When People Don't Stay in Line — The Ones Who Switched, and the Ones Who Left for Another Reason

The story begins with a lung cancer clinical trial. One group received a new targeted therapy, and the other group received conventional chemotherapy. This trial had a provision promised from the very beginning. If the disease of a patient receiving the conventional treatment worsened again, that person was also allowed to switch to the new drug.

It is a natural courtesy. When there is a better option right before the eyes of a person whose disease has worsened, you cannot say, "You are in the control group, so stay as you are."

However, this courtesy shakes the calculations. Later, when comparing the two groups, the "conventional treatment group" is a mixture of people who received only the conventional treatment until the end and people who switched to the new drug midway. Therefore, the difference between the two groups looks that much narrower.

That was actually the case. This trial also measured effectiveness as a "survival benefit reflecting even quality of life." It is a value measured by discounting the living period by the health state during that time. When measured strictly as assigned, this benefit was 0.23 years at the 60-week time point. When adjusted by including the people who switched in the calculation, the same value became 0.52 years. That is more than double. In an analysis looking longer, it went up to 0.63 years (PMID 35379563).

The same trial, the same patients, the same data. The only thing that changed is one counting method.

I will disclose in advance. The names of the treatments appearing in this article appear solely as examples to show the counting methods. What is asked here is how the counting method changes the answer, and whether that treatment is good is not covered. Each number has meaning only within the design, subjects, and time points of that study, and the clinical conclusions belong to those authors.

Before We Begin — Three Borrowed Terms, Six New Terms

This article borrows three terms covered in "What Is a Hazard Ratio of 0.7 the 0.7 Of? — How to Read a Survival Curve". They are reviewed just once here.

A survival curve is a graph showing what percentage of people who have not yet experienced the event remain as time goes on. It goes down a step each time an event occurs, making a staircase shape. Here, the event is an outcome predefined by the study, such as death or recurrence.

Censoring is the handling of people who had no event up to the end of observation and whose status afterward is unknown, recording them simply as "safe up to this point." This happens because the study ends, or because contact is lost.

A hazard ratio is the value obtained by dividing the rate at which events occur between two groups. It measures how quickly events happen at any given moment among people who have not yet experienced the event in each group, and divides the two.

The new terms to learn in this article are six, and each is explained where it first appears. Other necessary terms are also explained in a single phrase where they appear.

Why You Need to Know — People Refuse to Stay Put

A survival curve is a quiet picture. The people in this picture stand in a single line, receive the assigned treatment just as prescribed, and wait only for that event. Real people do not stay put like that. Before a study ends, people leave this line in two ways.

First, they switch treatments. If the disease worsens, both doctor and patient look for other options. If the study protocol allows, they cross over to the opposing drug.

Second, they leave for other reasons. While waiting to count a recurrence, that person passes away from a different illness. Then that person can never experience a recurrence.

In both cases, the steps still go down and the picture looks fine, but what those steps mean changes. This article covers which way and how much the numbers move in these two situations, and therefore what we are looking at instead.

Treatment Switching — When the Control Group Switches to the Experimental Drug

What Is It

Treatment switching is when participants stop the treatment they were first assigned to during a study and move over to the other treatment. In a clinical trial, the new drug being tested is called the investigational drug, and the group receiving standard care for comparison is called the control group. The problem arises when patients in the control group cross over to the investigational drug.

Imagine we divided 100 customers each to compare the satisfaction of two restaurants. But half of the customers from Restaurant B walked out midway and moved over to Restaurant A. Now, "the average satisfaction of the 100 people who went to Restaurant B" is contaminated by the food eaten at Restaurant A. That number can no longer be read as the satisfaction of Restaurant B alone.

How to count these mixed-up groups is the next problem. Intention-to-treat analysis is a method of counting participants in the group they were first assigned to, no matter what they actually received. Clinical trials usually decide who goes into which group by a draw, and this is called randomization. Because intention-to-treat analysis preserves the balance of the two groups obtained by this draw, it is the default for clinical trials. But when switching is frequent, the question this default answers changes. The numbers counted by intention-to-treat get closer to "how good is the policy of using this drug first" rather than "how good is this drug itself."

