Bias-corrected Cancer Incidence Rate 

to account for Differential Privacy 

Error in the Population Data

Mandi Yu, National Cancer Institute

Jiming Jiang, University of California, Davis

October 24-26, 2023

College Park, MD
Disclaimer: 

The opinions expressed in this presentation are the 

author's own and do not reflect the view of the National 

Cancer Institute, National Institutes of Health, the 

Department of Health and Human Services, or the 

United States government.
Outline

• Background

• NCI’s SEER program and Cancer Rates

• Differential Private (DP) Census Population Estimates

• Bias-corrected Rate Estimator

• Study Objective – performance of correcting for bias due to 

DP error in Population data

• Discussion
Cancer Surveillance and SEER Areas

• Surveillance, Epidemiology, and End 

Results (SEER) program is established and 

supported by the NCI since 1973.

• SEER collects and publishes cancer 

incidence and survival data from 

population-based registries across the 

nation.

• Information include patient 

demographics, primary tumor site, tumor 

morphology and stage at diagnosis, first 

course of treatment, and follow-up for 

vital status (survival)

SEER registries cover ~48% of 

the U.S. population.

Age-Adjusted Rate of Cancer Incidence

ccjj = number of tumors in age group jj

wwjj = age-adjusting weight in age group jj

NNjj = at risk population in age group jj, and it 

is assumed to be error-free (despite of small 

enumeration error)

Age Adjusted Rate = �JJwwjj

ccjj

NNjj
Bias-corrected Rate

Age Adjusted Ratebbbb = �JJwwjj

ccjj

NN�jj

11 − CCCC22

NN�jj = estimated population in age group jj

 CCCCjj = estimated Coefficient of Variation of population in age group jj
Differential Private Population Data

• A Topdown algorithm to adds noise – or variations from the actual 

count – to the collected data

• Geographic pop control totals were assigned a privacy budget (state 

totals are exactly matched)

• However, pop totals by demographics, such as age and race, are not 

controlled for and may be subject to systematic deviations

• Size of deviation tends to be greater for small groups despite of 

iterations of improvements from Census Bureau on the Topdown

algorithms
A Few Key Challenges for Calculating Cancer Rates

Local data 

not 

controlled 

for

Race/Ethnicity 

data may be 

compromised

Inaccurate 

AGE data 

for AgeAdjusting
Study Objectives and Methods

• Objectives:

• 1. Impact of DP on the validity of rates

• 2. Performance of bias-correction to alleviate the DP impact

• Use California data as a test case

• Stratification variables: county and 5-year age group

• Outcome: age-adjusted rates for counties

• Most challenging part is how to simulate DP population estimates

• Detailed algorithms are confidential and kept within Census Bureau

• Size of DP errors derived from Census 2010 demonstration dataset

• A TopDown approach similar in principle to Census’s algorithm
Population Simulation-A TopDown Appraoch

• Add normal-distributed noise to pops totals 

• With variance of noise proportional to the size of population 

totals (p=0.2)

• Resulted noise is similar to observed differences between the 

demonstration and real 2010 census data

• Optimized noise size using a two-step approach
Simulate Study

• Questions to be answered

• Whether Bias-correction helps to adjust for DP error?

• What is the population cutoffs for DP errors to be negligible for ageadjusted rates of incidence (AAR)? 

• Study Methods:

• Simulate Poisson incidence county by age and county (since cancers 

are random events)

• Calculate AARs using DP-pop and Real-pop

• Calculate % Relative Bias of AAR from simulation studies
Results: % Relative Bias in AAR (county-level)

Naïve No DP: Population does not have DP errors

Naïve with DP: Population has DP errors and AAR is calculated using the standard method (i.e. without bias correction)

Bias-correction with DP: Population has DP errors and AAR is bias-corrected
Boxplots of % Relative Bias

Note: Each dot 

corresponds to 

one county
% Relative Bias by County Population Size (log scale)

20%

Relative Bias (%)

-10%

10%

0%

Logarithm of Population

8 10 12 14 16 

Exp(10)~=20K

Exp (10.8)~=50K

Exp(11.5)~=100K
A further simulation of Sampling Error+ DP Error

• The case when DP 

error is added to 

survey samples

• E.g., DP modified 

American 

Community Survey 

estimates.

• ρρ is the measure of 

sampling fraction 

and gauges sampling 

error 

• qq gauges DP error
Discussion

• The magnitude of DP bias is not comparable to that of sampling error

• The impact of bias-correct on AARs is small in relative to sampling error

• DP error’s impacts become small/negligible only if the population is at 

least 100K or greater – limit the ability for detailed disparity analysis 

• Current simulation is limited to Age variable and the next step is to 

consider race/ethnicity
Policy Implications

• Health burden studies for small subpopulations or at local 

geographic level are becoming impossible, however policies are 

mostly ‘local’ and ‘specific’

• Noise metrics released by Census Bureau are not detailed enough 

to help understand the extend of impact on cancer rates

• User community would benefit a guidance from Census Bureau 

regarding to how to use the noise metrics, e.g., how to relate noise 

measure to variance for common statistics
Contact: Mandi Yu (mandi.yu@nih.gov)