Competing risk and informative censoring in a nutshell

So when we say competing risks nowadays we actually mean competing risk plus informative censoring. This is about survival analysis.

Survival analysis and censoring

This is something many of us know already, but let us just spend some time speak about it.

Survival analysis is typically done when we want to ask whether a treatment or exposure is associated with a different risk of an outcome in the future, such as whether prescribing tamoxifen (treatment) in high-risk patient can prevent cancer (outcome) in the future.

This can be done in many ways, but when the outcome is something that is irreversible, such as having cancer, one of the neat practices is to calculate the risk in a form of event per person-time, for example 1 event (or 1 cancer) per 1000 person-years in the treatment group, compared to 2 events per 1000 person-years in the control group. Here you have a relative risk of 50%, or treatment is associated with 50% protection of cancer.

In order to calculate this, one has to be careful about the denominator of this calculation (here it refers to the 1000 person-years), and it has to be eligible person-time, or person-time that is eligible to have an outcome. For example, any person-time after the diagnosis of cancer is usually not eligible. Any person-time after death is usually not eligible. Any person-time that is loss to follow up, or yet to follow up, cannot be eligible, either. This is because no event will happen, or will be detected during this time. Some person-time before some starting point tend not to be eligible if we cannot track whether they had cancer before that time point.

So censoring as a jargon basically means picking eligible person-time. Here we say individuals are censored at the time when they have cancer, when they die, or when they are loss to follow up, whichever the earliest.

Competing risk and informative censoring

‘Informative censoring’ is not a great term, either. It means the censoring itself informs us who the person might be. If the censoring is completely random (or ‘natural’), then anyone can be censored, and this is not expected to affect the rates. If the censoring is not random, censoring may affect the representativeness of the remaining individuals, causing the event rate to be open to some biases.

The issue rises most typically with individuals with high death rate. Tamoxifen is generally safe and this is why it is proposed to prevent breast cancer in high-risk patients. But let us imagine there is this new drug Svaloxifen. Svaloxifen may prevent breast cancer, too, but it is very toxic, and deadly toxic to an extent that patients may die shortly. What might happen is most patients die before any cancer can be observed, and artificially cause a reduction in cancer risk in individuals given Svaloxifen.

What happens here is a competing risk between death risk and cancer risk. When one event (death) obstructs the observation of the event of interest (cancer), there is a danger of some bias and incorrect conclusion. Here I say there is danger because in some situations there might not be necessarily a bias.

One main danger comes from the scenario when the obstructing event (death) is also caused by factor related to the main treatment or main exposure. Here, because death is partly caused by the prescription of this deadly drug Svaloxifen, causing different death rate between the treatment and the control group. This causes an unfair chance to observe cancer.

So here death is ‘informative’ because they are more likely to be those who have taken Svaloxifen, the deadly alternative to tamoxifen.

What to do when there is informative censoring

To discuss this further is impossible here. In trials, the best way is to design outcomes that is free of informative censoring, although this is not usually possible. In a cohort study or an observational study, there are statistical techniques to ‘deal with them,’ but we really need to be aware that these are mainly pragmatic approaches. When the death or the competing outcome is caused by the exposure itself, I don’t think there are realistic ways to deal with the counterfactual scenario to compare those who had not died in exposure group and who had not died in the control group, and say had them not died what the risk would have been looked like. I am 99% sure the grammar of the previous sentence is not correct, but I hope you could get it.

What can be more or less dealt with, and I am more comfortable with, is not when the competing event caused by the exposure, but the competing event caused by factors associated with exposure that cause confounding or selection bias. In this case one can try to reconstruct the comparison according to the confounding factor case-mix to get a like-for-like basis. I would be more comfortable with this.

But hey, when the reviewer ask you to do this subhazard ratio or Fine-Gray sub distribution hazards, who has the energy to argue with them? I would say just do it.