", c("M+F+","M+F-","M-F+", "M-F-"),
col = cols, lwd = 3,
lty = c(rep(lty.nsurv,3),1), bty = "n", cex = cex.leg)
if(do.leg) legend("left", c("HIV population prev in M", "HIV population prev in F"),
lty = 2:3, lwd = 3, col = "red", bty = "n", cex = cex.leg)
if(x.ticks)
{
axis(1, seq(xlim[1],xlim[2], by = 60), seq(xlim[1],xlim[2], by = 60)/12 + 1900, pos = 0, las = 2)
}else{
axis(1, seq(xlim[1],xlim[2], by = 60), labels = NA, pos = 0, las = 2)
}
axis(2, seq(0,1,l=5), las = 2)
bmb <- as.numeric(pars["bmb"])
bfb <- as.numeric(pars["bfb"])
bme <- as.numeric(pars["bme"])
bfe <- as.numeric(pars["bfe"])
bmp <- as.numeric(pars["bmp"])
rho <- exp(as.numeric(pars["lrho"]))
bfp <- bmp * rho
out <- data.frame(cmc = temp$tmar - temp$bd, ss = 1, mm = 0, ff = 0, hh = 0, mm.a = 0, ff.a = 0, hh.a = 0)
## pi.m.bef = 0, pi.f.bef = 0, pi.m.part = 0, pi.f.part = 0, pi.m.exc = 0, pi.f.exc = 0,
## pi.m.bef.a = 0, pi.f.bef.a = 0, pi.m.part.a = 0, pi.f.part.a = 0, pi.m.exc.a = 0, pi.f.exc.a = 0)
ssL <- 1
mmL <- 0
ffL <- 0
hhL <- 0
mm.aL <- 0
ff.aL <- 0
hh.aL <- 0
ss <- 1
mm <- 0
ff <- 0
hh <- 0
mm.a <- 0
ff.a <- 0
hh.a <- 0
for(tt in 1:max(temp$bd))
{
## probabilities are non-zero only for times after started having sex and before couple formation
m.sex <- temp$tmar-temp$bd+tt-1 >= temp$tms & temp$tmar-temp$bd+tt-1 < temp$tmar
f.sex <- temp$tmar-temp$bd+tt-1 >= temp$tfs & temp$tmar-temp$bd+tt-1 < temp$tmar
e.sex <- m.sex|f.sex # either are active
## probability infected in month tt
p.m.bef <- 0
p.f.bef <- 0
p.m.bef.a <- 0
p.f.bef.a <- 0
p.m.bef[m.sex] <- (1 - exp(-bmb * epicf[cbind(temp$tmar[m.sex]-temp$bd[m.sex]+tt-1, temp$epic.ind[m.sex])]))
p.f.bef[f.sex] <- (1 - exp(-bfb * epicm[cbind(temp$tmar[f.sex]-temp$bd[f.sex]+tt-1, temp$epic.ind[f.sex])]))
## probability infected in month tt and alive at sampling
p.m.bef.a[m.sex] <- p.m.bef[m.sex] * csurv[cbind(temp$mage[m.sex]-temp$cd[m.sex]-temp$bd[m.sex]+tt-1, temp$cd[m.sex]+temp$bd[m.sex]-tt+1)]
p.f.bef.a[f.sex] <- p.f.bef[f.sex] * csurv[cbind(temp$fage[f.sex]-temp$cd[f.sex]-temp$bd[f.sex]+tt-1, temp$cd[f.sex]+temp$bd[f.sex]-tt+1)]
## iterate probabilities based on previous values for only cases where it needs uptemping
ss[e.sex] <- ssL[e.sex]*(1-p.m.bef[e.sex])*(1-p.f.bef[e.sex])
mm[e.sex] <- mmL[e.sex]*(1 - p.f.bef[e.sex]) + ssL[e.sex]*p.m.bef[e.sex]*(1-p.f.bef[e.sex])
ff[e.sex] <- ffL[e.sex]*(1 - p.m.bef[e.sex]) + ssL[e.sex]*p.f.bef[e.sex]*(1-p.m.bef[e.sex])
hh[e.sex] <- hhL[e.sex] + ssL[e.sex]*p.m.bef[e.sex]*p.f.bef[e.sex] +
mmL[e.sex]*p.f.bef[e.sex] +
ffL[e.sex]*p.m.bef[e.sex]
######################################################################
## iterate joint probabilities with survival
mm.a[e.sex] <- mm.aL[e.sex]*(1 - p.f.bef[e.sex]) + ssL[e.sex]*p.m.bef.a[e.sex]*(1-p.f.bef[e.sex])
