HIV: TB and Survival (Baseline Data)

Description

Simulated dataset. Baseline data of 386 HIV positive individuals, including time of first active tuberculosis, time of death, individual end time. Time varying CD4 measurements of these patients are included in dataset timedat.

Usage

data(basdat)

Format

A data frame with 386 observations on the following 4 variables:

id

Patient ID.

Ttb

Time of first active tuberculosis, measured in days since HIV seroconversion.

Tdeath

Time of death, measured in days since HIV seroconversion.

Tend

Individual end time (either death or censoring), measured in days since HIV seroconversion.

Details

These simulated data are used together with data in timedat in a detailed causal modelling example using inverse probability weighting (IPW). See ipwtm for the example. Data were simulated using the algorithm described in Van der Wal e.a. (2009).#' [Image of a multistate model for HIV, TB, and death]

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13.

Van der Wal W.M., Prins M., Lumbreras B. & Geskus R.B. (2009). A simple G-computation algorithm to quantify the causal effect of a secondary illness on the progression of a chronic disease. Statistics in Medicine, 28(18), 2325-2337.

See Also

haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun

Examples

# Detailed examples can be found in the ipwtm documentation:
# ?ipwtm

HAART and Survival in HIV Patients

Description

Survival data measured in 1200 HIV positive patients. Start of follow-up is HIV seroconversion. Each row corresponds to a 100 day interval of follow-up time, using the counting process notation. Patients can initiate HAART therapy. CD4 count is a confounder for the effect of HAART on mortality.

Usage

data(haartdat)

Format

A data frame with 1200 patients and multiple observations per patient (counting process notation) on the following 8 variables:

patient

Patient ID.

tstart

Starting time for each interval of follow-up, measured in days since HIV seroconversion.

fuptime

End time for each interval of follow-up, measured in days since HIV seroconversion.

haartind

Indicator for the initiation of HAART therapy at the end of the interval (0 = HAART not initiated / 1 = HAART initiated).

event

Indicator for death at the end of the interval (0 = alive / 1 = died).

sex

Sex (0 = male / 1 = female).

age

Age at the start of follow-up (years).

cd4.sqrt

Square root of CD4 count, measured at fuptime, before haartind.

endtime

The final observed time point for the individual.

dropout

Indicator for dropout/censoring at the end of the interval (0 = no, 1 = yes).

#'

Details

These data were simulated to demonstrate Inverse Probability Weighting (IPW). To allow for models predicting the initiation of HAART at fuptime = 0, the starting time for the first interval of each patient is set to -100.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13.

See Also

basdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun

Examples

# For a full example of how to use this data with ipwtm, see:
# ?ipwtm

IQ, Income and Health

Description

A simulated dataset containing measurements of IQ, monthly income, and health scores for 1000 individuals.

Usage

data(healthdat)

Format

A data frame with 1000 rows, with each row corresponding to a separate individual. The following 4 variables are included:

id

Individual ID.

iq

IQ score.

income

Gross monthly income (EUR).

health

Health score (0-100).

Details

In these simulated data, IQ acts as a confounder for the causal effect of income on health. This dataset is primarily used to illustrate point-treatment inverse probability weighting.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun

Examples

# For an example of how to use this data with ipwpoint, see:
# ?ipwpoint

Plot Inverse Probability Weights

Description

For time varying weights: display boxplots within strata of follow-up time. For point treatment weights: display density plot.

Usage

ipwplot(
  weights,
  timevar = NULL,
  binwidth = NULL,
  logscale = TRUE,
  xlab = NULL,
  ylab = NULL,
  main = "",
  ref = TRUE,
  ...
)

Arguments

Value

A plot is displayed.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun.

Examples

#see ?ipwpoint and ?ipwtm for examples

Estimate Inverse Probability Weights (Point Treatment)

Description

Estimate inverse probability weights to fit marginal structural models in a point treatment situation. The exposure for which we want to estimate the causal effect can be binomial, multinomial, ordinal or continuous. Both stabilized and unstabilized weights can be estimated.

