12-ipw-msm-r.Rmd

# 12. IP Weighting and Marginal Structural Models{-}

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE) 
```

## Program 12.1

- Descriptive statistics from NHEFS data (Table 12.1)

```{r, results='hide', message=FALSE, warning=FALSE}
library(here)
```

```{r}
# install.packages("readxl") # install package if required
library("readxl")

nhefs <- read_excel(here("data", "NHEFS.xls"))
nhefs$cens <- ifelse(is.na(nhefs$wt82), 1, 0)

# provisionally ignore subjects with missing values for weight in 1982
nhefs.nmv <-
  nhefs[which(!is.na(nhefs$wt82)),] 

lm(wt82_71 ~ qsmk, data = nhefs.nmv)
# Smoking cessation
predict(lm(wt82_71 ~ qsmk, data = nhefs.nmv), data.frame(qsmk = 1))
# No smoking cessation
predict(lm(wt82_71 ~ qsmk, data = nhefs.nmv), data.frame(qsmk = 0)) 

# Table
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 0),]$age)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 0),]$wt71)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 0),]$smokeintensity)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 0),]$smokeyrs)

summary(nhefs.nmv[which(nhefs.nmv$qsmk == 1),]$age)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 1),]$wt71)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 1),]$smokeintensity)
summary(nhefs.nmv[which(nhefs.nmv$qsmk == 1),]$smokeyrs)

table(nhefs.nmv$qsmk, nhefs.nmv$sex)
prop.table(table(nhefs.nmv$qsmk, nhefs.nmv$sex), 1)

table(nhefs.nmv$qsmk, nhefs.nmv$race)
prop.table(table(nhefs.nmv$qsmk, nhefs.nmv$race), 1)

table(nhefs.nmv$qsmk, nhefs.nmv$education)
prop.table(table(nhefs.nmv$qsmk, nhefs.nmv$education), 1)

table(nhefs.nmv$qsmk, nhefs.nmv$exercise)
prop.table(table(nhefs.nmv$qsmk, nhefs.nmv$exercise), 1)

table(nhefs.nmv$qsmk, nhefs.nmv$active)
prop.table(table(nhefs.nmv$qsmk, nhefs.nmv$active), 1)
```


## Program 12.2

- Estimating IP weights
- Data from NHEFS

```{r}
# Estimation of ip weights via a logistic model
fit <- glm(
  qsmk ~ sex + race + age + I(age ^ 2) +
    as.factor(education) + smokeintensity +
    I(smokeintensity ^ 2) + smokeyrs + I(smokeyrs ^ 2) +
    as.factor(exercise) + as.factor(active) + wt71 + I(wt71 ^ 2),
  family = binomial(),
  data = nhefs.nmv
)
summary(fit)

p.qsmk.obs <-
  ifelse(nhefs.nmv$qsmk == 0,
         1 - predict(fit, type = "response"),
         predict(fit, type = "response"))

nhefs.nmv$w <- 1 / p.qsmk.obs
summary(nhefs.nmv$w)
sd(nhefs.nmv$w)

# install.packages("geepack") # install package if required
library("geepack")
msm.w <- geeglm(
  wt82_71 ~ qsmk,
  data = nhefs.nmv,
  weights = w,
  id = seqn,
  corstr = "independence"
)
summary(msm.w)

beta <- coef(msm.w)
SE <- coef(summary(msm.w))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)

# no association between sex and qsmk in pseudo-population
xtabs(nhefs.nmv$w ~ nhefs.nmv$sex + nhefs.nmv$qsmk)

# "check" for positivity (White women)
table(nhefs.nmv$age[nhefs.nmv$race == 0 & nhefs.nmv$sex == 1],
      nhefs.nmv$qsmk[nhefs.nmv$race == 0 & nhefs.nmv$sex == 1])
```

## Program 12.3

- Estimating stabilized IP weights
- Data from NHEFS