ff.a[e.sex] <- ff.aL[e.sex]*(1 - p.m.bef[e.sex]) + ssL[e.sex]*p.f.bef.a[e.sex]*(1-p.m.bef[e.sex])
hh.a[e.sex] <- hh.aL[e.sex] + ssL[e.sex]*p.m.bef.a[e.sex]*p.f.bef.a[e.sex] +
mm.aL[e.sex]*p.f.bef.a[e.sex] +
ff.aL[e.sex]*p.m.bef.a[e.sex]
## uptempe last month states
ssL[e.sex] <- ss[e.sex]
mmL[e.sex] <- mm[e.sex]
ffL[e.sex] <- ff[e.sex]
hhL[e.sex] <- hh[e.sex]
mm.aL[e.sex] <- mm.a[e.sex]
ff.aL[e.sex] <- ff.a[e.sex]
hh.aL[e.sex] <- hh.a[e.sex]
out <- rbind(out, c(cmc = temp$tmar-temp$bd+tt-1, ss, mm, ff, hh, mm.a, ff.a, hh.a))
}
## probability of infection before partnership
pi.m.bef <- mm+hh
pi.f.bef <- ff+hh
## probability of infection before partnership & both individuals living to interview
pi.m.bef.a <- mm.a+hh.a
pi.f.bef.a <- ff.a+hh.a
## probability of infection by partner
pi.m.part <- 0
pi.f.part <- 0
## probability of infection by partner & both individuals living to interview
pi.m.part.a <- 0
pi.f.part.a <- 0
## probability of infection extracouply
pi.m.exc <- 0
pi.f.exc <- 0
## probability of infection extracouply & both individuals living to interview
pi.m.exc.a <- 0
pi.f.exc.a <- 0
## Track serodiscordant couples by route of infection for bookkeeping later
mm.bef.a <- mm.a
ff.bef.a <- ff.a
mm.exc.a <- 0
ff.exc.a <- 0
mm.bef.aL <- mm.a
ff.bef.aL <- ff.a
mm.exc.aL <- 0
ff.exc.aL <- 0
## probability of being infected by partner (constant, used inside loop)
p.m.part <- 1 - exp(-bmp)
p.f.part <- 1 - exp(-bfp)
## Now loop through marriage
for(tt in 1:max(temp$cd-1))
{
## are partners formed in a couple?
fmd <- temp$cd >= tt
######################################################################
## everything below is automatically sum(fmd) length except p.m/f.part which are length 1
## Survival probabilities
s.p.m <- csurv[cbind(temp$mage[fmd]-temp$cd[fmd]+tt-1, temp$tint[fmd] - (temp$tmar[fmd] + tt - 1))]
s.p.f <- csurv[cbind(temp$fage[fmd]-temp$cd[fmd]+tt-1, temp$tint[fmd] - (temp$tmar[fmd] + tt - 1))]
## Transmission probabilities from partner (jointly with survival)
p.m.part.a <- p.m.part * s.p.m
p.f.part.a <- p.f.part * s.p.f
## probability infected extracouply in the ttc-th month of couple
p.m.exc <- (1 - exp(-bme*epicf[cbind(temp$tmar[fmd]+(tt-1), temp$epic.ind[fmd])]))
p.f.exc <- (1 - exp(-bfe*epicm[cbind(temp$tmar[fmd]+(tt-1), temp$epic.ind[fmd])]))
p.m.exc.a <- p.m.exc * s.p.m
p.f.exc.a <- p.f.exc * s.p.f
######################################################################
## iterate probabilities
ss[fmd] <- ssL[fmd]*(1-p.m.exc)*(1-p.f.exc)
mm[fmd] <- mmL[fmd]*(1-p.f.exc)*(1-p.f.part) + ssL[fmd]*p.m.exc*(1-p.f.exc)
ff[fmd] <- ffL[fmd]*(1-p.m.exc)*(1-p.m.part) + ssL[fmd]*p.f.exc*(1-p.m.exc)
hh[fmd] <- hhL[fmd] + ssL[fmd]* p.m.exc*p.f.exc +
