Impact of Separation on Surrogate Evaluation

When complete or quasi-complete separation occurs, this typically causes problems with maximum likelihood estimation for generalized linear models. The typical scenario (Allison, 2008) is that the model-fitting algorithm goes through several iterations, while attempting to converge. Upon each iteration the affected parameter estimate increases and this continues until a fixed iteration limit is exceeded. At this point the parameter estimate will typically be large and its standard error very large. Statistical software generally does not highlight this issue via error messages.

At the first stage of trial-level surrogacy estimation, two binary (S, Z) or an ordinal and a binary variable (T, Z) are regressed on one another for each trial in (11.4) and (11.5). This returns treatment effect estimates on the binary surrogate and ordinal true outcome. However, separation causes outlying data points at stage 2, where the effects of treatment on T are regressed on those on S as in (11.6). The LRF (11.7) is then based on a model with potentially highly influential outliers. This leads to unreliable estimation of R1, with a tendency to underestimate the true value.

TABLE 11.5

Quasi-complete separation example for an ordinal variable. A, Bi, C1, D,

Do, Eo, Fo, and Go are all greater than zero.

1

2

3

4

5

6

7

A i

Bi

Cl

0

0

0

0

0

0

Do

Eo

Fo

Go

 
Source
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