```{r}
# estimation of denominator of ip weights
denom.fit <-
  glm(
    qsmk ~ as.factor(sex) + as.factor(race) + age + I(age ^ 2) +
      as.factor(education) + smokeintensity +
      I(smokeintensity ^ 2) + smokeyrs + I(smokeyrs ^ 2) +
      as.factor(exercise) + as.factor(active) + wt71 + I(wt71 ^ 2),
    family = binomial(),
    data = nhefs.nmv
  )
summary(denom.fit)

pd.qsmk <- predict(denom.fit, type = "response")

# estimation of numerator of ip weights
numer.fit <- glm(qsmk ~ 1, family = binomial(), data = nhefs.nmv)
summary(numer.fit)

pn.qsmk <- predict(numer.fit, type = "response")

nhefs.nmv$sw <-
  ifelse(nhefs.nmv$qsmk == 0, ((1 - pn.qsmk) / (1 - pd.qsmk)),
         (pn.qsmk / pd.qsmk))

summary(nhefs.nmv$sw)


msm.sw <- geeglm(
  wt82_71 ~ qsmk,
  data = nhefs.nmv,
  weights = sw,
  id = seqn,
  corstr = "independence"
)
summary(msm.sw)

beta <- coef(msm.sw)
SE <- coef(summary(msm.sw))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)

# no association between sex and qsmk in pseudo-population
xtabs(nhefs.nmv$sw ~ nhefs.nmv$sex + nhefs.nmv$qsmk)
```

## Program 12.4

- Estimating the parameters of a marginal structural mean model with a continuous treatment Data from NHEFS

```{r}
# Analysis restricted to subjects reporting <=25 cig/day at baseline
nhefs.nmv.s <- subset(nhefs.nmv, smokeintensity <= 25)

# estimation of denominator of ip weights
den.fit.obj <- lm(
  smkintensity82_71 ~ as.factor(sex) +
    as.factor(race) + age + I(age ^ 2) +
    as.factor(education) + smokeintensity + I(smokeintensity ^ 2) +
    smokeyrs + I(smokeyrs ^ 2) + as.factor(exercise) + as.factor(active) + wt71 +
    I(wt71 ^ 2),
  data = nhefs.nmv.s
)
p.den <- predict(den.fit.obj, type = "response")
dens.den <-
  dnorm(nhefs.nmv.s$smkintensity82_71,
        p.den,
        summary(den.fit.obj)$sigma)

# estimation of numerator of ip weights
num.fit.obj <- lm(smkintensity82_71 ~ 1, data = nhefs.nmv.s)
p.num <- predict(num.fit.obj, type = "response")
dens.num <-
  dnorm(nhefs.nmv.s$smkintensity82_71,
        p.num,
        summary(num.fit.obj)$sigma)

nhefs.nmv.s$sw.a <- dens.num / dens.den
summary(nhefs.nmv.s$sw.a)

msm.sw.cont <-
  geeglm(
    wt82_71 ~ smkintensity82_71 + I(smkintensity82_71 * smkintensity82_71),
    data = nhefs.nmv.s,
    weights = sw.a,
    id = seqn,
    corstr = "independence"
  )
summary(msm.sw.cont)

beta <- coef(msm.sw.cont)
SE <- coef(summary(msm.sw.cont))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)
```

## Program 12.5

- Estimating the parameters of a marginal structural logistic model
- Data from NHEFS

```{r}
table(nhefs.nmv$qsmk, nhefs.nmv$death)

# First, estimation of stabilized weights sw (same as in Program 12.3)
# Second, fit logistic model below
msm.logistic <- geeglm(
  death ~ qsmk,
  data = nhefs.nmv,
  weights = sw,
  id = seqn,
  family = binomial(),
  corstr = "independence"
)
summary(msm.logistic)

beta <- coef(msm.logistic)
SE <- coef(summary(msm.logistic))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)
```

## Program 12.6

- Assessing effect modification by sex using a marginal structural mean model
- Data from NHEFS

```{r}
table(nhefs.nmv$sex)

