ML Interview Q Series: How would you query to visualize unsubscribe impact on login behavior over time using event and bucket data?
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Comprehensive Explanation
One way to approach this problem is to combine data from two tables: the events table (holding user actions such as login, nologin, and unsubscribe with timestamps) and the variants table (indicating which A/B group each user belongs to). By joining these tables on the user’s unique identifier, it becomes possible to break down unsubscribes and logins by variant group over time.
To understand how unsubscribes might correlate with login rates, a good strategy is to create a time series that shows unsubscribes versus logins on a daily (or weekly) basis for each bucket (control or treatment). From there, you can graph these metrics over time to see if higher unsubscribe counts on certain days coincide with changes in login patterns.
Key Formulas and Their Meanings
It is often useful to calculate some rates to get a normalized sense of changes in user behavior.
Unsubscribe_Rate = Unsubscribes / Total_Users
Where:
Unsubscribes is the total number of unsubscribe actions observed in the chosen time interval (e.g., daily).
Total_Users is the total number of users in that group or overall (depending on whether you want a group-specific or global unsubscribe rate).
Login_Rate = Logins / Total_Users
Where:
Logins is the number of login actions observed in the chosen time interval.
Total_Users is the total number of users in that same group or overall.
You can calculate these metrics by performing group-by operations on time intervals (such as date), variant group, and event type. Then you can join the data back to user-level tables or aggregated user counts to compute the rates.
Example of Constructing the Query
Below is an example of how you might write a query in Python (using a multi-line string) that joins these tables and aggregates unsubscribes and logins on a daily basis by variant. This example assumes that your tables are named events and variants, and that each record in events has a date, user_id, and action.
query = """
SELECT
e.event_date AS event_date,
v.variant_group AS variant_group,
SUM(CASE WHEN e.action = 'unsubscribe' THEN 1 ELSE 0 END) AS total_unsubscribes,
SUM(CASE WHEN e.action = 'login' THEN 1 ELSE 0 END) AS total_logins,
COUNT(DISTINCT e.user_id) AS unique_users_in_events
FROM events e
JOIN variants v
ON e.user_id = v.user_id
GROUP BY e.event_date, v.variant_group
ORDER BY e.event_date, v.variant_group
"""
In the above:
event_dateis used to group data on a daily basis.variant_groupdifferentiates the control group from the treatment group.SUM(CASE WHEN ...)counts how many actions of a certain type occurred.COUNT(DISTINCT e.user_id)is used to find the number of unique users who triggered events on that day (sometimes helpful to compare how many people are active).
Once you execute this query (for instance, via a SQL engine in Python), you can pull the resulting data into a Pandas DataFrame and create a graph of the unsubscribes versus logins over time. A typical next step is to compute unsubscribe_rate and login_rate from these raw counts to see how these rates change. For example, you could join it with a table of total assigned users per day (if daily population changes) or simply track it by total users in each variant.
Potential Follow-up Questions
Why do we use daily granularity instead of weekly, and how do we choose the right time bin?
When analyzing user behavior data, the choice of time window depends on traffic volume and business context. If there is enough data, daily snapshots give quicker feedback. If data is sparse or seasonality needs to be considered (for instance, weekly patterns), rolling or weekly windows might be more insightful.
How do we interpret a spike in unsubscribes in the experiment group?
A sudden increase in unsubscribes may indicate that the notifications irritate certain users. This might mean the notification strategy or content requires refinement. It can also hint at user fatigue or mismatch between notifications and user interests.
What if a large number of unsubscribers were never likely to log in again?
It is important to segment unsubscribers into groups such as “recently active” vs. “historically dormant” to see if unsubscribes come from previously engaged users or from inactive accounts. This difference might significantly affect how you interpret the unsubscribe rate’s impact on login behaviors.
How do we ensure that unsubscribes are truly impacting logins and not due to other confounders?
One approach is to analyze only users who unsubscribed and examine their login behavior before and after unsubscribing. Another approach is to ensure randomization was conducted properly, so that both variant and control groups share similar user distributions. You can also run statistical tests (e.g., difference-in-differences) if external factors occurred in the same timeframe.
How would we visualize this data effectively?
You could create:
A line chart over time with two lines (control vs. treatment) for login rates.
A secondary plot (or combined chart) that shows unsubscribes alongside it. Overlaying unsubscribes and login rates reveals how peaks in unsubscribes coincide (or not) with dips in login rates.
How do we determine statistical significance?
After aggregating metrics, apply standard A/B testing statistical analyses (e.g., z-tests, t-tests, or non-parametric tests) to see if any observed difference in unsubscribe or login rates is statistically meaningful. This might require capturing not only daily summaries but user-level data to get variance estimates.
How could we refine the notification system in light of these results?
Potential refinements include personalizing notifications so that relevant content is delivered at the right times, or giving users control over the frequency of notifications. If the data shows unsubscribes come from certain segments, you might adapt the strategy for those segments specifically.
Below are additional follow-up questions
How do we handle users who might be assigned to multiple variants or switch variants during the test?
This scenario can occur if your A/B testing system reassigns users due to unforeseen data pipeline glitches or because of how the bucketing logic was implemented. If a user’s variant assignment changes mid-test, it can muddy the results, since that user’s unsubscribe or login events might get attributed to multiple groups. A common approach is to lock user assignments at the beginning of the experiment, ensuring a user remains in the same variant throughout. If that is not possible, then it is important to track the user’s first assigned variant and only consider data recorded after that assignment. Another strategy might involve discarding or flagging inconsistent user assignments for post-analysis. You would examine how many users are affected to decide whether the portion is large enough to affect final metrics.
