Create a detailed report in Power BI DAX that extracts and summarizes data regarding students enrolled in various programs. Each student has unique program start and end dates and may participate in multiple programs. The program type is stored in a separate table. Students may receive multiple standardized questionnaires that consist primarily of yes/no questions and are categorized into five distinct groups. Note that not all students will complete a questionnaire, nor will all questions be answered. 

On a specific calendar date, your report should do the following:

1. Extract all student programs that ended within the specified period.
2. Find all questionnaires sent to each student during the program end dates.
3. Summarize responses, indicating the presence or absence of questionnaires and responses organized by question categories.

Ensure the report structure is illustrated using a star schema approach, including the following necessary tables: 
- Students
- Programs
- Questionnaires
- Responses
- Question Categories

Clearly identify the fact table and delineate the relationships among the tables, while also accounting for any missing data.