This paper presents three procedures for estimating age-specific prevalence ■ the Counting Method [GKMS99], the Transition Rate Method [GKMS99] [FKMN86] and a parametric method [CD97]. We have also developed a method to estimate age-specific non recovery prevalence using a transition rate model. The variances of these prevalences are estimated using the Delta-Method [DFSW88].

The Counting Method was developed by [GKMS99] [FKMN86] and is used to estimate prevalence based on tumor registry data. The estimates of the standard error for the Counting Method are based on the Poisson method [CGF02]. This method is implemented by the SEER*Stat software developed by the Statistical Research and Applications Branch.

Generally, publications about prevalence assume that the disease is irreversible, no return to the healthy state is allowed [MCFM00], [VC89]. But

Fig. 2. (a) Age-specific prevalence of colorectal cancer in 1999 estimated by the Transition Rate Method (TRM), the Counting Method (CM) and the Parametric Method (PM).(b)Age-specific prevalence of non recovery of colorectal cancer in 1999 estimated by the Transition Rate Method (TRM) and the Parametric Method PM).

Fig. 3. (a) Estimates of age-specific prevalence and prevalence of non recovery using the Transition Rate Method (TRM). (b) Estimates of age-specific prevalence and prevalence of non recovery using the Parametric Method (PM).

today, thanks to improvements of treatment, the word "cure" can be used for certain cancers. So, in order to better understand the burden of cancer on the population, it is important to estimate non recovery prevalence. Indeed, a subject considered as "cured" requires fewer health resources than a subject who is not cured. [CD97] provides models of prevalence with the hypothesis of disease reversibility. Both reports estimate cancer prevalence using mixture models for cancer survival. They model the relative survival function by a mixture model without covariates and an exponential distribution for non recovery survival. It is the parametric method which is presented here. This method requires a choice of model and programming with statistical software.

In our report, in order to estimate prevalence and non recovery prevalence, we proposed a transition rate estimate method. The added plus represents estimates of variance using the Delta-Method [DFSW88]. As regards rates estimates, these are estimated according to actuarial intervals. In order to use this method, we have developed a software called SSPIR [GDT04] that implements the Transition Rate Method. The Counting Method and the Transition Rate Method are therefore easy to use.

TRM |
PM |
CM | |

Type of database |
Cancer Registry |
Cancer Registry |
Cancer Registry |

+ Vital statistics |
+ Vital statistics | ||

Cancer Registry |
Exhaustive |
Exhaustive |
Exhaustive |

Closed Population |
Yes |
Yes |
No |

Estimation Method |
Actuarial |
Parametric |
Non Parametric |

Non recovery prevalence |
Yes |
Yes |
No |

Estimation Model | |||

Incidence Rate |
Observed incidence |
Exponential shape |
No |

No diseased mortality rate |
All other mortality |
No |
No |

Diseased mortality rate |
Vital tables method |
Relative Survival |
Survival of losts |

Cure rate |
Vital tables method |
Mixture model |
No |

Software |
SSPIR |
No |
SEER*Stat |

As regards the estimates of age-specific prevalence, we note that the estimates of using the three methods are close. But the variances of the Transition Rate Method are smaller than the variance of the Counting Method and the Parametric Method estimates. Moreover, the estimates of the Transition Rate Method are slightly higher than the estimates of the Parametric Method. The estimates of age-specific non recovery prevalence are slightly higher using the Transition Rate Method compared to using the parametric method. We can also note that the coefficients of variation are equivalent to the one of the parametric method. This parametric model seems to be well adapted to colorectal cancer but it may not be the case for other diseases.

We described three methods of estimating prevalence, two of which are non parametric methods. These are both attractive since they are easy to use and robust. The parametric method requires, when it is possible, to find the model which is best adapted to data. This point directly raises the well known problem of choice between parametric and non parametric methods.

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