How might external events, unrelated to notifications, skew unsubscribe or login patterns?
External events can cause fluctuations in user behavior independently of the A/B test. For instance, there might be a major sporting event or a global holiday season that affects usage patterns. Such factors can cause unusual spikes or dips in logins or unsubscribes, which may incorrectly be attributed to the increased notifications. To mitigate such confounding influences, you could measure and compare historical data for the same days or weeks in previous years, or use a difference-in-differences approach if your control group remains unaffected by the external event. Additionally, you can add “external event” indicators in your data, enabling you to filter out or control for those time windows in the final analysis.
How do we measure the long-term impact of unsubscribes on other key metrics, like user engagement or revenue?
An A/B test may show a short-term change in unsubscribe rates, but it is vital to see whether these unsubscribes cause a decline in broader metrics over time. For instance, do users who unsubscribe still visit via other channels, or do they gradually churn entirely? One approach is to track cohorts of unsubscribers and measure their subsequent visits, site duration, clicks, or purchases. You can mark a baseline of user behavior before unsubscribing and then see how it changes in the weeks or months afterward. If you notice a sharp drop in revenue or engagement from unsubscribers, you can conclude that the notifications might have driven them away.
What if the distribution of user segments (e.g., highly active vs. new sign-ups) is not balanced between control and treatment groups?
A key assumption of A/B testing is that random assignment leads to balanced segments between the two groups. However, if there is a systematic bias—say, brand new users are heavily overrepresented in the treatment—then differences in unsubscribe or login rates might reflect the user segment composition rather than the effect of notifications themselves. Detecting this requires segment-level checks (e.g., by user tenure, geography, device platform) to confirm randomization worked. If you find imbalances, you might re-run randomization, perform stratified sampling, or use methods like post-stratification weighting to correct for the imbalance in your analysis.
How do we interpret users who unsubscribe but continue to log in frequently afterward?
Users might decide to unsubscribe from push notifications but still remain highly active on the platform, perhaps accessing it through web or email channels. This group is interesting because they essentially reject notifications yet do not reduce their overall engagement. In analyzing this cohort, check whether the unsubscribes correlate with negative feedback about notifications or a desire to manage notifications differently. You might also see if these users become more reliant on other channels or if they drop off after a certain period. This insight can guide improvements to your notification strategies, such as personalization or frequency capping.
What are potential data integrity pitfalls or anomalies that might affect our unsubscribe and login metrics?
Data integrity issues could include:
Duplicate events, where a single user action is recorded multiple times, artificially inflating unsubscribe or login counts.
Event timing misalignment, when the time zone or timestamp logs are inconsistent, leading to off-by-one-day errors in daily aggregations.
Missing data due to ingestion failures or partial outages in your logging pipeline, creating dips in the metrics that do not reflect real user behavior.
Users who do not have a consistent user_id across sessions (e.g., logged in through different devices or used multiple accounts).
Addressing these problems typically involves cleaning data, consistently applying data schema rules, using well-defined user identifiers, and implementing robust data pipeline monitoring to detect anomalies quickly.
How can we separate the effect of more notifications from the effect of unsubscribes on driving logins?
The experiment might have two intertwined effects: (1) Additional notifications could either increase or decrease user logins. (2) Users who unsubscribe might log in less (or not at all). To dissect these effects:
Compare login rates among those who received more notifications but did not unsubscribe vs. those who unsubscribed.
Use a mediation analysis framework to see if unsubscribes mediate the relationship between more notifications and reduced (or increased) logins.
Consider a sequential approach: look at login behavior before any unsubscribes, then after. By separating these sub-populations, you gain clarity on whether unsubscribes themselves cause login changes or if it is the overall quantity of notifications that triggers both unsubscribes and login changes.
What if unsubscribing from push notifications only applies to specific devices or specific channels?
Not all users are equally dependent on the same device or channel. Some users may unsubscribe from mobile push notifications but still receive email alerts, or they may be active desktop web users. In this case, unsubscribes do not necessarily mean the user ceases to receive all notifications. You can refine your analysis by splitting unsubscribes by channel or device, then cross-referencing user behavior to see if an unsubscribe on one channel is offset by increased usage on another. You might also want to standardize how you define an “unsubscribe” event across channels to ensure consistent measurement.
In situations with large user bases, how do we efficiently store and process the event data for daily or real-time dashboards?
Handling large-scale data requires:
Distributed storage solutions (e.g., data warehouses like BigQuery, Snowflake, or Spark-based data lakes).
Batch or streaming ETL pipelines to handle high-throughput logs.
Partitioned or sharded tables by date or user_id, enabling faster queries.
Carefully designed indexing or segment-based caching (e.g., pre-aggregations for daily metrics). You can implement a star schema (fact table referencing dimension tables) or a wide table with partitioned columns. A real-time setup might involve streaming frameworks (like Kafka + Spark Streaming or Flink) to compute near real-time metrics, though you must ensure data consistency and handle late-arriving events appropriately.
What do we do if the control group also shows an increase in unsubscribes, making it challenging to interpret differences?
If both the control and the treatment see a spike in unsubscribes, you might suspect an external factor or a global change in user sentiment. In such a scenario:
Revisit your funnel analysis to see if any site-wide change (like a new privacy policy or product redesign) could be driving unsubscribes for everyone.
Look at historical data for the control group to see if the unsubscribe rate spike aligns with cyclical trends or newly introduced product features.
If the control group changes were minimal compared to the treatment group, a difference-in-differences approach can still yield insights.
If you find that both lines rise but the treatment line rises more sharply, you can focus on that relative effect.