Grouped survival data arise often in studies where the disease status is assessed at regular visits to clinic. The time to the event of interest can only be determined to be between two adjacent visits or is right censored at one visit. In data analysis, replacing the survival time with the endpoint or midpoint of the grouping interval leads to biased estimators of the effect size in group comparisons. Prentice and Gloeckler developed a maximum likelihood estimator for the proportional hazards model with grouped survival data and the method has been widely applied. Previous work on sample size calculation for designing studies with grouped data is based on either the exponential distribution assumption or the approximation of variance under the alternative with variance under the null. Motivated by studies in HIV trials, cancer trials and in vitro experiments to study drug toxicity, we develop a sample size formula for studies with grouped survival endpoints that use the method of Prentice and Gloeckler for comparing two arms under the proportional hazards assumption. We do not impose any distributional assumptions, nor do we use any approximation of variance of the test statistic. The sample size formula only requires estimates of the hazard ratio and survival probabilities of the event time of interest and the censoring time at the endpoints of the grouping intervals for one of the two arms. The formula is shown to perform well in a simulation study and its application is illustrated in the three motivating examples.
Background: Approximately half of all cancer patients receive radiotherapy and, as cancer survivorship rates increase with more effective therapies, the very low rate of radiation-associated sarcomas is rising. Radiation-associated sarcomas are life-threatening cancers, and radiation exposure is a primary risk factor for sarcoma development. During radiotherapy or other genotoxic cancer therapy for p53 mutant cancers, pharmacological inhibition of p53 has been proposed to ameliorate acute injury of normal tissues. However, enhancing the survival of normal cells that sustain DNA damage by temporarily inhibiting p53 has the potential to increase the risk of cancer development. Here, we use in vivo shRNA technology to examine the consequences of temporarily reducing p53 expression on radiation-induced sarcoma development. Methods: We utilized a mouse model of radiation-induced sarcoma where mice express a doxycycline (dox)-inducible p53 shRNA to temporarily and reversibly reduce p53 expression. Mice were placed on a dox diet 10 days prior to receiving 30 or 40 Gy hind limb irradiation in a single fraction and then returned to normal chow. Mice were examined weekly for sarcoma development and scored for radiation-induced normal tissue injuries. Radiation-induced sarcomas were harvested and subjected to RNA sequencing. Results: Following single high-dose irradiation, 21% of temporary p53 knockdown animals developed a sarcoma in the radiation field compared to 2% of control animals. Mice with more severe acute injuries in the first 3 months after irradiation had a significantly increased risk of developing late persistent wounds in the soft tissue and bone. Chronic radiation-induced wounds were associated with sarcomagenesis. Examination of muscle stem cells by flow cytometry following hind limb irradiation indicated p53 knockdown preserves muscle stem cells in the irradiated limb, supporting the notion that temporary p53 knockdown at the time of irradiation reduces death of cells with DNA damage which may then persist to develop into a sarcoma. We performed RNA sequencing on 16 radiation-induced sarcomas compared to normal muscle controls. Gene set enrichment analysis revealed upregulation in the sarcomas of genes related to translation, epithelial mesenchymal transition (EMT), inflammation, and the cell cycle versus downregulation of genes related to myogenesis and tumor metabolism. Furthermore, genes with increased copy number such as Met and Cdk4 were overexpressed in tumors. Conclusions: Temporary reduction of p53 during high-dose irradiation increases late effects including tissue injuries and sarcoma development.
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