# estimation of denominator of ip weights
denom.fit <-
  glm(
    qsmk ~ as.factor(sex) + as.factor(race) + age + I(age ^ 2) +
      as.factor(education) + smokeintensity +
      I(smokeintensity ^ 2) + smokeyrs + I(smokeyrs ^ 2) +
      as.factor(exercise) + as.factor(active) + wt71 + I(wt71 ^ 2),
    family = binomial(),
    data = nhefs.nmv
  )
summary(denom.fit)

pd.qsmk <- predict(denom.fit, type = "response")

# estimation of numerator of ip weights
numer.fit <-
  glm(qsmk ~ as.factor(sex), family = binomial(), data = nhefs.nmv)
summary(numer.fit)
pn.qsmk <- predict(numer.fit, type = "response")

nhefs.nmv$sw.a <-
  ifelse(nhefs.nmv$qsmk == 0, ((1 - pn.qsmk) / (1 - pd.qsmk)),
         (pn.qsmk / pd.qsmk))

summary(nhefs.nmv$sw.a)
sd(nhefs.nmv$sw.a)

# Estimating parameters of a marginal structural mean model
msm.emm <- geeglm(
  wt82_71 ~ as.factor(qsmk) + as.factor(sex)
  + as.factor(qsmk):as.factor(sex),
  data = nhefs.nmv,
  weights = sw.a,
  id = seqn,
  corstr = "independence"
)
summary(msm.emm)

beta <- coef(msm.emm)
SE <- coef(summary(msm.emm))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)
```

## Program 12.7

- Estimating IP weights to adjust for selection bias due to censoring
- Data from NHEFS

```{r}
table(nhefs$qsmk, nhefs$cens)

summary(nhefs[which(nhefs$cens == 0),]$wt71)
summary(nhefs[which(nhefs$cens == 1),]$wt71)

# estimation of denominator of ip weights for A
denom.fit <-
  glm(
    qsmk ~ as.factor(sex) + as.factor(race) + age + I(age ^ 2) +
      as.factor(education) + smokeintensity +
      I(smokeintensity ^ 2) + smokeyrs + I(smokeyrs ^ 2) +
      as.factor(exercise) + as.factor(active) + wt71 + I(wt71 ^ 2),
    family = binomial(),
    data = nhefs
  )
summary(denom.fit)

pd.qsmk <- predict(denom.fit, type = "response")

# estimation of numerator of ip weights for A
numer.fit <- glm(qsmk ~ 1, family = binomial(), data = nhefs)
summary(numer.fit)
pn.qsmk <- predict(numer.fit, type = "response")

# estimation of denominator of ip weights for C
denom.cens <- glm(
  cens ~ as.factor(qsmk) + as.factor(sex) +
    as.factor(race) + age + I(age ^ 2) +
    as.factor(education) + smokeintensity +
    I(smokeintensity ^ 2) + smokeyrs + I(smokeyrs ^ 2) +
    as.factor(exercise) + as.factor(active) + wt71 + I(wt71 ^ 2),
  family = binomial(),
  data = nhefs
)
summary(denom.cens)

pd.cens <- 1 - predict(denom.cens, type = "response")

# estimation of numerator of ip weights for C
numer.cens <-
  glm(cens ~ as.factor(qsmk), family = binomial(), data = nhefs)
summary(numer.cens)
pn.cens <- 1 - predict(numer.cens, type = "response")

nhefs$sw.a <-
  ifelse(nhefs$qsmk == 0, ((1 - pn.qsmk) / (1 - pd.qsmk)),
         (pn.qsmk / pd.qsmk))
nhefs$sw.c <- pn.cens / pd.cens
nhefs$sw <- nhefs$sw.c * nhefs$sw.a

summary(nhefs$sw.a)
sd(nhefs$sw.a)
summary(nhefs$sw.c)
sd(nhefs$sw.c)
summary(nhefs$sw)
sd(nhefs$sw)

msm.sw <- geeglm(
  wt82_71 ~ qsmk,
  data = nhefs,
  weights = sw,
  id = seqn,
  corstr = "independence"
)
summary(msm.sw)

beta <- coef(msm.sw)
SE <- coef(summary(msm.sw))[, 2]
lcl <- beta - qnorm(0.975) * SE
ucl <- beta + qnorm(0.975) * SE
cbind(beta, lcl, ucl)
```