Why Not Prevent Switching?

Switching is not prevented because it must not be prevented. Allowing the control group to switch in cancer treatment trials is often an ethically necessary thing, and a methodological paper addressing this issue writes that in its very first sentence (PMID 41026983). If you block a treatment that can be used for patients whose disease has progressed, you put the convenience of the design ahead of human welfare. Therefore, only one problem remains: how to count it after it has happened.

Which Way Does It Move?

When control patients receive a share of the experimental drug, the control group's performance goes up. Then the difference between the two groups shrinks. The lung cancer trial from earlier was precisely such a case. The authors concluded that if switching is not accounted for, the new drug's benefit is underestimated (PMID 35379563).

Even so, we cannot simply dismiss an as-treated analysis as a "safe, conservative value because it captures less benefit" and move on. There is a trap on the side of adjusting as well, and that trap occurs in the opposite direction—namely, toward inflating the benefit.

How They Adjust — And What They Pay in Return

Adjustment methods fall broadly into three paths. Each has a formal name, but here we call them by what they do.

• The reverse-calculation method works backward to estimate how long people would have lived if they had not switched. It views the time gained after switching as "time extended by the drug effect" and rewinds the clock by that amount.
• The weighting method removes switchers at that point and gives more weight to the people who remain. It makes people who had similar situations and did not switch represent the share of the switchers.
• The two-stage counting method uses the point when the disease progressed as a baseline. It calculates the time after progression separately.

All three methods stand on assumptions that cannot be verified with the data. The weighting method assumes that "we measured all the factors that determined whether to switch." The reverse-calculation method assumes that "the magnitude of the drug effect is the same for everyone, whenever it is used." The conclusion of a guideline paper that lists these assumptions side by side is this: adjustment methods often yield biased values in realistic situations, in some situations both methods are biased together, and sometimes the by-protocol analysis may be the least biased of all (PMID 24449433). Here, biased means that the calculated value deviates to one side from the true value.

Simulations pitting adjustment methods against each other reveal a few more things. A simulation is an experiment where virtual trials with pre-determined true values are run on a computer multiple times to see how closely each method hits that true value.

First, what most greatly influences bias is what percentage switched, namely the switching proportion. In simulations running through various sample sizes, switching proportions, and disease severities, all three methods consistently showed less bias than the by-protocol analysis. Sample size or the censoring proportion mattered less than the switching proportion (PMID 27114326).

Second, when the switching proportion is very high, the adjustments also break down. Once the switching proportion exceeded 85%, two methods, including the weighting method, showed substantial bias. When the drug effect changed over time, the reverse-calculation method also showed bias to a degree similar to the weighting method. However, in the same paper, a simplified two-stage method showed low bias across all virtual scenarios (PMID 25416688).

Third, problems arise if there is a time lag between when the disease progressed and when the switch actually happened. The patient's condition keeps changing during that interval as well. Ignoring this change and simply splitting it into two stages introduces considerable bias (PMID 32223524).

Fourth, there are forks in the road even within adjustments, and the two sides of a fork pull in opposite directions. The reverse-calculation family has an extra choice of where to cut the adjusted data again. Choosing one side biased the treatment effect toward an overestimation, while choosing the other biased it toward an underestimation. Therefore, the authors recommend trying both and reporting both. Doing so leaves behind information about roughly where the true value lies (PMID 29940824).

Recently, methods have also been proposed that pull in real-world clinical data from outside the trial to reinforce the "non-switched group." This method comes with additional assumptions. There is a condition that trial participants and outside patients must be similar enough that they could be swapped for one another. In the authors' simulations, when this condition was actually met, there was less bias and the values fluctuated less than with existing methods (PMID 41026983).

So What Should the Reader Look For?

