A modified least-squares regression approach to the estimation of risk difference.
Abstract
Risk ratio and risk difference are parameters of interest in many medical studies. The risk ratio has a property that the value for the outcome Y = 0 is not the inverse of the risk ratio for the outcome Y = 1. This property makes risk ratios inappropriate in some situations. Estimation of risk difference often encounters the problem that the binomial regression model fails to converge. Recently discussed alternatives may have the same problem of nonconvergence or are difficult to implement. Here the author proposes a modified least-squares regression approach--unweighted least-squares regression with a Huber-White robust standard error--for estimation of risk differences. Four versions of the robust standard error are considered. The binomial, ordinary least-squares, and modified least-squares estimators are compared analytically in a simple situation of one exposure variable. Multivariable regression analyses are simulated to demonstrate the usefulness of the approach. For sample sizes of approximately 200 or less, a small-sample version of the robust standard error is recommended. The method is illustrated with data from a patient survey in which the binomial regression fails to converge in the analyses of four out of five outcome variables.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Statistical Power Analysis for the Behavioral Sciences
Muller, K. E., & Cohen, J. (1989) · Technometrics · doi:10.2307/1270020 · Cited by 99,588 · see citing works
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,415 · see citing works
Limited-Dependent and Qualitative Variables in Econometrics
Maddala, G. S. (1983) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810176 · Cited by 13,268 · see citing works
Toxicity and response criteria of the Eastern Cooperative Oncology Group
Oken, M. M., Creech, R. H., Tormey, D. C., Horton, J., Davis, T. E., Mcfadden, E. T., & Carbone, P. P. (1982) · American Journal of Clinical Oncology · doi:10.1097/00000421-198212000-00014 · Cited by 11,683 · see citing works
A Modified Poisson Regression Approach to Prospective Studies with Binary Data
Zou, G. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh090 · Cited by 9,767 · see citing works
EQ-SD: a measure of health status from the EuroQol Group
Rabin, R., & Charro, F. D. (2001) · Annals of Medicine · doi:10.3109/07853890109002087 · Cited by 5,613 · see citing works
Introduction to Linear Regression Analysis.
Assunção, R., Sampson, P. D., Montgomery, D. C., & Peck, E. A. (1993) · Journal of the American Statistical Association · doi:10.2307/2290746 · Cited by 5,389 · see citing works
Estimating the Relative Risk in Cohort Studies and Clinical Trials of Common Outcomes
McNutt, L. (2003) · American Journal of Epidemiology · doi:10.1093/aje/kwg074 · Cited by 2,098 · see citing works
Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model
Long, J. S., & Ervin, L. H. (2000) · The American Statistician · doi:10.1080/00031305.2000.10474549 · Cited by 1,779 · see citing works
Easy SAS Calculations for Risk or Prevalence Ratios and Differences
Spiegelman, D. L. (2005) · American Journal of Epidemiology · doi:10.1093/aje/kwi188 · Cited by 1,729 · see citing works
Introduction to Linear Regression Analysis.
Cass, J. M., Montgomery, D. C., & Peck, E. A. (1983) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2348054 · Cited by 1,412 · see citing works
Generalized Linear Models and Extensions
Hardin, J. W., & Hilbe, J. M. (2012) · Cited by 853 · see citing works
Greenland, S. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh221 · Cited by 728 · see citing works
INTERPRETATION AND CHOICE OF EFFECT MEASURES IN EPIDEMIOLOGIC ANALYSES1
Greenland, S. (1987) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a114593 · Cited by 546 · see citing works
Generalized Linear Models and Extensions
Kateri, M. (2014) · Springer eBooks · doi:10.1007/978-0-8176-4811-4_5 · Cited by 506 · see citing works
Limited-Dependent and Qualitative Variables in Econometrics
(1983) · Cambridge University Press eBooks · doi:10.1017/ccol052124143x · Cited by 448 · see citing works
Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model
Long, J. S., & Ervin, L. H. (2000) · The American Statistician · doi:10.2307/2685594 · Cited by 401 · see citing works
Clinically useful measures of effect in binary analyses of randomized trials
Sinclair, J. C., & Bracken, M. B. (1994) · Journal of Clinical Epidemiology · doi:10.1016/0895-4356(94)90191-0 · Cited by 271 · see citing works
Introduction to Linear Regression Analysis (3rd ed.)