Usage

ipwpoint(
  exposure,
  family,
  link,
  numerator = NULL,
  denominator,
  data,
  trunc = NULL,
  ...
)

Arguments

Details

For each unit under observation, this function computes an inverse probability weight, which is the ratio of two probabilities:

• the numerator contains the probability of the observed exposure level given observed values of stabilization factors (usually a set of baseline covariates). These probabilities are estimated using the model regressing exposure on the terms in numerator, using the link function indicated by family and link.

• the denominator contains the probability of the observed exposure level given the observed values of a set of confounders, as well as the stabilization factors in the numerator. These probabilities are estimated using the model regressing exposure on the terms in denominator, using the link function indicated by family and link.

When the models from which the elements in the numerator and denominator are predicted are correctly specified, and there is no unmeasured confounding, weighting the observations by the inverse probability weights adjusts for confounding of the effect of the exposure of interest. On the weighted dataset a marginal structural model can then be fitted, quantifying the causal effect of the exposure on the outcome of interest.

With numerator specified, stabilized weights are computed, otherwise unstabilized weighs with a numerator of 1 are computed. With a continuous exposure, using family = "gaussian", weights are computed using the ratio of predicted densities. Therefore, for family = "gaussian" only stabilized weights can be used, since unstabilized weights would have infinity variance.

Value

A list containing the following elements:

Missing values

Currently, the exposure variable and the variables used in numerator and denominator should not contain missing values.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Cole, S.R. & Hernán, M.A. (2008). Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168(6), 656-664.

Robins, J.M., Hernán, M.A. & Brumback, B.A. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550-560.

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13.

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun.

Examples

# Simulate data with continuous confounder and outcome, binomial exposure.
# Marginal causal effect of exposure on outcome: 10.
n <- 1000
simdat <- data.frame(l = rnorm(n, 10, 5))
a.lin <- simdat$l - 10
pa <- exp(a.lin)/(1 + exp(a.lin))
simdat$a <- rbinom(n, 1, prob = pa)
simdat$y <- 10*simdat$a + 0.5*simdat$l + rnorm(n, -10, 5)
simdat[1:5,]

# Estimate ipw weights.
temp <- ipwpoint(
  exposure = a,
  family = "binomial",
  link = "logit",
  numerator = ~ 1,
  denominator = ~ l,
  data = simdat)
summary(temp$ipw.weights)

# Plot inverse probability weights
# ipwplot(weights = temp$ipw.weights, logscale = FALSE,
#         main = "Stabilized weights", xlim = c(0, 8))

#Examine numerator and denominator models.
summary(temp$num.mod)
summary(temp$den.mod)

#Paste inverse probability weights
simdat$sw <- temp$ipw.weights

#Marginal structural model for the causal effect of a on y
#corrected for confounding by l using inverse probability weighting
#with robust standard error from the survey package.
if (requireNamespace("survey", quietly = TRUE)) {
  library(survey)
  msm <- svyglm(y ~ a,
                design = svydesign(~1, weights = ~temp$ipw.weights,
                data = simdat))
  summary(msm)
}
## Not run: 
# Compute basic bootstrap confidence interval
# require(boot)
# boot.fun <- function(dat, index){
#   coef(glm(
#       formula = y ~ a,
#       data = dat[index,],
#       weights = ipwpoint(
#           exposure = a,
#           family = "gaussian",
#           numerator = ~ 1,
#           denominator = ~ l,
#           data = dat[index,])$ipw.weights))[2]
#   }
# bootres <- boot(simdat, boot.fun, 499);bootres
# boot.ci(bootres, type = "basic")

## End(Not run)

Estimate Inverse Probability Weights (Time Varying)

Description

Estimate inverse probability weights to fit marginal structural models, with a time-varying exposure and time-varying confounders. Within each unit under observation this function computes inverse probability weights at each time point during follow-up. The exposure can be binomial, multinomial, ordinal or continuous. Both stabilized and unstabilized weights can be estimated.

