Discrimination-based sample size calculations for multivariable prognostic models for time-to-event data.

BACKGROUND: Prognostic studies of time-to-event data, where researchers aim to develop or validate multivariable prognostic models in order to predict survival, are commonly seen in the medical literature; however, most are performed retrospectively and few consider sample size prior to analysis. Events per variable rules are sometimes cited, but these are based on bias and coverage of confidence intervals for model terms, which are not of primary interest when developing a model to predict outcome. In this paper we aim to develop sample size recommendations for multivariable models of time-to-event data, based on their prognostic ability. METHODS: We derive formulae for determining the sample size required for multivariable prognostic models in time-to-event data, based on a measure of discrimination, D, developed by Royston and Sauerbrei. These formulae fall into two categories: either based on the significance of the value of D in a new study compared to a previous estimate, or based on the precision of the estimate of D in a new study in terms of confidence interval width. Using simulation we show that they give the desired power and type I error and are not affected by random censoring. Additionally, we conduct a literature review to collate published values of D in different disease areas. RESULTS: We illustrate our methods using parameters from a published prognostic study in liver cancer. The resulting sample sizes can be large, and we suggest controlling study size by expressing the desired accuracy in the new study as a relative value as well as an absolute value. To improve usability we use the values of D obtained from the literature review to develop an equation to approximately convert the commonly reported Harrell's c-index to D. A flow chart is provided to aid decision making when using these methods. CONCLUSION: We have developed a suite of sample size calculations based on the prognostic ability of a survival model, rather than the magnitude or significance of model coefficients. We have taken care to develop the practical utility of the calculations and give recommendations for their use in contemporary clinical research.

Cardiovascular outcomes in patients with locally advanced and metastatic prostate cancer treated with luteinising-hormone-releasing-hormone agonists or transdermal oestrogen: the randomised, phase 2 MRC PATCH trial (PR09).

BACKGROUND: Luteinising-hormone-releasing-hormone agonists (LHRHa) to treat prostate cancer are associated with long-term toxic effects, including osteoporosis. Use of parenteral oestrogen could avoid the long-term complications associated with LHRHa and the thromboembolic complications associated with oral oestrogen. METHODS: In this multicentre, open-label, randomised, phase 2 trial, we enrolled men with locally advanced or metastatic prostate cancer scheduled to start indefinite hormone therapy. Randomisation was by minimisation, in a 2:1 ratio, to four self-administered oestrogen patches (100 µg per 24 h) changed twice weekly or LHRHa given according to local practice. After castrate testosterone concentrations were reached (1·7 nmol/L or lower) men received three oestrogen patches changed twice weekly. The primary outcome, cardiovascular morbidity and mortality, was analysed by modified intention to treat and by therapy at the time of the event to account for treatment crossover in cases of disease progression. This study is registered with ClinicalTrials.gov, number NCT00303784. FINDINGS: 85 patients were randomly assigned to receive LHRHa and 169 to receive oestrogen patches. All 85 patients started LHRHa, and 168 started oestrogen patches. At 3 months, 70 (93%) of 75 receiving LHRHa and 111 (92%) of 121 receiving oestrogen had achieved castrate testosterone concentrations. After a median follow-up of 19 months (IQR 12-31), 24 cardiovascular events were reported, six events in six (7·1%) men in the LHRHa group (95% CI 2·7-14·9) and 18 events in 17 (10·1%) men in the oestrogen-patch group (6·0-15·6). Nine (50%) of 18 events in the oestrogen group occurred after crossover to LHRHa. Mean 12-month changes in fasting glucose concentrations were 0·33 mmol/L (5·5%) in the LHRHa group and -0·16 mmol/L (-2·4%) in the oestrogen-patch group (p=0·004), and for fasting cholesterol were 0·20 mmol/L (4·1%) and -0·23 mmol/L (-3·3%), respectively (p<0·0001). Other adverse events reported by 6 months included gynaecomastia (15 [19%] of 78 patients in the LHRHa group vs 104 [75%] of 138 in the oestrogen-patch group), hot flushes (44 [56%] vs 35 [25%]), and dermatological problems (10 [13%] vs 58 [42%]). INTERPRETATION: Parenteral oestrogen could be a potential alternative to LHRHa in management of prostate cancer if efficacy is confirmed. On the basis of our findings, enrolment in the PATCH trial has been extended, with a primary outcome of progression-free survival. FUNDING: Cancer Research UK, MRC Clinical Trials Unit.

