Problem with Wald CI in transreg with weibull model option for internal and external infection models

[yushuf]

#Recently I was trying transreg with dist = "weibull", xdist = "weibull" options. I get the following errors while estimating the confidence intervals.
First one is Wald and second one is LR.

ci_unobs_tr_w <- confint(unobs_tr)
Warning message:
In sqrt(diag(treg$var)[parm]) : NaNs produced

ci_unobs_tr_lr <- confint(unobs_tr, type = "lr")#
Error in if (!is.numeric(lower) || !is.numeric(upper) || lower >= upper) stop("lower < upper is not fulfilled") :
missing value where TRUE/FALSE needed
In addition: Warning message:
In sqrt(diag(treg$var)[parm]) : NaNs produced

### **My message, this is not the only problem with LR which might happen with Wald. I tried two simulation and both of the times I get that error with Wald though in some different command line.

This is for your information. The detail code is as follows along with data**

data.zip

library(transtat)
pdata <- read.csv("pdata.csv")
xdata <- read.csv("xdata.csv")
coef <- read.csv("coef.csv", header = TRUE)

pairwise data to be combined with external data

pdat <- pdata
pdat$interval <- pdat$exit - pdat$entry
pdat$external <- 0
pdat$trace <- 1
pdat$start <- 0
pdat$stop <- pdat$interval

external data

xdat <- xdata
names(xdat)[names(xdat) == "x"] <- "susx"

xdat$external <- 1
xdat$infectious <- NA
xdat$infx <- 0
xdat$interval <- xdat$exit # entry is at time 0
xdat$start <- xdat$entry
xdat$stop <- xdat$exit

dat <- rbind(pdat, xdat)

AFT model all data

Who-infects-whom observed

obs <- transreg(
Surv(interval, infector) ~ infx + susx + ext(external),
sus = "susceptible", data = dat,
dist = "weibull", xdist = "weibull"
)

Who-infects-whom not observed

unobs <- transreg(
Surv(interval, infset) ~ infx + susx + ext(external),
sus = "susceptible", data = dat,
dist = "weibull", xdist = "weibull"
)

AFT model with contact tracing and left-truncation (delayed entry)

Who-infects-whom observed

obs_tr <- transreg(
Surv(start, stop, infector) ~ infx + susx + ext(external),
sus = "susceptible", data = dat, subset = (trace == 1),
dist = "weibull", xdist = "weibull"
)

Who-infects-whom not observed

unobs_tr <- transreg(
Surv(start, stop, infset) ~ infx + susx + ext(external),
sus = "susceptible", data = dat, subset = (trace == 1),
dist = "weibull", xdist = "weibull"
)

AFT model with no external data

Who-infects-whom observed

obs_nx <- transreg(
Surv(interval, infector) ~ infx + susx,
sus = "susceptible", data = dat, subset = (external == 0),
dist = "weibull", xdist = "weibull"
)

Who-infects-whom not observed

unobs_nx <- transreg(
Surv(interval, infset) ~ infx + susx,
sus = "susceptible", data = dat, subset = (external == 0),
dist = "weibull", xdist = "weibull"
)

AFT model with contact tracing but no left truncation

Who-infects-whom observed

obs_trx <- transreg(
Surv(interval, infector) ~ infx + susx + ext(external),
sus = "susceptible", dat = dat, subset = (trace == 1 | infector == 1),
dist = "weibull", xdist = "weibull"
)

Who-infects-whom not observed

unobs_trx <- transreg(
Surv(interval, infset) ~ infx + susx + ext(external),
sus = "susceptible", data = dat, subset = (trace == 1 | infector == 1),
dist = "weibull", xdist = "weibull"
)

ci_obs_w <-confint(obs)
ci_obs_lr <- confint(obs, type = "lr")
ci_unobs_w <-confint(unobs)
ci_unobs_lr <- confint(unobs, type = "lr")
ci_obs_tr_w <- confint(obs_tr)
ci_obs_tr_lr <- confint(obs_tr, type = 'lr')
ci_unobs_tr_w <- confint(unobs_tr)
ci_unobs_tr_lr <- confint(unobs_tr, type = "lr")#
ci_obs_nx_w <- confint(obs_nx)
ci_obs_nx_lr <- confint(obs_nx, type = "lr")
ci_unobs_nx_w <- confint(unobs_nx)
ci_unobs_nx_lr <- confint(unobs_nx, type = "lr")
ci_obs_trx_w <- confint(obs_trx)
ci_obs_trx_lr <- confint(obs_trx, type = "lr")
ci_unobs_trx_w <- confint(unobs_trx)
ci_unobs_trx_lr <- confint(unobs_trx, type = "lr")

[ekenah]

The problem is a negative variance. This seems to happen only if who-infects-whom is not observed. How often does this problem occur (e.g., per thousand simulations)?

[yushuf]

The problem appears when who-infected-whom is not observed with contact tracing true for external intercept and external log(shape) parameters interval estimates. The probabilities of happening the event are

P(xintercept_unobs_tr_w) = 0.497 and P(lxshape_unobs_tr_w) = 0.454

This is based on one thousand simulation for Wald CI. I never tried LR, in these cases LR stops running the program.

[ekenah]

When there are no external infections, there should be no external intercept or shape parameters. Can you explain the second case where the problem appears again?

[yushuf]

Sorry I made a mistake in description, That never happened when we ignored the external source of infection. I have updated my previous comment. Thanks for figure that out.

[yushuf]

Python data generation script attached without .py extension. I guess you are looking for this one.

datsim.txt

[ekenah]

This appears to be numerical instability caused by the rapidly decreasing hazard of external infection, not an error in the code. Please re-run the simulations with exponential external contact intervals.