Identification of distributions for risks based on the first moment and c-statistic
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929679193079808 |
|---|---|
| author | Sadatsafavi, Mohsen Lee, Tae Yoon Petkau, John |
| author_facet | Sadatsafavi, Mohsen Lee, Tae Yoon Petkau, John |
| contents | We show that for any family of distributions with support on [0,1] with strictly monotonic cumulative distribution function that has no jumps and is quantile-identifiable (i.e., any two distinct quantiles identify the distribution), knowing the first moment and c-statistic is enough to identify the distribution. The derivations motivate numerical algorithms for mapping a given pair of expected value and c-statistic to the parameters of specified two-parameter distributions for probabilities. We implemented these algorithms in R and in a simulation study evaluated their numerical accuracy for common families of distributions for risks (beta, logit-normal, and probit-normal). An area of application for these developments is in risk prediction modeling (e.g., sample size calculations and Value of Information analysis), where one might need to estimate the parameters of the distribution of predicted risks from the reported summary statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identification of distributions for risks based on the first moment and c-statistic Sadatsafavi, Mohsen Lee, Tae Yoon Petkau, John Methodology Computation We show that for any family of distributions with support on [0,1] with strictly monotonic cumulative distribution function that has no jumps and is quantile-identifiable (i.e., any two distinct quantiles identify the distribution), knowing the first moment and c-statistic is enough to identify the distribution. The derivations motivate numerical algorithms for mapping a given pair of expected value and c-statistic to the parameters of specified two-parameter distributions for probabilities. We implemented these algorithms in R and in a simulation study evaluated their numerical accuracy for common families of distributions for risks (beta, logit-normal, and probit-normal). An area of application for these developments is in risk prediction modeling (e.g., sample size calculations and Value of Information analysis), where one might need to estimate the parameters of the distribution of predicted risks from the reported summary statistics. |
| title | Identification of distributions for risks based on the first moment and c-statistic |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2409.09178 |