Calculating Cumulative Distinct Patients per Day Using Window Functions in SQLite

Understanding the Challenge: Cumulative Distinct Patient Counts with Date Partitioning

The core objective in this scenario is to compute a running total of distinct patients seen up to each timestamp within a given day. The challenge arises from the need to track patient visits over time, ensuring that each patient is counted only once per day, even if they have multiple visits. The desired output requires two key calculations:

1. Identifying the first occurrence of a patient’s visit each day (marking it as 1, subsequent visits as 0).
2. Summing these markers cumulatively within the same day to reflect the total distinct patients seen up to each timestamp.

The initial approach uses a window function to flag first visits but does not compute the cumulative sum across these flags. This leads us to explore why the cumulative aggregation isn’t behaving as expected and how to resolve it.

Critical Analysis of the Initial Query and Window Function Behavior

The original query uses a CASE expression with a COUNT() OVER window function to determine whether a patient’s visit is their first of the day:

CASE 
  WHEN COUNT() OVER (
    PARTITION BY datestring, patient 
    ORDER BY timestring 
    ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
  ) > 1 THEN 0 
  ELSE 1 
END AS distinct_count

This logic works correctly to mark the first visit of each patient per day as 1 and subsequent visits as 0. However, the missing piece is aggregating these 1 values cumulatively within each day. Attempting to add a SUM() window function directly to distinct_count without proper partitioning and ordering will fail to produce the desired running total.

Key Observations:

• The PARTITION BY datestring, patient clause in the initial window function ensures that each patient’s visits are isolated within a day.
• The ORDER BY timestring clause sequences visits chronologically.
• The absence of a secondary window function to sum distinct_count across the entire day’s partition prevents cumulative aggregation.

Step-by-Step Solutions: Nested Window Functions and Subquery Strategies

Solution 1: Layered Window Functions via Subquery

To achieve the cumulative sum of distinct_count, nest the initial query inside a subquery and apply a second window function to aggregate the results:

SELECT 
  datestring,
  timestring,
  patient,
  distinct_count,
  SUM(distinct_count) OVER (
    PARTITION BY datestring 
    ORDER BY timestring 
    ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
  ) AS what_I_want
FROM (
  SELECT 
    datestring,
    timestring,
    patient,
    CASE 
      WHEN COUNT() OVER (
        PARTITION BY datestring, patient 
        ORDER BY timestring 
        ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
      ) > 1 THEN 0 
      ELSE 1 
    END AS distinct_count
  FROM visit
) AS flagged_visits
ORDER BY datestring, timestring;

Breakdown:

1. Inner Subquery (flagged_visits): Identifies first visits using the CASE and COUNT() window function.
2. Outer Query: Computes the cumulative sum of distinct_count using SUM() OVER, partitioned by datestring and ordered by timestring.

Solution 2: Combining DENSE_RANK for First Visit Detection

An alternative approach uses DENSE_RANK() to detect first visits:

SELECT 
  datestring,
  timestring,
  patient,
  (CASE WHEN visit_rank = 1 THEN 1 ELSE 0 END) AS distinct_count,
  SUM(CASE WHEN visit_rank = 1 THEN 1 ELSE 0 END) OVER (
    PARTITION BY datestring 
    ORDER BY timestring 
    ROWS UNBOUNDED PRECEDING
  ) AS what_I_want
FROM (
  SELECT 
    datestring,
    timestring,
    patient,
    DENSE_RANK() OVER (
      PARTITION BY datestring, patient 
      ORDER BY timestring
    ) AS visit_rank
  FROM visit
) AS ranked_visits
ORDER BY datestring, timestring;

Advantages:

• DENSE_RANK() assigns a rank of 1 to the first visit of each patient per day, simplifying the flagging logic.
• The cumulative sum logic remains unchanged but operates on a more intuitive ranking system.

Solution 3: Materialized Intermediate Results for Large Datasets

For datasets with millions of rows, materializing intermediate results (e.g., first visits per patient per day) in a temporary table can optimize performance:

CREATE TEMP TABLE first_visits AS
SELECT 
  datestring,
  patient,
  MIN(timestring) AS first_timestring
FROM visit
GROUP BY datestring, patient;

SELECT 
  v.datestring,
  v.timestring,
  v.patient,
  (CASE WHEN v.timestring = fv.first_timestring THEN 1 ELSE 0 END) AS distinct_count,
  SUM(CASE WHEN v.timestring = fv.first_timestring THEN 1 ELSE 0 END) OVER (
    PARTITION BY v.datestring 
    ORDER BY v.timestring 
    ROWS UNBOUNDED PRECEDING
  ) AS what_I_want
FROM visit v
LEFT JOIN first_visits fv 
  ON v.datestring = fv.datestring 
  AND v.patient = fv.patient
ORDER BY v.datestring, v.timestring;

Performance Considerations:

• Precomputing first visits reduces redundant calculations in the main query.
• Indexes on datestring, patient, and timestring can significantly speed up both the temporary table creation and the final join.