mmL[fmd]*(p.f.part + (1-p.f.part)*p.f.exc) +
ffL[fmd]*(p.m.part + (1-p.m.part)*p.m.exc)
######################################################################
## iterate probabilities jointly with survival until survey
## Note for probabilities of not being infected, we don't use the joint probability with being alive at sampling
mm.a[fmd] <- mm.aL[fmd]*(1-p.f.exc)*(1-p.f.part) + ssL[fmd]*p.m.exc.a*(1-p.f.exc)
ff.a[fmd] <- ff.aL[fmd]*(1-p.m.exc)*(1-p.m.part) + ssL[fmd]*p.f.exc.a*(1-p.m.exc)
hh.a[fmd] <- hh.aL[fmd] + ssL[fmd] *p.m.exc.a*p.f.exc.a +
mm.aL[fmd]*(p.f.part.a + (1-p.f.part)*p.f.exc.a) +
ff.aL[fmd]*(p.m.part.a + (1-p.m.part)*p.m.exc.a)
## Track cumulative incidence probabilities for partner infections
pi.m.part[fmd] <- pi.m.part[fmd] + ffL[fmd]*p.m.part
pi.f.part[fmd] <- pi.f.part[fmd] + mmL[fmd]*p.f.part
pi.m.part.a[fmd] <- pi.m.part.a[fmd] + ff.aL[fmd]*p.m.part.a
pi.f.part.a[fmd] <- pi.f.part.a[fmd] + mm.aL[fmd]*p.f.part.a
## Track how many serodiscordant couples there are with
## infections from before partnership
mm.bef.a[fmd] <- mm.bef.aL[fmd]*(1-p.f.exc)*(1-p.f.part)
ff.bef.a[fmd] <- ff.bef.aL[fmd]*(1-p.m.exc)*(1-p.m.part)
## Track cumulative incidence probabilities for infections
## prior to partnership just subtracting off partners with
## incident infections that die and remove couple from
## sample-able couples
pi.m.bef.a[fmd] <- pi.m.bef.a[fmd] - mm.bef.aL[fmd]*(p.f.part + (1-p.f.part)*p.f.exc)*(1-s.p.f)
pi.f.bef.a[fmd] <- pi.f.bef.a[fmd] - ff.bef.aL[fmd]*(p.m.part + (1-p.m.part)*p.m.exc)*(1-s.p.m)
## Track cumulative incidence probabilties for extracouple infections
mm.exc.a[fmd] <- mm.aL[fmd]-mm.bef.aL[fmd]
ff.exc.a[fmd] <- ff.aL[fmd]-ff.bef.aL[fmd]
pi.m.exc[fmd] <- pi.m.exc[fmd] + (ssL[fmd] + ffL[fmd]*(1-p.m.part))*p.m.exc
pi.f.exc[fmd] <- pi.f.exc[fmd] + (ssL[fmd] + mmL[fmd]*(1-p.f.part))*p.f.exc
pi.m.exc.a[fmd] <- pi.m.exc.a[fmd] + (ssL[fmd] + ff.aL[fmd]*(1-p.m.part))*p.m.exc.a -
mm.exc.aL[fmd]*(1-p.f.part)*p.f.exc*(1-s.p.f)
pi.f.exc.a[fmd] <- pi.f.exc.a[fmd] + (ssL[fmd] + mm.aL[fmd]*(1-p.f.part))*p.f.exc.a -
ff.exc.aL[fmd]*(1-p.m.part)*p.m.exc*(1-s.p.m)
## update last month states
ssL[fmd] <- ss[fmd]
mmL[fmd] <- mm[fmd]
ffL[fmd] <- ff[fmd]
hhL[fmd] <- hh[fmd]
mm.aL[fmd] <- mm.a[fmd]
ff.aL[fmd] <- ff.a[fmd]
hh.aL[fmd] <- hh.a[fmd]
mm.exc.aL[fmd] <- mm.exc.a[fmd]
ff.exc.aL[fmd] <- ff.exc.a[fmd]
mm.bef.aL[fmd] <- mm.bef.a[fmd]
ff.bef.aL[fmd] <- ff.bef.a[fmd]
out <- rbind(out, c(cmc = temp$tmar+tt-1, ss, mm, ff, hh, mm.a, ff.a, hh.a))
}
pser.a <- cbind(hh.a, mm.a, ff.a, ss)
pser <- cbind(hh, mm, ff, ss)
if(cprob)
{
scalar <- out$mm.a + out$ff.a + out$hh.a + out$ss
}else{
scalar <- 1
}
if(show.susc) lines(out$cmc, out$ss/scalar, col = cols[4], lty = 1, lwd = 2)
if(nsurv)