Usage

ipwtm(
  exposure,
  family,
  link,
  numerator = NULL,
  denominator,
  id,
  tstart,
  timevar,
  type,
  data,
  corstr = "ar1",
  trunc = NULL,
  ...
)

Arguments

Details

Within each unit under observation i (usually patients), this function computes inverse probability weights at each time point j during follow-up. These weights are the cumulative product over all previous time points up to j of the ratio of two probabilities:

• the numerator contains at each time point the probability of the observed exposure level given observed values of stabilization factors and the observed exposure history up to the time point before j. These probabilities are estimated using the model regressing exposure on the terms in numerator, using the link function indicated by family and link.

• the denominator contains at each time point the probability of the observed exposure level given the observed history of time varying confounders up to j, as well as the stabilization factors in the numerator and the observed exposure history up to the time point before j. These probabilities are estimated using the model regressing exposure on the terms in denominator, using the link function indicated by family and link.

When the models from which the elements in the numerator and denominator are predicted are correctly specified, and there is no unmeasured confounding, weighting observations ij by the inverse probability weights adjusts for confounding of the effect of the exposure of interest. On the weighted dataset a marginal structural model can then be fitted, quantifying the causal effect of the exposure on the outcome of interest.

With numerator specified, stabilized weights are computed, otherwise unstabilized weights with a numerator of 1 are computed. With a continuous exposure, using family = "gaussian", weights are computed using the ratio of predicted densities at each time point. Therefore, for family = "gaussian" only stabilized weights can be used, since unstabilized weights would have infinity variance.

Value

A list containing the following elements:

Missing values

Currently, the exposure variable and the variables used in numerator and denominator, id, tstart and timevar should not contain missing values.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Cole, S.R. & Hernán, M.A. (2008). Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168(6), 656-664. https://pubmed.ncbi.nlm.nih.gov:443/18682488/.

Robins, J.M., Hernán, M.A. & Brumback, B.A. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550-560. https://pubmed.ncbi.nlm.nih.gov/10955408/.

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun.

Examples

########################################################################
#EXAMPLE 1

#Load longitudinal data from HIV positive individuals.
data(haartdat)

#CD4 is confounder for the effect of initiation of HAART therapy on mortality.
#Estimate inverse probability weights to correct for confounding.
#Exposure allocation model is Cox proportional hazards model.
temp <- ipwtm(
  exposure = haartind,
  family = "survival",
  numerator = ~ sex + age,
  denominator = ~ sex + age + cd4.sqrt,
  id = patient,
  tstart = tstart,
  timevar = fuptime,
  type = "first",
  data = haartdat)

#plot inverse probability weights
graphics.off()
ipwplot(weights = temp$ipw.weights, timevar = haartdat$fuptime,
        binwidth = 100, ylim = c(-1.5, 1.5), main = "Stabilized inverse probability weights")

#CD4 count has an effect both on dropout and mortality, which causes informative censoring.
#Use inverse probability of censoring weighting to correct for effect of CD4 on dropout.
#Use Cox proportional hazards model for dropout.
temp2 <- ipwtm(
  exposure = dropout,
  family = "survival",
  numerator = ~ sex + age,
  denominator = ~ sex + age + cd4.sqrt,
  id = patient,
  tstart = tstart,
  timevar = fuptime,
  type = "cens",
  data = haartdat)

#plot inverse probability of censoring weights
graphics.off()
ipwplot(weights = temp2$ipw.weights, timevar = haartdat$fuptime,
        binwidth = 100, ylim = c(-1.5, 1.5),
        main = "Stabilized inverse probability of censoring weights")

#MSM for the causal effect of initiation of HAART on mortality.
#Corrected both for confounding and informative censoring.
#With robust standard error obtained using cluster().
require(survival)
summary(coxph(Surv(tstart, fuptime, event) ~ haartind + cluster(patient),
              data = haartdat, weights = temp$ipw.weights*temp2$ipw.weights))

#uncorrected model
summary(coxph(Surv(tstart, fuptime, event) ~ haartind, data = haartdat))

########################################################################
#EXAMPLE 2

data(basdat)
data(timedat)

#Aim: to model the causal effect of active tuberculosis (TB) on mortality.
#Longitudinal CD4 is a confounder as well as intermediate for the effect of TB.