When reading a trial that allowed switching, there are two things to check. What percentage switched, and what adjustments were made. If these two are not in the main text, you cannot judge the drug's effect with a hazard ratio alone.

Competing Risks — When Someone Leaves for Another Reason Before the Event You Want to Count Arrives

What It Is

There is a major treatment for blood cancer patients that infuses cells that make healthy blood. It is called hematopoietic stem cell transplantation. Let us say we track people who received this treatment and count relapses. However, after the transplant, there is another path by which people are lost besides relapse: death due to complications from the transplant itself.

A person who has passed away due to transplant-related mortality can never relapse afterward. Another event that permanently blocks an event of interest from being able to occur like this is called a competing risk.

Death in a study counting relapses, death in a study counting reoperations, and death in a study counting dementia all share the same structure.

Why Using a Survival Curve As-Is Explicates Relapse

If you count relapses using a survival curve, people who died without relapse are treated as censored. However, the calculation of a survival curve assumes that the censored person could have experienced the event later. Therefore, it distributes the share of the person who dropped out among the remaining people.

This is a correct treatment for someone who dropped out because the follow-up period ended. That is because that person could have relapsed later. It is an incorrect treatment for someone who dropped out due to death. Even though that person is someone who will never relapse, the calculation adds that person's share to the relapse side. As a result, the cumulative probability of relapse, in other words the probability of having experienced relapse up to that point, is inflated compared to reality.

This inflation grows larger as time goes on. When actually calculated using hematopoietic stem cell transplantation data, the cumulative probability of relapse obtained by the traditional survival curve method was increasingly inflated over time. The conclusion of the authors who summarized this issue for surgical researchers is clear: when there are two competing events, do not predict cumulative risk using the survival curve method (PMID 18269491).

The bias does not stop at the curve. The test to determine whether the difference between two curves is due to chance, and even the standard model that incorporates multiple factors together, are biased in parallel. This is the result demonstrated by comparing them one by one with hypothetical numerical examples and actual data (PMID 17255278). This problem was already raised back in 1993 (PMID 8516591).

What to Look at Instead — Cumulative Incidence

Cumulative incidence is the value representing what percentage of the total, from the starting point until now, have actually experienced that event of interest.

The core is "actually." It does not revive someone who left first for another reason. It neither removes that person from the denominator nor places them on the recurrence side, but leaves them as "recurrence did not occur in this person." Therefore, even if you add up the cumulative incidences of multiple events like recurrence and death, they do not exceed 1. Values read as 'the proportion of the side that experienced the event' by flipping the survival curve upside down are not like that.

How Much Can It Change — Examples Where Conclusions Flip Both Ways

Data on metal stents inserted into patients with blocked bile ducts is a good example. In 476 patients, the event of interest was stent blockage. The competing risk was the patient dying before the stent blocked.

When calculated using the conventional method, the difference in stent blockage between men and women was statistically significant. Statistically significant means the difference was clear enough that it was hard to attribute to chance. However, once competing risks were accounted for, that significance disappeared.

Results in the opposite direction also appeared in the same data. With the conventional method, stent blockage looked similar between the group that received chemotherapy and the group that did not. Once competing risks were accounted for, stent blockage appeared significantly lower in the group that did not receive chemotherapy (PMID 23650933).

If you ignore competing risks, differences that were not there can appear, and differences that were there can vanish. This means the direction of the error is not fixed to one side.

Two Questions, Two Answers

When competing risks exist, the questions you can ask split into two, and the two questions yield different answers.

① "Does this factor change the speed at which recurrence itself occurs?" ② "Does this factor change the number of people who eventually experience recurrence?"

The reason the two answers diverge is as follows. Suppose a factor significantly increases competing death without touching the speed of recurrence at all. Then the number of people who will experience recurrence decreases by that much. The answer to the first question is "no effect," and the answer to the second question is "reduces recurrence." Both are correct.

This split has been confirmed in both virtual data and real data. In simulations, even a factor with no direct effect on the speed of the primary event could be significantly associated with the cumulative probability of the primary event if it affected the competing event. In prostate cancer clinical trial data, the effects of age and tumor grade varied depending on which question was chosen (PMID 22282466).

