Background

Validation of the use of the lognormal model for predicting long-term survival rates using short-term follow-up data.

Methods

907 cases of laryngeal cancer were treated from 1973–1977 by radiation and surgery (248), radiation alone (345), and surgery alone (314), in registries of Connecticut and Metropolitan Detroit of the SEER database, with known survival status up to 1999. Phase 1 of this study used the minimum chi-square test to assess the goodness of fit of the survival times of those who died with disease to a lognormal distribution. Phase 2 used the maximum likelihood method to estimate long-term survival rates using short-term follow-up data. In order to validate the lognormal model, the estimated long-term cancer-specific survival rates (CSSR) were compared with the values calculated by the Kaplan-Meier (KM) method using long-term data.

Results

The 25-year CSSR were predicted to be 72%, 68% and 65% for treatments by radiation and surgery, by radiation alone, and by surgery alone respectively, using short-term follow-up data by the lognormal model. Corresponding results calculated by the KM method were: 72+/-3%, 68+/-3% and 66+/-4% respectively.

Conclusions

The lognormal model was validated for the prediction of the long-term survival rates of laryngeal cancer patients treated by these different methods. The lognormal model may become a useful tool in research on outcomes.

Background

Literature review [1] indicated that local control, laryngeal preservation, and survival rates of larynegeal cancer patients were similar after transoral laser resection, open partial laryngectomy, and radiotherapy. Open partial laryngectomy was reserved for patients with locally recurrent tumors. There are still some unanswered questions. Will radiation combined with surgery give a better result than single modality treatment alone? Will treatment results from the community centers follow published data from prestigious centers? After radiotherapy, radio-resistant cells theoretically may take some time to grow before recurrence. Short-term data may not reflect long-term local control and survival rates. We attempt to address these questions in the present study.

The lognormal distribution is defined as the distribution of a random variable whose logarithm is normally distributed. The purpose of this study is to validate the use of the lognormal model [2-4] by estimating the long-term survival from short-term follow-up data of laryngeal cancer treated by three different treatment methods: radiation and surgery, radiation alone, and surgery alone. We have previously validated the application of the lognormal model for small cell lung cancer [5], glottic laryngeal cancer [6], prostate cancer [7] and breast cancer [8].

This model may be useful for randomized clinical trials because it allows the prediction of long-term survival rates several years earlier than is possible by using the standard actuarial life table/Kaplan-Meier method of calculation [9].

The idea that long-term survival rates can be estimated from short-term follow-up data is attractive because this method shortens the delay in further research to improve cancer treatment. The validation of the lognormal model has two phases. Phase 1 tests the goodness of fit to a lognormal distribution of the survival times of those cancer patients who died with disease.

Phase 2 attempts to verify the lognormal model, which uses short-term follow-up data to predict long-term survival rates. These survival rates are then compared with values calculated by the Kaplan-Meier life table method from available long-term data. The second phase has been difficult to implement because of the general lack of large number of patients with sufficiently long follow-up information. With the SEER database [10], the validation of the lognormal model is now possible.

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