Presence of chemotherapy-induced toxicity predicts improved survival in patients with localised extremity osteosarcoma treated with doxorubicin and cisplatin: a report from the European Osteosarcoma Intergroup.

AIM: Chemotherapy-induced toxicity is an independent prognostic indicator in several cancers. We aimed to determine whether toxicity was related to survival and histological response in high-grade localised extremity osteosarcoma. We undertook a retrospective analysis of patients treated within three consecutive randomised controlled trials (RCTs) of the European Osteosarcoma Intergroup. METHODS: Between 1982 and 2002, 533 patients were randomised to six cycles of doxorubicin 75 mg/m(2) and cisplatin 100 mg/m(2). Toxicity data were collected prospectively and graded according to the World Health Organisation (WHO) criteria. Standard univariate and multivariate models were constructed to examine the relationship between reported toxicity, survival, and histological response. RESULTS: Five- and 10-year overall survival was 57% (95% confidence interval (CI) 52-61%) and 53% (49-58%), respectively. Grades 3-4 oral mucositis (hazard ratio (HR) 0.51, 95% CI 0.29-0.91), grades 1-2 nausea/vomiting (HR 0.37, 95% CI 0.16-0.85), grades 1-2 thrombocytopenia (HR 0.49, 95% CI 0.27-0.87), good histological response (HR 0.42, 95% CI 0.27-0.65), and distal tumour site (HR 0.45, 95% CI 0.28-0.71) were associated with improved survival in multivariate analysis. The only factors that were independently associated with histological response were older age (odds ratio (OR) 0.18, 95% CI 0.04-0.72) and chondroblastic tumour (OR 0.28, 95% CI 0.10-0.77), both being associated with a significantly lower chance of achieving a good response. CONCLUSION: Chemotherapy-induced toxicity predicts survival in patients with localised extremity osteosarcoma. Investigation of the pharmacogenomic mechanisms of constitutional chemosensitivity underlying these observations will present opportunities for personalising treatment and could lead to improved outcomes.

Survival after recurrent osteosarcoma: data from 3 European Osteosarcoma Intergroup (EOI) randomized controlled trials.

BACKGROUND: Recurrence after osteosarcoma usually leads to death; thus prognostic factors for survival are of great importance. METHODS: Between 1983 and 2002, the European Osteosarcoma Intergroup accrued 1067 patients to 3 randomized controlled trials of pre- and post-operative chemotherapy for patients with resectable non-metastatic high-grade osteosarcoma of the extremity. Control treatment in all trials was doxorubicin 75 mg/m² and cisplatin 100mg/m². The comparators were additional high-dose methotrexate (BO02), T10-based multi-drug regimen (BO03) and G-CSF intensified-DC (BO06). Post-recurrence survival (PRS) was investigated on combined data with standard survival analysis methods. RESULTS: Median recurrence-free survival was 31 months; 8 recurrences were reported more than 5 years after the diagnosis. In 564 patients with a recurrence (median 13 months post-randomisation), there was no difference in post-relapse survival between treatment arms. Patients whose disease recurred within 2 years after randomization had a worse prognosis than those recurring after 2 years. Patients with good initial histological response to pre-operative chemotherapy had a better overall survival after recurrence than poor responders. Local relapse was more often reported after limb-saving procedures (2 versus 8%; amputation versus limb-saving), independent of the primary tumour site. Site of first recurrence (local 20%, lung 62%, "other" 19%) affected survival, as patients recurring with non-lung distant metastases only or any combination of local relapse, lung metastases and non-lung metastases (=group "other") had significantly worse overall survival (local 39%, lung 19%, "other" 9% at 5 years). CONCLUSIONS: These data describing a large series of patients with recurrent extremity osteosarcoma confirm the relationship between early recurrence and poor survival. There was better PRS in patients after good histological response to pre-operative chemotherapy, or with local-only recurrence.