Therefore, recommendations have emerged to report the answers to both questions. The argument is that to fully understand how events move, speed and cumulative counts must be placed side by side, and that this is the most rigorous approach (PMID 23415868). The design stage is the same. The sample size required varies considerably depending on which question is taken as the primary yardstick (PMID 26711503).

Where Answers Flip in Real Data — Sleep and Dementia

The relationship between sleep difficulties and dementia risk has yielded contradictory results for a long time. This is because there were studies in which people who slept poorly actually appeared less likely to develop dementia.

This issue was re-examined using data from 457,367 participants in the UK Biobank in the UK. The hypothesis was this: if people with sleep difficulties die before being diagnosed with dementia, their dementia risk could be masked. Therefore, the researchers handled dementia incidence and death together within a single calculation.

In the calculation handling them together, habitual sleep difficulties slightly increased the risk of vascular dementia (hazard ratio 1.14, 95% confidence interval 1.02–1.28). A confidence interval is the range where the true value is likely to lie. The authors noted that the risk of all-cause dementia was also slightly increased. However, the hazard ratio for all-cause dementia was 1.03 (95% confidence interval 0.98–1.08), and because this range includes 1, which means "the speed is the same," it is not statistically significant.

On the other hand, in calculations using the traditional method that did not handle death separately, sleep difficulties appeared to protect against all-cause dementia instead. Previous studies using the same UK Biobank data pointed in the same direction. The authors wrote that this discrepancy shows how risk estimates can be distorted by people dying first (PMID 40833209).

The authors' own conclusion is this: handling death together reveals the direct dementia risk of sleep difficulties, and sleep management after middle age can be a modifiable target in dementia prevention. However, what was statistically significant in this study was vascular dementia, while all-cause dementia was not. These two facts must be read side by side. What this article aims to take away from this case is a lesson about counting methods rather than a clinical conclusion. Even the exact same data gives the impression of completely opposite directions depending on how it is counted.

When competing events exist, the phrase "the effect of that treatment" can point to several things. That is why a recent review paper pointed out that we must first decide what we are trying to estimate (PMID 42091486). Which of those to choose is determined by the clinical question, not statistics.

So What Do We Look At — Restricted Mean Survival Time

The previous two sections looked at where numbers wobble. This section covers one metric that can be looked at together then.

What Is It

Restricted mean survival time is the value representing the average number of months people spent without the event within a pre-determined period.

Let us suppose we decided to look at 3 years. For people who died within 3 years, we count only as much as they lived; for those who exceeded 3 years, we count up to 3 years. And we take the average of all. In pictures, this is the area under the survival curve cut off up to a designated time point.

Therefore, the answer comes out in a unit of time, "how many months." Hazard ratios only give out ratios, so they cannot give this kind of answer.

Why It Is Needed — The Same Effect Sounds Different

When the same trial is measured with two indicators, the size of the effect sounds quite different. There is a result confirming this using 54 randomized cancer trials (33,212 patients) published in five major journals in the latter half of 2014. This is the result of recovering individual patient data from the published survival curves and calculating the two indicators side by side.

• The median (middle value) of the hazard ratios was 0.84.
• In the same trials, the median difference in restricted mean survival time was 1.12 months.
• The hazard ratio pointed to a larger effect on average than the ratio of restricted mean survival times (mean ratio 1.11, 95% confidence interval 1.07–1.15). However, the authors also noted that the variation across trials was large.

In the authors' own words, it is as follows. When the absolute effect is small, the hazard ratio can look large (PMID 26884584). This means an effect that sounds big when heard as a ratio might translate to just over a month when converted into time.

It was rare for the two indicators to disagree on the presence or absence of an effect. In these 54 trials, the significance judgments of the two indicators matched all except for one case. What the restricted mean survival time primarily changes is not the answer to "Is there an effect?", but the way the answer to "How much?" sounds.

