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To construct a complex database query in CakePHP that involves associated tables, you can use the following steps:

1. Define the models and associations in CakePHP's model files.

2. Use CakePHP's query builder to create the necessary SQL query.

3. To join associated tables, use the join() method and provide the Alias, Association Type, and conditions.

4. You can use the select() method to select specific fields from tables and provide aliases for the fields.

5. Finally, execute the query using the execute() method and retrieve the resulting data.

Here is an example code snippet that demonstrates a complex database query in CakePHP that involves associated tables:

$users = $this->Users->find() ->select(['Users.username', 'SUM(Orders.total) as totalsales']) ->join([ 'table' => 'orders', 'alias' => 'Orders', 'type' => 'INNER', 'conditions' => 'Users.id = Orders.userid' ]) ->group('Users.id') ->order(['total_sales' => 'DESC']) ->limit(10) ->toArray();

This query retrieves the top 10 users with the highest total sales by joining the Orders table with the Users table, selecting the username field from the Users table and calculated the totalsales from the orders table using the SUM aggregate function. The result is then grouped by user id and ordered in descending order by the totalsales. Finally, the query is limited to the top 10 results and returned as an array.