Cutaneous Squamous-Cell Carcinoma in Patients Treated with PUVA

Expected Number of Tumors

To calculate the expected number of tumors for a given stratum, we totaled the expected number for every patient in this stratum during each of the five periods defined in Table 1. Only the patients who received a dermatologic examination after the beginning of a period (Table 1) were included in the calculation of the expected number of tumors for this period.

To calculate the expected risk of the development of a tumor, we used the following methods. (1) The expected numbers of squamous-cell and basal-cell carcinomas were calculated separately.

(2) Using specific incidence data for age, sex, and geographic residence, determined by a federal survey,⁵ we calculated the annual incidences of basal-cell and squamous-cell carcinoma for each patient at the age when he or she entered the study and at the age when the final follow-up examination was performed.

(3) Residence at the time of entry was used to classify each patient's geographic area.

Classification of each patient's exposure to ionizing radiation (yes, no) and to tar and sunburn-spectrum ultraviolet-B therapy (high, low) was based on historical data. These classifications remained constant throughout the study. Each patient was assigned to a PUVA-dose group for each of the five periods according to the total number of PUVA treatments received before the corresponding interview (Table 1).

Patients tended to remain in the same PUVA-dose group throughout the study. For example, a comparison of group assignments in the first three periods (Table 1) shows that only 6 per cent of the patients changed from the low-dose to the high-dose group or vice versa. Sixty-eight per cent of the patients remained in the same group for all three periods.

To study the time-dependent dose effects of PUVA, we considered separately observed and expected tumors developing 22 to 45 months after the first treatment with PUVA from those developing more than 45 months after the first treatment. We also considered both periods together. The total expected number of tumors for a given stratum equals the sum of the expected number for each patient in that stratum in each of the five periods.

(4) To determine the expected annual incidence for each patient in each of the five periods defined in Table 1, we interpolated linearly between the annual incidence rate for the patient's age at entry to the study and for the age at the final interview (an average of six years later).

(5) The risk of a tumor developing in a patient during a given period (Table 1) equals the product of that patient's annual incidence and the length of the period. This product represents the patient's contribution to the expected number of tumors in the period.

Table 7. Table 7. Calculation of Expected Number of Squamous-Cell Carcinomas and Determination of PUVA-Dose Group for a Single Patient.

Our method of calculating the expected risk of squamous-cell carcinoma in a patient for each period and of assigning that expected number to a PUVA-dose group for each period is illustrated in Table 7. In this example, the patient contributed 0.00549 to the expected number for the high-dose group for the first three periods and 0.00321 to the medium-dose group for the last two periods.

As a result of our method of calculation, the expected number of tumors in each stratum (Tables 3 and 5) was a function of the number of patients in the stratum and the length of follow-up for these patients as well as the distribution of age, sex, and residence. For example, although there were more than 12 times as many patients in the low-tar/no-ionizing-radiation group as in the high-tar/ionizing-radiation group, the age, sex, and geographic distributions were such that the ratio of expected tumors in these groups was only eight to one.

Observed Number of Tumors

Except as specified for Table 2, each patient in whom a squamous-cell or basal-cell carcinoma occurred was counted only once, even if multiple tumors of a given type developed in the patient at least 22 months after the first treatment with PUVA. Therefore, when skin tumors developed in an individual patient at different intervals, the method we used to calculate the number of observed tumors resulted in a lower number than would have been calculated with the methods employed in the federal survey.⁵

In most cases, detection of a tumor resulted in either cessation of PUVA or substantial reduction in the rate of treatment. In the first months of the study, there was little difference among patients with respect to the total number of treatments received. Therefore, we excluded from our analysis 10 patients in whom a first tumor developed within 16 months after the first treatment and in whom additional tumors developed later in the study. We used PUVA-dose classification of low (less than 60 treatments), medium (60 to 79), and high (more than 79) for the four patients in whom a first tumor was detected 16 to 21 months after the first treatment and in whom additional tumors were detected at least 22 months after the first treatment.

Statistical Methods

The standard morbidity ratio for each PUVA-dose group was computed as the ratio of the total number of tumors observed to the total number expected (Table 2).⁷ As described above, we computed the ratios twice: first by counting as an incident tumor up to one tumor per year of each type that occurred in patients at least 22 months after the first PUVA treatment (the method most comparable to that used to determine the population incidence rates in the federal survey), and then by counting only the first tumor of a given type that was observed in a patient at least 22 months after the start of PUVA.

Ninety-five per cent confidence intervals for the log standard morbidity ratios were calculated as ln (observed/expected) ± 1.96 times the square root of the observed number of tumors. To calculate the 95 per cent confidence intervals for the standard morbidity ratios, we obtained the antilog of the end points calculated according to the method described above.

Although standard morbidity ratios are commonly used in cohort studies, they may be unsatisfactory if the population prevalence rates are inappropriate. Thus, it may be more appropriate to compare the excess risk in the high-dose group with that in the medium-and low-dose groups by effectively calculating relative standard morbidity ratios (Table 3). Even such relative ratios may be unsatisfactory if the excess risk due to PUVA depends on the length of exposure to treatment or if there are other confounding factors that may cause differential tumor risk among patients exposed to PUVA. Possible confounding factors in our analysis included prior exposure to tar or ionizing radiation.

Recently developed statistical models for cohort studies make it possible to control for these factors and to estimate the relative risk attributable to the use of tar and ionizing radiation and to the level of exposure to PUVA. In our study, we used the Poisson regression model.⁷ We calculated separately both the observed and expected numbers of tumors for each stratum of the PUVA-dose groups (tar, ionizing radiation, and time [22 to 45 months, or more than 45 months] since the first treatment). For observed tumors, only the first observed after 22 months of treatment was counted. Tables 3 and 5 show both the observed and expected numbers of squamous-cell and basal-cell carcinomas for each stratum except time. The expected numbers in Tables 3 and 5 have been rounded off to one decimal place; as a result, standard morbidity ratios calculated from numbers shown in these tables differ slightly from those shown in Table 2. Also, since our analysis did not detect an important effect of time, in the tables we pooled the data from all periods.

The general method of analysis is to fit a standard multiple linear regression model to the log of the standard morbidity ratios, stratified by PUVA-dose group, tar-exposure level, ionizing-radiation exposure, and time. As detailed above, our method of calculating expected numbers of tumors adjusts for group differences due to age, sex, and geographic region. The estimated variables in the regression model are used to summarize the excess risk for each exposure variable, adjusting for all others, and can thus be regarded as "adjusted" relative standard morbidity ratios. The estimated regression variables are calculated by applying maximum likelihood to a model that assumes that the observed counts follow a Poisson distribution. We used the likelihood ratio test, which compares the fit of a model with all effects included with it and omits only the effect being tested, to determine the significance of an estimated effect.

Since there were fewer subjects in the high-tar group than in the low-tar group, our analysis had less power for detecting the effect of ionizing radiation in the high-tar group. The data presented in Table 3 do not support a consistent effect for high levels of tar exposure.

Patients exposed to high levels of tar had no adverse effects from exposure to ionizing radiation. For patients with low levels of tar exposure, the relative risk associated with ionizing-radiation exposure equaled 2.3 (Table 4). Since only 18 per cent of the patients reported high levels of exposure to tar, these results must be interpreted cautiously.