A concrete example is biliary tract cancer. This is a combined analysis of two phase 3 trials—meaning the final-stage trials to confirm effectiveness with a large number of patients ahead of commercial approval—adding immunotherapy to existing chemotherapy. The participants in both trials totaled 1,754 people, and calculations were based on up to 24 months. In the first trial, average survival within 24 months was 13.52 months for the group with added immunotherapy and 12.21 months for the group with conventional treatment alone. In the second trial, it was 13.60 months versus 12.45 months. The combined difference of the two trials was 1.21 months (95% confidence interval 0.49–1.93) (PMID 38893196).

The authors' conclusion is that immunotherapy improved survival in both trials, and that conclusion remains the same. What has changed is the way the magnitude of that benefit hits the ear. The authors conclude that with an effect of this size, individual patients' circumstances, preferences, and side effect risks must be weighed together.

An Index That Still Works Even with Competing Risks

Restricted mean survival time remains valid even when the assumptions that hazard ratios rely on are broken. That assumption is that the speed of events at any given moment maintains a constant ratio between the two groups over time. This index also accommodates situations with competing risks and calculations that adjust for other variables (PMID 41887163). This means the index can be used on data with the competing risk problem we saw in the previous section.

The argument to place this index alongside the hazard ratio is long-standing. There are points that because hazard ratios are frequently misread, a complementary index with fewer assumptions and easier reading is needed (PMID 31031048), and proposals even exist to use this index as the primary yardstick starting from the trial design stage (PMID 24314264).

⚠️ It Is Not a Silver Bullet — Humans Must Decide How Far to Look

Restricted mean survival time comes with a handle that the hazard ratio does not have. The truncation time is the point set in advance to decide how far to look when calculating the restricted mean survival time. Whether to cut at 3 years or 5 years is this choice.

The problem is that turning this handle makes the answer move along. Practical guidelines for designing trials with this metric state this point most clearly. "The biggest challenge of this metric is the choice of the truncation time." The same paper also shows that this single choice heavily dictates the trial's ability to catch a difference. This means that even in the same trial, depending on where the truncation time is placed, a difference can be caught or missed. The paper's recommendation is to "choose a clinically meaningful time point." This recommendation is less of an answer and more of a statement passing the decision back to humans (PMID 32063031).

Furthermore, the truncation time cannot be chosen arbitrarily. If one of the curves for the two groups ends first, current standard methods require setting the truncation time at or before the end of the shorter curve. In cases like immunotherapy where the benefit appears at the tail of the curve—that is, a long time later—it becomes impossible to look at the exact spot one wants to see. Attempts to lift this restriction do exist. However, those authors themselves state that their method is only a supplementary result and cannot be the primary analysis (PMID 36596962).

In situations where effects appear late, there is one more thing to decide. Not only the end point, but even the point to start the calculation must be decided. Methods that do not require pre-specifying the start point have been proposed, and doing so lost almost nothing (PMID 36653933). There is also an approach that, instead of picking a single truncation time, presents how the results change wholesale depending on the truncation time (PMID 33616953).

And — Do They Really Communicate Better to People?

One big reason for recommending this metric is that "patients find it easy to understand." There are two randomized comparisons that directly tested this reason, and the results are cautious.

The first study divided 200 adults aged 65 and older with hypertension into two groups by a draw. To one side, the benefits and harms of treatment were explained using this metric, and to the other side, in the traditional way. Then, the decision conflict scores were measured. This score is a value measuring how hesitant one is about a decision, where lower means less hesitation. The result was no difference at 25.2 points versus 25.6 points, and there was no difference in treatment preference either. The authors did not read this result as a failure, but as a proof of concept, soon the first evidence that the new method can actually be used. This means the metric is at least as effective as the existing method, and the two can be used together (PMID 33901300). Therefore, what has been confirmed is not "it communicates better," but up to "it is not worse."

