Background
Length-time bias is sometimes referred to as “length bias”, “length-time effect”, “length-biased sampling”, or “length-weighted sampling”. It refers to the fact that the chance of detection depends on the rate of progression of disease.
The bias occurs when comparing survival time between individuals detected by a diagnostic screen and those diagnosed symptomatically. Survival times will appear longer in people detected by screening because screening is more likely to identify slower-progressing disease.
Length-time bias is therefore a preferential selection of people whose disease progresses slowly, even without any intervention. Hence, comparisons of survival time between screen-detected and symptomatically detected individuals are biased in favour of screening.
Most diseases and medical conditions progress at different rates. For some people, the disease will progress rapidly to the end-stage, whilst in others the disease can take years to reach the same stage; in some cases the progression is so slow that they never reach the end-stage and die from another cause. Screening tends to find the slow-progressing forms of disease and miss the rapidly progressing forms (see Figure).
For example, prostate cancer can progress rapidly in some men but take many years in others, and many men die with prostate cancer rather than from it. Although this effect is well recognised in cancer screening, length-time bias will occur whenever there is variation in disease progression. Abdominal aortic aneurysms (AAA) also grow at different rates; screening is more likely to detect slowly growing aneurysms that remain within the screening window and miss aneurysms that enlarge rapidly.
It is therefore important to adjust or account for length-time bias when making comparisons between individuals who have their disease detected by screening and those not detected by screening.
Figure: Length-time bias in disease screening. Horizontal bars represent the asymptomatic disease phase: left end is onset, right is symptom appearance. Long bars signify slow-progressing diseases; short bars, fast-progressing. A dashed line marks a single screening event. Blue bars are screen-detected cases; orange bars are missed. Due to longer asymptomatic durations, slow-growing diseases (long blue bars) are disproportionately detected by screening, demonstrating length time bias.
Example
Barrett’s oesophagus (BO), a precursor to oesophageal adenocarcinoma (OAC) is mainly detected following investigations for stomach pain. Surveillance for this condition then provides an opportunity to diagnose OAC in an earlier stage. Patients with OAC and a prior Barrett’s oesophagus diagnosis are known to survive for longer than OAC patients without a diagnosis of Barrett’s oesophagus. As these patients undergo screening for OAC, comparisons of survival time are likely to be biased by both length (and lead) time bias.
Impact
Bhat et al sought to determine the survival advantage of OAC patients with a prior Barrett’s diagnosis after accounting for length time bias. A greater proportion of OAC patients with a prior diagnosis of BO had low-grade or intermediate-grade tumours compared with OAC patients without a previous BO diagnosis (46.2% vs 26.5%; p=0.011). In their study, although correcting for lead time impacted the hazard ratio, further adjustment for length bias did not.
Preventive steps
In randomised screening studies, an intention to screen analysis where all participants randomised to the invitation to screening are included is not susceptible to length time bias. The problem arises whenever, only the screen detected cases are included. In some cases, it may be possible to construct an intention-to-screen using retrospective data. For example, Cucchetti et al suggested that in their example of surveillance for hepatocellular carcinoma, that lead time bias can be viewed as a selection bias occurring when patients diagnosed with tumor at screening appointments are analyzed separately from those who had cancer detected because of symptoms and regardless of surveillance. The inclusion of those diagnosed symptomatically and those diagnosed through screening can minimise lead time bias.
Finally, it may be possible to correct for length time bias in studies when only the screen detected cases have been analyzed. Duffy et al showed that a correction was possible if the relative rate of screen detection and fatality in the length-bias group, and group’s size was known. Although these may not always be available, a range of corrected results can be calculated based on a set of plausible values. The correction is simple in principle but makes strong assumptions.