Edge Cases and Validation

1. Same Timestamp for Multiple Patients:

   • If two patients have the same timestring, the ORDER BY timestring clause will process them in an undefined order unless secondary sorting (e.g., patient) is added. This could lead to inconsistent what_I_want values. To resolve this, include a tiebreaker column in the ORDER BY clause (e.g., patient).

2. Time Zone Variations:

   • If datestring and timestring do not account for time zones, daylight saving changes, or server-local time, the partitioning by date may misalign with actual calendar days. Ensure all timestamps are stored in a consistent time zone.

3. Data Type Mismatches:

   • Storing dates and times as strings (e.g., datestring TEXT) can lead to incorrect ordering if the format varies (e.g., 2021-9-1 vs. 2021-09-01). Convert these columns to proper DATE and TIME types or enforce consistent string formatting.

4. Patient Name Variations:

   • Inconsistent patient identifiers (e.g., case sensitivity: ‘A’ vs. ‘a’) will cause distinct counts to fail. Apply normalization (e.g., UPPER(patient)) during insertion or querying.

Performance Optimization Techniques

1. Indexing Strategy:

   • Create composite indexes to support the window function partitions and ordering:

     CREATE INDEX idx_visit_date_patient_time ON visit(datestring, patient, timestring);
     

   • This index accelerates the PARTITION BY datestring, patient ORDER BY timestring operations in the window functions.

2. Window Frame Optimization:

   • Explicitly define the window frame as ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW to avoid default RANGE behavior, which can be slower due to implied sorting.

3. Query Simplification:

   • Avoid redundant columns in the output if they’re not needed (e.g., timestring in the final report). Fewer columns reduce data shuffling.

Alternative Approaches and Trade-offs

1. Using Common Table Expressions (CTEs):

   WITH flagged_visits AS (
     SELECT 
       datestring,
       timestring,
       patient,
       CASE 
         WHEN COUNT() OVER (
           PARTITION BY datestring, patient 
           ORDER BY timestring 
           ROWS UNBOUNDED PRECEDING
         ) = 1 THEN 1 
         ELSE 0 
       END AS distinct_count
     FROM visit
   )
   SELECT 
     datestring,
     timestring,
     patient,
     distinct_count,
     SUM(distinct_count) OVER (
       PARTITION BY datestring 
       ORDER BY timestring 
       ROWS UNBOUNDED PRECEDING
     ) AS what_I_want
   FROM flagged_visits
   ORDER BY datestring, timestring;
   

   • Pros: Improves readability by separating logical steps.
   • Cons: May not offer performance benefits over subqueries in SQLite.

2. Pre-Aggregating First Visits:
   Compute first visits in a separate aggregation and join back to the original data:

   SELECT 
     v.datestring,
     v.timestring,
     v.patient,
     (CASE WHEN v.timestring = fv.first_time THEN 1 ELSE 0 END) AS distinct_count,
     SUM(CASE WHEN v.timestring = fv.first_time THEN 1 ELSE 0 END) OVER (
       PARTITION BY v.datestring 
       ORDER BY v.timestring 
       ROWS UNBOUNDED PRECEDING
     ) AS what_I_want
   FROM visit v
   LEFT JOIN (
     SELECT 
       datestring,
       patient,
       MIN(timestring) AS first_time
     FROM visit
     GROUP BY datestring, patient
   ) fv ON v.datestring = fv.datestring AND v.patient = fv.patient
   ORDER BY v.datestring, v.timestring;
   

   • Pros: Leverages SQLite’s optimized aggregate functions (MIN()).
   • Cons: Requires a join, which may be less efficient than window functions for large datasets.

Final Recommendations

1. Adopt Solution 1 (Nested Window Functions): This approach balances readability and performance for most use cases. Ensure proper indexing is in place.
2. Validate Data Consistency: Sanitize datestring and timestring values to avoid formatting issues.
3. Benchmark with Real Data: Test queries on representative datasets to identify bottlenecks, especially if dealing with high-volume visit records.