A follow-up study targeting 102 residents of senior living facilities was slightly better. The average conflict score was 22.0 points for the traditional method group and 16.7 points for this metric group, but the difference fell short of significance. The proportion of people classified as having low conflict showed a difference: 49.1% for the traditional method group and 69.4% for this metric group. However, the authors state that the sample was small, lacking the power to catch the difference. And they concluded that because people's preferences vary so widely, it would be better to show both methods together (PMID 36318788).

So, the definite strength of this metric lies on the side of its statistical properties. It has few assumptions and gives the absolute magnitude of the effect.

Common Misconceptions

① "Can't we just block switching?" This is a problem that must not be blocked. If you block treatments that can be used for patients whose disease has progressed, you are putting the convenience of the study design ahead of the people. This is why a methodological paper addressing this issue describes allowing switching as "often ethically necessary" practice (PMID 41026983).

② "Switching adjustment is manipulation to make results look good." Adjusting usually increases the benefit, but that direction is not determined automatically. Just changing one detail in the adjustment method split the results toward overestimation and underestimation, which is why the recommendation was to "report both" (PMID 29940824). It has also been pointed out that in some situations, the unadjusted intention-to-treat analysis is the least biased (PMID 24449433).

③ "Competing risks only need to be worried about in studies of older adults." This has nothing to do with age. Whenever there is an event that makes the event of interest impossible before it happens—such as relapse after a transplant, a blocked stent, or reoperation—the same structure arises anywhere.

④ "Flipped survival curves are the cumulative incidence." This is only true when there is a single type of event. When there are competing events, the value obtained by flipping the survival curve becomes larger than the cumulative incidence. In hematopoietic stem cell transplant data, that gap widened as time went on (PMID 18269491).

⑤ "Then should we just ditch the hazard ratio?" There is no need to ditch it. In a reanalysis of 54 papers, the two metrics gave almost always the same answer in significance testing (PMID 26884584). What changes is the way the effect size is communicated, and the recommendation is to report both metrics together (PMID 23415868, PMID 36318788).

⑥ "Setting the restriction time to the end of follow-up is fair." The tail of the curve is unstable because few people remain, and by design, the restriction time is tied to the shorter of the two curves (PMID 36596962). Therefore, the restriction time is a judgment that must be stated in advance before calculation.

Honest Unsolved Questions

① There is no rule for setting the cutoff time. All that exists is the principle to "choose a clinically meaningful time point," and that principle hands the decision back to humans (PMID 32063031). If you choose the cutoff time after looking at the results, it is indistinguishable from picking the answer you want.

② There is no consensus on which switching adjustment method to use. Which method is better depended on conditions such as the switching rate, whether the drug effect changes over time, and the time lag between progression and switching. In some situations, the two main methods were biased together (PMID 24449433). However, methods that hold up well even under such conditions have each been reported (PMID 25416688, PMID 32223524).

③ What a "treatment effect" points to when competing risks are present is still being sorted out. The risk in a world where competing events are eliminated, the risk in a world where they are not, and various definitions in between have been proposed side by side (PMID 42091486). The clinical question determines which one to choose.

④ Evidence on whether absolute metrics actually communicate better is thin. One of the two previous randomized comparisons showed no difference (the authors read this as a proof of concept that it is "as effective as the traditional method"). The other had too small a sample to draw a conclusion (PMID 33901300, PMID 36318788).

⑤ Whether long conclusions can be replaced by short-term values is also not yet known. When 26 immunotherapy trials (12,892 people) are gathered, the ratio of restricted mean survival time calculated up to 12 months moved together with the hazard ratio of final death. The value representing the degree to which they moved together was 0.64 (95% confidence interval 0.42–0.78). The value calculated using the period lived without the disease worsening did not move together with the hazard ratio of final death (PMID 31050784). The authors view this value as a candidate surrogate endpoint to be studied further in the future.

To Go Deeper

This article purposely avoided calling the three ways of adjusting for switching and the two types of models handling competing risks by their formal names. Those names are included in the English titles of the reference paper list below, so just browsing the list will get you search terms.

