8.5 Stratification

A simple way to eliminate the effect of clustering is to stratify on the clusters. In the birth intervals example, it would mean that intervals are only compared to other birth intervals from the same mother. The drawback with a stratified analysis is that it is not possible to estimate the effect of covariates that are constant within clusters. In the birth intervals case, it is probable that ses, socio-economic status, would vary little within families. On the other hand, the effet of birth order or mother's age would be suitable to analyze in a stratified setting.

library(glmmML)
fit2 <- coxreg(Surv(next.ivl, event) ~ parity + prev.ivl + 
               strata(id), data = fe)

## Warning in coxreg.fit(X, Y, rs, weights, t.offset, strats, offset, init, :
## [get1_gam] gamma positive infinite

summary(fit2)

## Warning in coxreg.fit(X, Y, rs, weights, t.offset, strats, offset, init, :
## [get1_gam] gamma positive infinite

## Warning in coxreg.fit(X, Y, rs, weights, t.offset, strats, offset, init, :
## [get1_gam] gamma positive infinite

## Covariate           Mean       Coef     Rel.Risk   S.E.    LR p
## parity              4.242    -0.329     0.720     0.008    0.000 
## prev.ivl            2.423    -0.054     0.948     0.016    0.001 
## 
## Events                    8458 
## Total time at risk         29806 
## Max. log. likelihood      -9557.9 
## LR test statistic         2988.66 
## Degrees of freedom        2 
## Overall p-value           0

Contrast this result with an unstratified analysis.

fit3 <- coxreg(Surv(next.ivl, event) ~ parity + prev.ivl, 
               data = fe)
summary(fit3)

## Covariate           Mean       Coef     Rel.Risk   S.E.    LR p
## parity              4.242    -0.084     0.920     0.005    0.000 
## prev.ivl            2.423    -0.319     0.727     0.011    0.000 
## 
## Events                    8458 
## Total time at risk         29806 
## Max. log. likelihood      -70391 
## LR test statistic         1834.85 
## Degrees of freedom        2 
## Overall p-value           0

Note how the effect of parity is diminished when aggregating comparison over all women, while the effect of the length of the previous interval is enlarged. Try to explain why this result is expected!

Example 8.2 (Matched data.) Under certain circumstances it is actually possible to estimate an effect of a covariate that is constant within strata, but only if it is interacted with a covariate that is not constant within strata. See Example ?? in Chapter 9.