Time-to-Event Data, Censoring, and Hazard Functions › Disadvantages

The main assumption concerns the censoring mechanism. For the likelihood in this chapter, event and censoring times are independent conditional on the covariates used in the analysis, and the censoring law has parameters distinct from the event-time parameters. If unobserved prognosis affects both times, the ordinary likelihood need not estimate the target event-time distribution correctly. Conditional independent censoring resembles a missing-at-random assumption, but it is a statement about the observation process for event times and must be justified for the study.

Interpreting survival output requires choosing the right scale. The coefficient in a Cox model is a log hazard ratio, not a change in expected duration. The same coefficient can be interpreted as a change in the log of the ratio of hazards, and translating that into "how many more months do patients live" requires additional work. If you are used to linear models, you may approach survival output cautiously.

Censoring also reduces information relative to observing the same subjects' complete event times. Precision depends on the number and timing of events, follow-up, risk-set sizes, and model assumptions, rather than on a censoring-percentage threshold alone. A sample with ninety percent censoring may still contain many observed events if the study is large; a small study with fewer censored records can remain imprecise.

Finally, the framework cannot compensate for poor study design. If the observation window is misaligned, if event times are rounded so aggressively that dates become unreliable, or if the time origin is chosen differently across subgroups, estimates can acquire bias or artificial patterns. Fitting a survival model does not automatically repair those data-construction errors. The mathematics assumes we have correctly identified the time origin, the event, the censoring mechanism, and the covariates that matter.

Consider treating every observed duration $Y_i=\min(T_i,C_i)$ as an event time. Since $Y_i\le T_i$, the observed-duration mean cannot exceed the latent event-time mean when those means exist. The inequality is strict if censoring shortens durations with positive probability. An intercept-only least-squares fit to $Y$ therefore estimates $\mathbb{E}[Y]$, not $\mathbb{E}[T]$. For the exponential example below, counting censorings as events also inflates the fitted rate. These facts do not imply that every misspecified distribution or every regression coefficient has the same bias direction.

Dropping censored records selects subjects with $T\le C$. Under independent censoring, the event-time density among observed events is proportional to $f_T(t)\Pr(C\ge t)$, so longer event times receive no more selection weight than shorter ones. This can pull complete-case averages downward; strictness requires a nontrivial change in that weight over event times. It does not mean every censored subject lived longer than every observed event. With covariates, the selection can differ across groups, so coefficient bias needs a separate analysis. Ordinary Least Squares (OLS) residual diagnostics alone do not restore the lost observation mechanism.

If covariates affect both event and censoring times, unconditional independence may fail even when conditional independence holds. For example, groups with different prognoses may also have different follow-up schedules. Conditioning on the relevant measured covariates can make an independent-censoring analysis defensible. Dependence that remains after conditioning needs additional assumptions, models, or sensitivity analysis; the ordinary survival likelihood cannot automatically repair it.