When reading a paper, checking three things leads to writing most of this article.

1. Was switching allowed in this trial, and if so, what percentage crossed over and what adjustment was used?
2. Are there competing events for this outcome measure, and if so, are they using inverted survival curve values or cumulative incidence?
3. Is the effect size presented only as a ratio, or are absolute values like "several months" included as well? If so, where is the time horizon for that value set?

Source Papers

English titles have been shortened. Original titles can be verified via PMID.

Treatment Switching

• PMID 35379563 — "…EQ-5D Adjusting for Treatment Switching" (2022). AURA3. 0.23 years → 0.52 years (150 weeks 0.63 years).
• PMID 24449433 — "Adjusting survival time estimates…switching" (2014). Sometimes unadjusted is least biased.
• PMID 27114326 — "Assessing methods for…switching" (2018).
• PMID 25416688 — "Adjusting for treatment switching in RCTs…" (2017). Simplified two-stage has low bias across all scenarios.
• PMID 32223524 — "Improved two-stage estimation…switching" (2020).
• PMID 29940824 — "Causal inference for long-term survival…switching" (2019). Direction of bias reverses depending on recensoring.
• PMID 41026983 — "Augmented two-stage estimation…switching" (2025).

Competing Risks

• PMID 18269491 — "…pitfalls of Kaplan-Meier plots" (2008). Overestimation of cumulative recurrence probability.
• PMID 17255278 — "Cumulative incidence in competing risks data…" (2007).
• PMID 8516591 — "Kaplan-Meier, marginal or conditional probability curves…?" (1993).
• PMID 23650933 — "…cumulative incidences of biliary stent dysfunction…" (2014). 476 patients. Men and women p 0.044→0.115, chemotherapy comparison p 0.647→0.031.
• PMID 22282466 — "The use and interpretation of competing risks regression models" (2012).
• PMID 23415868 — "A competing risks analysis should report…all hazards and CIFs" (2013).
• PMID 26711503 — "Estimating sample size…competing risks" (2018).
• PMID 40833209 — "Re-evaluating sleep difficulty…dementia…" (2025). 457,367 people. Vascular 1.14 (1.02–1.28), overall 1.03 (0.98–1.08, not significant). Authors' conclusion = sleep management is a preventive target.
• PMID 42091486 — "Beyond the Hazard Ratio…" (2026).

Restricted Mean Survival Time

• PMID 26884584 — "Comparison of Treatment Effects…Hazard Ratio and…RMST" (2016). 54 papers and 33,212 participants. Median 0.84 versus 1.12 months, mean ratio 1.11 (1.07–1.15), heterogeneity I²=86%. Significance agreed except in one case.
• PMID 38893196 — "Evaluation of Overall Survival by RMST…Biliary Tract Cancer" (2024). 2 papers and 1,754 participants.
• PMID 41887163 — "A Primer on RMST in Surgical Research" (2026).
• PMID 31031048 — "…RMST to Improve Communication of Evidence" (2019).
• PMID 24314264 — "RMST: an alternative to the hazard ratio…" (2013).
• PMID 32063031 — "Designing clinical trials with…RMST endpoint" (2020). "The biggest challenge is choosing the restriction time."
• PMID 36596962 — "Sensitivity Analysis for RMST…Divergent Tails" (2023).
• PMID 36653933 — "On assessing…immunotherapy using long-term RMST" (2023).
• PMID 33616953 — "RMST as a function of restriction time" (2022).
• PMID 33901300 — "RMST versus conventional measures…" (2021). 25.2 versus 25.6, p = 0.84. Authors' interpretation = proof of concept (combinable).
• PMID 36318788 — "RMST versus conventional effect summary…" (2023). 102 participants. 22.0 versus 16.7 (p = 0.06), 49.1% versus 69.4% (p = 0.04).
• PMID 31050784 — "Correlation of Milestone RMST Ratio With OS Hazard Ratio" (2019). 26 papers and 12,892 participants.