Editing Survival analysis (section)

==Censoring==

[[Censoring (statistics)|Censoring]] is a form of missing data problem in which time to event is not observed for reasons such as termination of study before all recruited subjects have shown the event of interest or the subject has left the study prior to experiencing an event. Censoring is common in survival analysis.

If only the lower limit ''l'' for the true event time ''T'' is known such that ''T'' > ''l'', this is called ''right censoring''. Right censoring will occur, for example, for those subjects whose birth date is known but who are still alive when they are [[lost to follow-up]] or when the study ends. We generally encounter right-censored data.

If the event of interest has already happened before the subject is included in the study but it is not known when it occurred, the data is said to be ''left-censored''.<ref>{{cite book |chapter=Censoring, Left and Right |title=International Encyclopedia of the Social Sciences |editor-first=William A. Jr. |editor-last=Darity |edition=2nd |volume=1 |publisher=Macmillan |year=2008 |pages=473–474 |chapter-url=http://ic.galegroup.com/ic/uhic/ReferenceDetailsPage/ReferenceDetailsWindow?disableHighlighting=false&displayGroupName=Reference&currPage=&scanId=&query=&prodId=UHIC&search_within_results=&p=UHIC%3AWHIC&mode=view&catId=&limiter=&display-query=&displayGroups=&contentModules=&action=e&sortBy=&documentId=GALE%7CCX3045300295&windowstate=normal&activityType=&failOverType=&commentary=&source=Bookmark&u=mlin_w_amhercol&jsid=0938fef854cc86b83b5fe8a2c4bcb54b |access-date=6 November 2016 }}</ref> When it can only be said that the event happened between two observations or examinations, this is ''interval censoring''.

Left censoring occurs for example when a permanent tooth has already emerged prior to the start of a dental study that aims to estimate its emergence distribution. In the same study, an emergence time is interval-censored when the permanent tooth is present in the mouth at the current examination but not yet at the previous examination. Interval censoring often occurs in HIV/AIDS studies. Indeed, time to HIV seroconversion can be determined only by a laboratory assessment which is usually initiated after a visit to the physician. Then one can only conclude that HIV seroconversion has happened between two examinations. The same is true for the diagnosis of AIDS, which is based on clinical symptoms and needs to be confirmed by a medical examination.

It may also happen that subjects with a lifetime less than some threshold may not be observed at all: this is called [[Truncation (statistics)|''truncation'']]. Note that truncation is different from left censoring, since for a left censored datum, we know the subject exists, but for a truncated datum, we may be completely unaware of the subject. Truncation is also common. In a so-called ''delayed entry'' study, subjects are not observed at all until they have reached a certain age. For example, people may not be observed until they have reached the age to enter school. Any deceased subjects in the pre-school age group would be unknown. Left-truncated data are common in [[Actuarial science|actuarial work]] for [[life insurance]] and [[pensions]].<ref>{{cite journal |last=Richards |first=S. J. |title=A handbook of parametric survival models for actuarial use |journal=Scandinavian Actuarial Journal |volume=2012 |year=2012 |issue=4 |pages=233–257 |doi=10.1080/03461238.2010.506688 |s2cid=119577304 }}</ref>

Left-censored data can occur when a person's survival time becomes incomplete on the left side of the follow-up period for the person. For example, in an epidemiological example, we may monitor a patient for an infectious disorder starting from the time when he or she is tested positive for the infection. Although we may know the right-hand side of the duration of interest, we may never know the exact time of exposure to the infectious agent.<ref>{{cite journal |last1=Singh |first1=R. |last2=Mukhopadhyay |first2=K. |title=Survival analysis in clinical trials: Basics and must know areas |journal=[[Perspectives in Clinical Research|Perspect Clin Res]] |year=2011 |volume=2 |issue=4 |pages=145–148 |doi=10.4103/2229-3485.86872 |pmid=22145125 |pmc=3227332 |doi-access=free }}</ref>