#process original measurements
#check for ties (not allowed)
table(duplicated(timedat[,c("id", "fuptime")]))
#take square root of CD4 because of skewness
timedat$cd4.sqrt <- sqrt(timedat$cd4count)
#add TB time to dataframe
timedat <- merge(timedat, basdat[,c("id", "Ttb")], by = "id", all.x = TRUE)
#compute TB status
timedat$tb.lag <- ifelse(with(timedat, !is.na(Ttb) & fuptime > Ttb), 1, 0)
#longitudinal CD4-model
require(nlme)
cd4.lme <- lme(cd4.sqrt ~ fuptime + tb.lag, random = ~ fuptime | id,
               data = timedat)

#build new dataset:
#rows corresponding to TB-status switches, and individual end times
times <- sort(unique(c(basdat$Ttb, basdat$Tend)))
startstop <- data.frame(
  id = rep(basdat$id, each = length(times)),
  fuptime = rep(times, nrow(basdat)))
#add baseline data to dataframe
startstop <- merge(startstop, basdat, by = "id", all.x = TRUE)
#limit individual follow-up using Tend
startstop <- startstop[with(startstop, fuptime <= Tend),]
startstop$tstart <- tstartfun(id, fuptime, startstop) #compute tstart (?tstartfun)
#indicate TB status
startstop$tb <- ifelse(with(startstop, !is.na(Ttb) & fuptime >= Ttb), 1, 0)
#indicate TB status at previous time point
startstop$tb.lag <- ifelse(with(startstop, !is.na(Ttb) & fuptime > Ttb), 1, 0)
#indicate death
startstop$event <- ifelse(with(startstop, !is.na(Tdeath) & fuptime >= Tdeath),
                          1, 0)
#impute CD4, based on TB status at previous time point.
startstop$cd4.sqrt <- predict(cd4.lme,
                              newdata = data.frame(id = startstop$id,
                                                   fuptime = startstop$fuptime,
                                                   tb.lag = startstop$tb.lag))
#compute inverse probability weights
temp <- ipwtm(
  exposure = tb,
  family = "survival",
  numerator = ~ 1,
  denominator = ~ cd4.sqrt,
  id = id,
  tstart = tstart,
  timevar = fuptime,
  type = "first",
  data = startstop)
summary(temp$ipw.weights)
ipwplot(weights = temp$ipw.weights, timevar = startstop$fuptime, binwidth = 100)

#models
#IPW-fitted MSM, using cluster() to obtain robust standard error estimate
require(survival)
summary(coxph(Surv(tstart, fuptime, event) ~ tb + cluster(id),
              data = startstop, weights = temp$ipw.weights))
#unadjusted
summary(coxph(Surv(tstart, fuptime, event) ~ tb, data = startstop))
#adjusted using conditioning: part of the effect of TB is adjusted away
summary(coxph(Surv(tstart, fuptime, event) ~ tb + cd4.sqrt, data = startstop))

