Update on my reply: hours after posting this thread, I found not only that I could no longer change its contents but also solutions to this problem.
An insidious tactic of finding the solution lies in correctly specifying the keyword in the search engine. I used "competing risks" and virtually retrieved no result on my problem. However, when substituting the words for "cause-specific hazard", a subdomain of competing risks analysis, things worked.
To summarize my finding, there is a research paper (Population-based absolute risk estimation with survey data | Lifetime Data Analysis) that discusses this issue. From the first sentence of its abstract (i.e., "Absolute risk is the probability that a cause-specific event occurs in a given time interval in the presence of competing events."), I came to know "absolute risk", a term whose meaning puzzled me before, could also serve as a keyword in search engines in this setting. I then found a book entitled Absolute Risk: Methods and Applications in Clinical Management and Public Health (Chapman & Hall/CRC Monographs on Statistics and Applied Probability Book 154), Pfeiffer, Ruth M., Gail, Mitchell H., eBook - Amazon.com, whose cover contained a picture depicting competing risks. It was exciting to find in the book that the intersection of complex survey data analysis and competing risks modeling was introduced as a few sections in this book, including an independent section on variance estimation. You- and of course, I- can refer to it for more details.
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