The dose for an incremental lifetime cancer risk of 10-6

(a) Increases as the estimated cancer slope factor increases
(b) Decreases as the estimated cancer slope factor increases
(c) Is independent of the value of the cancer slope factor

(b) At a higher risk/dose slope factor, a smaller dose is needed to increase the risk by a given amount.

To determine the correct answer, we need to understand the relationship between the dose and the estimated cancer slope factor.

The dose for an incremental lifetime cancer risk of 10-6 refers to the amount of exposure to a specific substance or radiation that will result in a one in a million increase in the lifetime risk of developing cancer.

Now, let's look at the options:

(a) Increases as the estimated cancer slope factor increases.
(b) Decreases as the estimated cancer slope factor increases.
(c) Is independent of the value of the cancer slope factor.

To find the correct answer, we need to understand the concept of the cancer slope factor. The cancer slope factor is a measure of the potency of a particular substance or radiation in causing cancer. It represents the increased risk of cancer associated with an incremental increase in exposure to that substance or radiation. A higher cancer slope factor implies a greater potency in causing cancer per unit of exposure.

Given that we want to maintain a constant incremental lifetime cancer risk of 10-6, it means that the risk remains the same regardless of the estimated cancer slope factor. Therefore, the correct answer is:

(c) Is independent of the value of the cancer slope factor.

In other words, the dose required to achieve an incremental lifetime cancer risk of 10-6 will remain the same regardless of how potent the substance or radiation is (as indicated by the cancer slope factor).