How to evaluate the inclusion probability of the patients

[Legarraudien]

I adopted a two-stage sampling strategy to conduct a study on patient medical expenses. Instead of going to the households,
We decided in the first stage to select health institutions and in the second stage 50 patients in each institution selected in the first stage of sampling.
We can evaluate the inclusion probability for the primary sampling units, but we have doubts to do for the patients.
Knowing that on the day of the team's visit, the number of patients attending the institution may be less than the number of patients to be investigated per institution (50 patients);
At this time a second day of visit is necessary to complete the number of patients.
We do not know if each patient corresponds to a unique household.
In this case, how to determine the inclusion probability of a patient? Knowing that if the institution does not have a lot of attendance on the day of the visit, we survey all the patients present. Otherwise, from the consultation register, we draw the 50 patients using the systematic sampling method.

We also know the number of patients who made their first visit per month and per year (for the year prior to the study) and the number of total visits.
We also want to evaluate the sampling weight of the household from the patient.
Is it possible to determine the weight,survey for the household? Or we should not analyze this data using the weighting process.

[ChrisCharlton]

As this section of the forum is for questions related to the Stat-JR software package are you able to provide any more detail on how you are using it for this analysis, e.g. which templates and underlying statistics package you are using/planning to use?

[florencepugh]

To evaluate the inclusion probability of patients in your two-stage sampling strategy, calculate the probability for health institutions first and then determine patient probabilities based on attendance: if fewer than 50 patients are present, all are included; if more, use systematic sampling for 50.