Imputing partial birth dates using day of the week

Imputing partial birth dates using day of the week | medRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-P4HH5NV'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search Imputing partial birth dates using day of the week View ORCID Profile Candice Y. Johnson doi: https://doi.org/10.1101/2025.10.08.25337453 Candice Y. Johnson 1 Department of Epidemiology and Biostatistics, Michigan State University Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Candice Y. Johnson For correspondence: candice{at}msu.edu Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF ABSTRACT Background In deidentified data, exact dates are suppressed to maintain confidentiality of research participants. When the partial date includes only month and year, researchers who need exact dates must impute a day of the month. In some deidentified datasets, day of the week is also provided, but this variable is uncommonly incorporated into the imputation of partial dates. Our objective was to examine the extent to which misclassification is reduced by incorporating day of the week into partial date imputation. Methods We simulated a population of 594,677 people using the distribution of birthdays in England and Wales in 2024. We imputed birth dates using four methods: (1) first day of the month, (2) 15 th of the month, (3) randomly selecting a day of the month, and (4) randomly selecting a day of the month conditional on day of the week. We quantified misclassification as the median number of days between the imputed and true birth date and as the cumulative percentage of the population whose imputed birth date fell within a given number of weeks of their true birth date. Results Incorporating day of the week reduced misclassification, with a median of 7 days between imputed and exact birth date compared to 8–15 for the other methods. For nearly a quarter of the population, their imputed birth date was their true birth date, compared to 3% in other methods. However, using the 15 th day of the month was the best method to ensure that no misclassification was greater than 3 weeks. Conclusion Incorporating day of the week into random day selection reduced misclassification. This method is easily accomplished in standard statistical software. IMPUTING PARTIAL BIRTH DATES USING DAY OF THE WEEK In deidentified data, exact dates are suppressed to maintain confidentiality of research participants. When the partial date includes only month and year, researchers who need exact dates must impute a day of the month. Selecting an imputation method that minimizes misclassification is important to reduce bias. 1 Commonly used imputation methods include selecting the first or last day of the month, the 15 th day of the month, or randomly selecting a day of the month. 2 – 4 In some deidentified datasets, day of the week is also provided because outcomes occur unevenly across the week; examples include U.S. birth and death certificates and hospital discharge data. However, day of the week is uncommonly incorporated into the imputation of partial dates. This omission is a missed opportunity to reduce misclassification because when year and month are known, day of the week narrows the candidate imputed dates from approximately 30 to 5. Our objective was to examine the extent to which misclassification is reduced by incorporating day of the week into partial date imputation. We simulated a population of 594,677 people and their true birth dates using the distribution of birthdays in England and Wales in 2024. 5 We used Stata version 19 (College Station, Texas) for analyses and used its date functions to extract the year, month, day, and day of the week from each true birth date. Using only year, month, and day of the week, we imputed birth dates using four methods: (1) first day of the month, (2) 15 th of the month, (3) randomly selecting a day of the month, and (4) randomly selecting a day of the month conditional on day of the week. The fourth method involved identifying only the dates that fell on the given day of the week (e.g., Mondays in January 2024) and selecting randomly among those dates. We quantified misclassification as the median number of days between the imputed and true birth date and as the cumulative percentage of the population whose imputed birth date fell within 0 (no misclassification), 1, 2, 3, 4, or 5 weeks of their true birth date. Incorporating day of the week reduced misclassification compared to the other methods, with a median of 7 days between imputed and exact birth date compared to 8–15 for the other methods ( Table ). As expected, by narrowing down the possible dates using day of the week, for nearly a quarter of the population their imputed birth date was their true birth date, compared to 3% in other methods. However, using the 15 th day of the month was the best method to ensure that no misclassification was greater than 3 weeks. View this table: View inline View popup Download powerpoint Table Median difference between imputed and true birth dates and cumulative percentage of the imputed birth dates falling within a given distance of the true birth dates using four imputation methods. Researchers may have good reasons to choose imputation methods that do not incorporate day of the week or minimize misclassification. The first and last days of the month may be desired for start and stop dates to provide conservative estimates of duration. The 15 th day may be useful when it is important for all imputed dates to be as close to the true dates as possible but a realistic distribution of dates across the month is not needed. Randomly selecting a day is a commonly-used method to produce a realistic distribution of dates across the month. 