Jammalamadaka, S. R. (2003) · The American Statistician · Cited by 263 · see citing works
von Seidlein, L., Milligan, P. J., Pinder, M., et al. (2000) · The Lancet · doi:10.1016/s0140-6736(99)10237-x · Cited by 190 · see citing works
Maximum Likelihood Estimation with StataPreprint
Gould, W., Pitblado, J. S., & Poi, B. P. (1999) · RePEc: Research Papers in Economics · Cited by 164 · see citing works
Parameter Estimation and Goodness-of-Fit in Log Binomial Regression
Blizzard, L., & Hosmer, W. (2006) · Biometrical Journal · doi:10.1002/bimj.200410165 · Cited by 162 · see citing works
Review of Generalized Linear Models and Extensions by Hardin and Hilbe
Newson, R. B. (2001) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x0100100107 · Cited by 91 · see citing works
Do English and Chinese EQ-5D versions demonstrate measurement equivalence? An exploratory study.
Luo, N., Chew, L.-H., Fong, K., Koh, D.-R., Ng, S., Yoon, K. H., Vasoo, S., Li, S., & Thumboo, J. (2003) · Health and Quality of Life Outcomes · doi:10.1186/1477-7525-1-7 · Cited by 69 · see citing works
Cheung, Y., Thumboo, J., Goh, C. R., et al. (2004) · Cancer · doi:10.1002/cncr.20681 · Cited by 51 · see citing works
Self-citationRE: "ESTIMATING THE RELATIVE RISK IN COHORT STUDIES AND CLINICAL TRIALS OF COMMON OUTCOMES"
Deddens, J. A. (2004) · American Journal of Epidemiology · doi:10.1093/aje/kwh022 · Cited by 47 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Muller, C. J., & MacLehose, R. F. (2014) · International Journal of Epidemiology · doi:10.1093/ije/dyu029 · Cited by 775 · see citing works
Lowe, W. L., Scholtens, D. M., Lowe, L. P., Kuang, A., Nodzenski, M., Talbot, O., Catalano, P. M., Linder, B., Brickman, W. J., Clayton, P., et al. (2018) · JAMA · doi:10.1001/jama.2018.11628 · Cited by 591 · see citing works
Lowe, W. L., Scholtens, D. M., Kuang, A., Linder, B., Lawrence, J. M., Lebenthal, Y., McCance, D., Hamilton, J., Nodzenski, M., Talbot, O., et al. (2019) · Diabetes Care · doi:10.2337/dc18-1646 · Cited by 574 · see citing works
Sufficient cause interactions and statistical interactions
VanderWeele, T. J. (2009) · Epidemiology · doi:10.1097/ede.0b013e31818f69e7 · Cited by 163 · see citing works
Lipska, K. J., Parker, M. M., Moffet, H. H., Huang, E. S., & Karter, A. J. (2018) · JAMA · doi:10.1001/jama.2018.7993 · Cited by 76 · see citing works
- Authors
- Cheung, Y. B.
- Affiliations
- London School of Hygiene & Tropical Medicine (GB)
- Corresponding author
- Cheung, Y. B.
- Venue
- American Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2007-08-28
- Volume
- 166
- Issue
- 11
- Pages
- 1337-1344
- ISSN
- 0002-9262 (ISSN-L)
- 1476-6256
- OpenAlex
- W2099312240
- Cited by
- 189
- References
- 26
- Citations by year
- 2026: 18 · 2025: 19 · 2024: 12 · 2023: 7 · 2022: 9 · 2021: 12 · 2020: 5 · 2019: 12 · 2018: 17 · 2017: 14 · 2016: 14 · 2015: 7 · 2014: 8 · 2013: 4 · 2012: 9
- FWCI
- 4.72
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- LSHTM Research Online (London School of Hygiene and Tropical Medicine) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- risk difference, relative risk, multivariable regression, exposure-outcome association, patient survey data
- MeSH terms
- Clinical Trials as Topic, Data Interpretation, Statistical, Epidemiologic Methods, Humans, Risk, Least-Squares Analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
