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I am working with matched case-control data that used risk-set sampling with replacement (a control can be matched to more than one case). I am trying to figure out the correct syntax for conditional logistic regression with appropriate variance estimation.

This is the syntax I used for the unadjusted OR without cluster robust SEs:

clogit(case_status ~ exposed + strata(match_id), data = data_analysis) |>
  broom::tidy(exp=TRUE, conf.int=TRUE) 

# OR = 1.134 (95% CI: 0.898, 1.433) 
# Got same result with method="exact" (default) as other methods

This is the syntax I used to get cluster robust SEs to account for within-subject correlation. However, the robust SEs were smaller than the original SEs, which is the opposite of what I would expect.

clogit(case_status ~ exposed + strata(match_id), data = data_analysis, 
  method="breslow", cluster = subject_id) |>
  broom::tidy(exp=TRUE, conf.int=TRUE) 

# OR = 1.134 (95% CI: 0.931, 1.382) 
# method="exact" doesn't work with cluster option

Any help to understand why I may be getting smaller robust SEs or suggestions to modify my analysis would be greatly appreciated.

Thank you!

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