3 Incorporating day of the week into this random selection reduced misclassification and should be used when day of the week is available. Incorporating day of the week into the imputation is easily accomplished in standard statistical software. We include example Stata and SAS code in the Supplementary Materials. Data Availability The data used for this research is available from the UK Office for National Statistics website. https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/bulletins/birthsummarytablesenglandandwales/2024 Footnotes Data and Code Availability Statement: The data used for this research is available from the Office for National Statistics website at https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/bulletins/birthsummarytablesenglandandwales/2024 . The code is available in the Supplementary Materials. Source of Funding: None Ethics Approval: Not applicable Conflicts of Interest: None declared REFERENCES 1. ↵ Woods LM , Rachet B , Ellis L , Coleman MP . Full dates (day, month, year) should be used in population-based cancer survival studies . International Journal of Cancer . 2012 ; 131 ( 7 ): E1120 – E1124 . doi: 10.1002/ijc.27545 OpenUrl CrossRef PubMed 2. ↵ Coles RH , Barnes P , Fingerhut LA , Gentleman JF , Schenker N , Warner M. Imputation of Missing Date Information for Injuries and Poisonings Reported in the National Health Interview Survey . Northeast SAS Users Group 2006 . https://www.lexjansen.com/nesug/nesug06/an/da03.pdf 3. ↵ Samuels SJ , Cox NJ . Stata Tip 105: Daily Dates with Missing Days . The Stata Journal . 2012 ; 12 ( 1 ): 159 – 161 . doi: 10.1177/1536867X1201200110 OpenUrl CrossRef 4. ↵ Bowman R. Partial dates; decisions and implications of handling partially missing dates . PHUSE 2006 . https://www.lexjansen.com/phuse/2006/po/PO11.pdf 5. ↵ Office for National Statistics . Births in England and Wales: Birth Registrations . 2025 . https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/datasets/birthsinenglandandwalesbirthregistrations View the discussion thread. Back to top Previous Next Posted October 13, 2025. Download PDF Supplementary Material Data/Code Email Thank you for your interest in spreading the word about medRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following Imputing partial birth dates using day of the week Message Subject (Your Name) has forwarded a page to you from medRxiv Message Body (Your Name) thought you would like to see this page from the medRxiv website. Your Personal Message CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. 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Johnson medRxiv 2025.10.08.25337453; doi: https://doi.org/10.1101/2025.10.08.25337453 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Epidemiology Subject Areas All Articles Addiction Medicine (568) Allergy and Immunology (863) Anesthesia (300) Cardiovascular Medicine (4435) Dentistry and Oral Medicine (444) Dermatology (382) Emergency Medicine (608) Endocrinology (including Diabetes Mellitus and Metabolic Disease) (1509) Epidemiology (15228) Forensic Medicine (30) Gastroenterology (1124) Genetic and Genomic Medicine (6599) Geriatric Medicine (668) Health Economics (997) Health Informatics (4536) Health Policy (1368) Health Systems and Quality Improvement (1613) Hematology (540) HIV/AIDS (1264) Infectious Diseases (except HIV/AIDS) (15916) Intensive Care and Critical Care Medicine (1103) Medical Education (623) Medical Ethics (146) Nephrology (667) Neurology (6599) Nursing (346) Nutrition (998) Obstetrics and Gynecology (1144) Occupational and Environmental Health (957) Oncology (3332) Ophthalmology (974) Orthopedics (369) Otolaryngology (420) Pain Medicine (436) Palliative Medicine (130) Pathology (663) Pediatrics (1693) Pharmacology and Therapeutics (691) Primary Care Research (711) Psychiatry and Clinical Psychology (5447) Public and Global Health (9231) Radiology and Imaging (2198) Rehabilitation Medicine and Physical Therapy (1370) Respiratory Medicine (1196) Rheumatology (593) Sexual and Reproductive Health (712) Sports Medicine (530) Surgery (712) Toxicology (99) Transplantation (289) Urology (265) (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'a006b7019f9f52ad',t:'MTc3OTU2NzE0MA=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();