### Patients

Between 1981 and 1998, 1417 cases of SCLC were diagnosed in Saskatchewan, Canada and entered in the Saskatchewan cancer electronic registry prospectively. Of these, 244 had limited stage disease and were treated with chemotherapy and thoracic radiotherapy delivered with curative intent, with or without prophylactic cranial irradiation [12]. For the whole series, only six patients did not have any chemotherapy. Cisplatin-containing regimen was given to 54 patients. The remaining patients had non-cisplatin-containing regimens.

To facilitate the comparison of the different fractionation schemes used for radiotherapy, we calculated the biologically effective dose (BED) [17, 18], using the linear-quadratic model:

BED=nd\times \left[1+\frac{d}{\alpha /\beta}\right]

The median BED to the chest was 46.9 Gy_{10} (range 22.6–66.1), corresponding to a median dose of 37.5 Gy in 15 fractions within 19 days (range 20 Gy in 15 fractions within 20 days to 60 Gy in 30 fractions within 44 days), where Gy_{10} is the BED when α/β is 10. Chemotherapy regimens and radiotherapy techniques were those utilized by clinicians during the study period. Current patient management may differ; however, the focus of this work is the comparison of DSS assessed by different statistical methods in the same cohort of patients.

More detailed data for the current study were obtained from the chart review for individual patients, followed to the end of 2005 by a health record technician, and checked by an oncologist (PT).

### Statistical Methods

#### Event

Death with or from lung cancer, for DSS, was the event of interest here. The last recorded SCLC death was at 1966 days of follow-up (5.4 years), and the second last event was at 1789 days (4.9 years). The lack of events after 1966 days precluded comparison after 5 years. Follow-up was censored at death from other causes for the Kaplan-Meier, Cox, and log-normal survival analyses. One patient had unknown status at last follow-up, and was excluded from the analyses since the Boag cure-rate model requires alive/dead categorization for each patient, and where appropriate, knowledge of type of death.

### Statistical Modeling

Cox and log-normal survival analyses utilized both censored and uncensored data towards the estimation of a common set of factor effects [19]. For these survival analyses frameworks [19], we considered the values of the survivor functions at a time when few (or no) events are expected as reasonable estimates of the proportion cured, without specifying a cured-rate parameter [19].

### Cox model

The Cox model assumes proportional hazards; this assumption was checked graphically with plots of cumulative hazard against follow-up time [19].

### Log-normal models

Neither the Boag cure-rate nor log-normal survival analysis require the Cox assumption of proportional hazards. Both the Boag (log-normal) cure-rate model and log-normal survival analyses assume that the logarithm of lung cancer survival time has a standard normal distribution; quantiles obtained for times of SCLC cancer deaths were utilized to check this assumption for the 2005 update with a quantile-quantile (Q-Q) plot and a chi-square goodness of fit test against the normal distribution.

#### 1. Boag (log-normal) cure-rate model

Boag (log-normal) cure-rate modeling begins with the classification of patients as being "cured" (C) or "uncured" (1-C) at a particular length of follow-up [7], to define four groups: Group 1 patients died of SCLC; Group 2 died without any SCLC; Group 3 were alive with no sign of SCLC; Group 4 were alive with SCLC cancer present either as local, regional or metastatic disease.

For the proportion who are not cured, 1-C, the survival time T is assumed to be log-normally distributed; Y = ln (T) is normally distributed with mean μ and variance σ^{2} [7]. Generally, one has to jointly estimate C (>0), μ, and σ at some point in time when the group who will be classified as cured may include patients who are not cured, although they have not yet had an event. Sufficiently long follow-up with a disease like lung cancer will minimize misclassification, since it is well known that few lung cancer patients will recur after 4 or 5 years. C is estimated for the full patient group. The focus of these investigations was the estimation of DSS, as described below.

#### 2. Log-normal survival analysis model

For all patients, the survival time T is log-normally distributed if Y = ln (T) is normally distributed with mean μ (= α + **zβ**), and variance σ^{2}, where z are covariate(s). A patient without an event is censored at the last follow-up time for that patient. There is no specific parameter to estimate the proportion cured, but one is not needed since the survivor function provides an estimate of the proportion cured at any point in time, with the estimate improving as follow-up time increases to a period when few (or no) events are expected. The survivor function, S(t), is given by S(t) = 1 - Φ [(ln(t) - μ)/σ], where Φ is the standard normal cumulative distribution.

### Statistical Analyses

Estimates of DSS using the Boag cure-rate model and Kaplan-Meier methods are based on outcomes in defined (sub)groups of patients. Thus, to maintain maximal power here, estimation with the Boag and Kaplan-Meier methods required the full cohort of patients. We reported DSS at 1-, 3- and 5-years and 95% confidence limits for all patients, using the four methods: Boag log-normal, Kaplan-Meier, Cox, and log-normal survival analysis.

The following clinical factors were assessed for effect on DSS in step-wise forward model building with both Cox and log-normal survival analysis: gender, age, site of primary, side of lung cancer, lymphadenopathy, pleural effusion, bronchial obstruction, superior vena cava obstruction, surgical resection, performance status, weight loss greater than 5% in 3 months, and hemoglobin level. Continuous factor values were used where possible, along with full patient follow-up.

Best medical practice in Saskatchewan, under the Canadian National Health system was employed throughout accrual of the patient cohort. In clinical practice, the administration of more aggressive therapy to higher risk patients may mask therapeutic benefit. Changing chemotherapy and radiotherapy management schema and the small size of this cohort precluded investigations by current practice categorizations: type of chemotherapy (platinum vs. non-platinum), use of radiotherapy, radiotherapy dose/schedule, lactic dehydrogenase (LDH) or other lab results. Incomplete or no surgical resection in 230 (94%) of the 244 patients prevented the assignment of TNM stage. We did not systematically collect smoking history nor clinical history about prior malignancies or other co-morbid diseases in the database. However, the extensive clinical follow-up for this cohort was useful for the investigation's focus on survival analyses.

Boag log-normal analysis was performed with an Excel programme [12], a computerization of Boag's original spreadsheet, with some macros that improve efficiency of the iterative maximization; it is available from PT on request. Multivariate regressions and residual checks for log-normal survival analyses were performed with Dynamic 7.0 version of the Biomedical Data Package [20, same as BMDP-XP: program 2L, for log-normal ("accel=lnormal.")]. All other analyses were performed with SAS Version 9.1.3.

Cox and log-normal step-wise forward multivariate regressions involved the addition of a factor if there was a significant likelihood ratio test statistic (p ≤ 0.05 for a χ^{2}
_{(1)} test), and factors are reported here if p ≤ 0.10 in both Cox and log-normal survival analyses. Cox-Snell residual checks were used to assess the final models for both Cox and log-normal survival analyses, and standardized residual checks were made for the log-normal model.

When the same factors were indicated as significantly affecting DSS with both the Cox and log-normal models, categorizations of these factors were used to specify sets of clinical characteristics of interest, for quantitation of DSS by the two model-types. DSS was determined quantitatively at 1-, 3-, and 5- years, and graphically demonstrated with survivor plots across the entire time period.