## Not run:
#compute bootstrap CI for TB parameter (takes a few hours)
#taking into account the uncertainty introduced by modelling longitudinal CD4
#taking into account the uncertainty introduced by estimating the inverse probability weights
#robust with regard to weights unequal to 1
#  require(boot)
#  boot.fun <- function(data, index, data.tm){
#     data.samp <- data[index,]
#     data.samp$id.samp <- 1:nrow(data.samp)
#     data.tm.samp <- do.call("rbind", lapply(data.samp$id.samp, function(id.samp) {
#       cbind(data.tm[data.tm$id == data.samp$id[data.samp$id.samp == id.samp],],
#         id.samp = id.samp)
#       }
#     ))
#     cd4.lme <- lme(cd4.sqrt ~ fuptime + tb.lag, random = ~ fuptime | id.samp, data = data.tm.samp)
#     times <- sort(unique(c(data.samp$Ttb, data.samp$Tend)))
#     startstop.samp <- data.frame(id.samp = rep(data.samp$id.samp, each = length(times)),
#                                  fuptime = rep(times, nrow(data.samp)))
#     startstop.samp <- merge(startstop.samp, data.samp, by = "id.samp", all.x = TRUE)
#     startstop.samp <- startstop.samp[with(startstop.samp, fuptime <= Tend),]
#     startstop.samp$tstart <- tstartfun(id.samp, fuptime, startstop.samp)
#     startstop.samp$tb <- ifelse(with(startstop.samp, !is.na(Ttb) & fuptime >= Ttb), 1, 0)
#     startstop.samp$tb.lag <- ifelse(with(startstop.samp, !is.na(Ttb) & fuptime > Ttb), 1, 0)
#     startstop.samp$event <- ifelse(with(startstop.samp, !is.na(Tdeath) & fuptime >= Tdeath), 1, 0)
#     startstop.samp$cd4.sqrt <- predict(cd4.lme, newdata = data.frame(id.samp =
#       startstop.samp$id.samp, fuptime = startstop.samp$fuptime, tb.lag = startstop.samp$tb.lag))
#
#     return(coef(coxph(Surv(tstart, fuptime, event) ~ tb, data = startstop.samp,
#        weights = ipwtm(
#             exposure = tb,
#             family = "survival",
#             numerator = ~ 1,
#             denominator = ~ cd4.sqrt,
#             id = id.samp,
#             tstart = tstart,
#             timevar = fuptime,
#             type = "first",
#             data = startstop.samp)$ipw.weights))[1])
#     }
#  bootres <- boot(data = basdat, statistic = boot.fun, R = 999, data.tm = timedat)
#  bootres
#  boot.ci(bootres, type = "basic")
#
## End(Not run)

HIV: TB and Survival (Longitudinal Measurements)

Description

A simulated dataset containing time-varying CD4 measurements for 386 HIV-positive individuals. Corresponding baseline data, including timing of tuberculosis and death, are available in basdat.

Usage

data(timedat)

Format

A data frame with 6291 observations on the following 3 variables:

id

Patient ID.

fuptime

Follow-up time (days since HIV seroconversion).

cd4count

CD4 count measured at fuptime.

Details

These simulated data are used together with basdat in a detailed causal modeling example using inverse probability weighting (IPW). See ipwtm for the full example. Data were simulated using the algorithm described in Van der Wal et al. (2009).

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Cole, S.R. & Hernán, M.A. (2008). Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168(6), 656-664.

Robins, J.M., Hernán, M.A. & Brumback, B.A. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550-560.

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13

Van der Wal W.M., Prins M., Lumbreras B. & Geskus R.B. (2009). A simple G-computation algorithm to quantify the causal effect of a secondary illness on the progression of a chronic disease. Statistics in Medicine, 28(18), 2325-2337.

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, tstartfun

Examples

# For an example of how to use these longitudinal measurements with basdat, see:
# ?ipwtm

Compute Starting Time For Counting Process Notation

Description

Function to compute starting time for intervals of follow-up, when using the counting process notation. Within each unit under observation (usually individuals), computes starting time equal to:

• time of previous record when there is a previous record.

• -1 for first record.

Usage

tstartfun(id, timevar, data)

Arguments

Value

Numerical vector containing starting time for each record. In the same order as the records in data, to facilitate merging.

Missing values

Currently, id and timevar should not contain missing values.

Author(s)

Willem M. van der Wal willem@vanderwalresearch.com, Ronald B. Geskus rgeskus@oucru.org

References

Van der Wal W.M. & Geskus R.B. (2011). ipw: An R Package for Inverse Probability Weighting. Journal of Statistical Software, 43(13), 1-23. doi:10.18637/jss.v043.i13.

See Also

basdat, haartdat, ipwplot, ipwpoint, ipwtm, timedat, tstartfun.

Examples

#data
mydata1 <- data.frame(
  patient = c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2),
  time.days = c(14, 34, 41, 56, 72, 98, 0, 11, 28, 35))

#compute starting time for each interval
mydata1$tstart <- tstartfun(patient, time.days, mydata1)

#result
mydata1

#see also ?ipwtm for example