**Core Concept**
Proportional mortality is a measure used in epidemiology to describe the proportion of deaths due to a specific cause within a population. It is calculated by dividing the number of deaths due to a particular cause by the total number of deaths from all causes.

**Why the Correct Answer is Right**
The correct denominator for calculating proportional mortality is the total number of deaths from all causes. This is because proportional mortality aims to express the relative contribution of a specific cause to the overall mortality burden in a population. By using the total number of deaths as the denominator, the proportion of deaths due to each cause can be accurately compared. This helps in identifying the leading causes of death and their relative impact on mortality rates.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it is not a complete or accurate statement. The denominator for proportional mortality should be the total number of deaths, not just a subset of deaths.
**Option B:** This option is incorrect because it is not a relevant or standard measure in epidemiology. The number of people at risk or the population size is not the correct denominator for calculating proportional mortality.
**Option C:** This option is incorrect because it is not a valid measure in epidemiology. The total number of people with a specific disease is not the correct denominator for calculating proportional mortality.

**Clinical Pearl / High-Yield Fact**
When interpreting proportional mortality rates, it is essential to consider the total number of deaths from all causes as the denominator. This ensures that the proportion of deaths due to each cause is accurately represented and can be compared across different populations or time periods.

**Correct Answer: C. Total number of deaths from all causes.**