I am estimating the global risk of infection risk in a population of patients, but these patients are clustered in hospitals and wards/departments. If I just take the crude prevalence (infected patients over the total), ignoring clusters, I get a certain value, around 8%.

If instead, I use an intercept-only model with a random intercept at the hospital level, I get a lower risk (~6%) which becomes even lower (5%) if you add another hierarchy, nesting wards into hospitals.

How should I describe these lower risks; should I say that it's a more robust estimate and I would see less variance if I repeat the study with a different selection of hospitals and wards? Are these estimates also more robust in the case of non-random sampling choosing of hospitals and wards (we have a convenience sample).

Note that the characteristic of the hospital (such the size) and the ward (such the specialty) do influence the risk. Furthermore, I noticed that taking the average of the per-hospital risks gives again a number around 6%.

  • $\begingroup$ "I would see less variance if I repeat the study with a different selection of hospitals and wards? " - less variance of what ? $\endgroup$ Feb 15, 2019 at 15:22
  • $\begingroup$ I meant, if hypothetically I would repeat the study, with different hospitals, using random effect models the sample estimates would vary less between studies; that is, more precision. $\endgroup$
    – Bakaburg
    Feb 15, 2019 at 16:48

1 Answer 1


When data are clustered, this leads to observations that are more similar to others in the same cluster than to those in other clusters. That is, there is intra-class correlation. Failure to adequately adjust for this can lead to biased fixed effects (in your case, the risk estimate).

One way to account for this is to fit random intercepts. By doing so, you are therefore reducing bias, and this is regardless of whether you use convenience sampling or random sampling of cluster units.

By fitting random effects, some of the variability in the response variable is being partitioned to each "level" - patients, wards and hospitals in your case - and "variance partition coefficients" can be calculated to see how much of the response variance is at each level.

  • $\begingroup$ Hello, I am already using a random effect model. I have clear the effect on the variances. What I don't know how to interpret is the difference in the baseline risk (the intercept coefficient) between a fixed effect only and a random intercept model. $\endgroup$
    – Bakaburg
    Feb 15, 2019 at 16:59
  • 1
    $\begingroup$ @Bakaburg you should not interpret the fixed-effects-only model because you have clustered data. You should only interpret a model that adjusts for clustering in some way (such as random intercepts, or fixed effects for all the clusters, or generalised estimating equations) $\endgroup$ Feb 15, 2019 at 17:05
  • $\begingroup$ Ok this is unexpected, can you elaborate on why? $\endgroup$
    – Bakaburg
    Feb 16, 2019 at 2:00
  • $\begingroup$ @Bakaburg I think I have explained why. Perhaps you can explain why you think it is good idea to interpret something you know is biased ? If you are doing a write-up there is nothing wrong with stating the value of the biased raw prevalence, but just leave it at that $\endgroup$ Feb 16, 2019 at 12:44
  • $\begingroup$ Ok, I think we are not understanding each other. I am already using a random effect model "f(y) ≈ Beta_intercept + sigma + u" where u is the error for the random intercept part. And I get a certain value for Beta_intercept that I understood you say it's less biased. I would like to know in practical term how to interpret this beta_intercept and its difference from the raw beta_intercept (or simply the cases/total patient ratio) I would have got from the fixed effect model. $\endgroup$
    – Bakaburg
    Feb 18, 2019 at 18:45

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