Japanese Journal of Clinical Oncology

Disease-free survival time (DFS) is defined as the time between the complete remission and the onset of relapse. Although the date of complete remission can be specified by the date of operation, the diagnosis of relapse has to be established by various medical examinations and the onset of relapse could not be confirmed before a certain delay time has passed after the true onset. Interval censoring occurs if the variable of interest cannot be observed exactly, but an interval can be specified in which the observation lies (1). The concept of interval-censored analysis arose in the context of many experimental designs using survival analysis (2,3). When patients in a clinical trial are in outpatients and are therefore not monitored continuously by a physician, DFS will not reflect the accurate time of recurrence and we believe that it will surely meet the definition of interval-censored data.

In a previous randomized clinical trial against curatively resected gastric cancer, we compared the effect of immunochemotherapy with that of chemotherapy and obtained significantly better survival (p = 0.044) and DFS (p = 0.047) in a combined therapy group (4). Although DFS was analysed with a conventional approach in which the onset of relapse was defined as the diagnosis of relapse, we think it necessary to re-analyse the data and compare the results of an interval-censored approach to the conventional approach, in order to examine whether the conclusion might be altered depending on the approach.

The maximum DFS rate estimated from the date of diagnosis of relapse and the minimum DFS rate estimated from the date of the last negative examination were calculated. The maximum DFS rates from 1 to 5 years were 84.0, 75.4, 69.7, 67.5 and 65.0%, whereas the minimum DFS rates were 82.8, 75.1, 69.7, 67.5 and 65.0%, respectively. The biggest difference between the maximum and minimum DFS rates was only 1.2% at 1 and 4 years, suggesting that a delay in diagnosis of relapse was not critical to the estimation of DFS. The comparison of DFS was performed with the interval-censored approach and the conventional approach based on the Weibull regression model, using the LIFEREG procedure of SAS. Although the estimated regression coefficient and standard error in each comparison were always slightly higher in the interval-censored analysis than in the conventional analysis, no substantial difference in terms of p values was detected (Table 1).

To avoid discrepancies between conventional and interval-censored analysis and to obtain more plausible conclusions with regard to DFS, we believe that two important points should be considered in the study design. First, the schedule for the outpatient visits and examinations has to be as similar as possible in both treatment arms. If the interval of outpatient visits in one arm were shorter than the interval in the other, detection of relapse could be faster in the former group but delayed in the latter. This kind of uneven follow-up schedule can sometimes be seen in a clinical trial in which one of the arms is assigned to a simple observation group after the initial treatment and may cause a large bias in the comparison of DFS. Second, the follow-up schedule in a clinical trial should be planned taking the risk of recurrence into consideration.

Table 1 . Analysis of DFS data using the conventional approach and the interval-censored approach

Group	Conventional analysis			Interval-censored analysis
	Regression coefficient	Standard error	p	Regression coefficient	Standard error	p
PSK vs control	-0.665	0.255	0.009	-0.703	0.268	0.009
Stage I vs II	-1.735	0.730	0.018	-1.826	0.768	0.018
Stage I vs IIIa	-2.371	0.721	0.001	-2.496	0.759	0.001
Stage I vs IIIb	-3.772	0.747	0.001	-3.961	0.786	0.001
Stage I vs IV	-4.817	0.808	0.001	-5.070	0.851	0.001
Histology: intestinal vs diffuse	-0.243	0.259	0.348	-0.255	0.272	0.349
Estimate of scale parameter	1.128	0.104	1.187	0.110

The hazard rate for recurrence in gastric cancers is high within a year but decreases steeply thereafter and remains low 18 months after the operation. We believe that the intervals of outpatient visits and follow-up examinations should be planned according to the hazard curve which is specific to each type of cancer. Therefore, intervals have to be shorter when the risk of recurrence is high (i.e. 1 year in our gastric cancer trial), but it could be set longer when the risk is lower. Minimal differences between DFS results of conventional and interval-censored analyses in our present study might have been achieved by the accumulation of knowledge with regard to the natural history of gastric cancer.

We believe that this kind of re-analysis by the interval-censored approach is particularly important for reconfirmation of DFS results in a randomized clinical trial. Prompt establishment of a relevant and appropriate method is essential. Further examples must be studied and probably a sophisticated simulation study would help in finding the best examination schedule for a given disease.