Denna uppsats har undersökt tid-till-försäljning på Uppsala kommuns bostadsmarknad för lägenheter under året 2021. För att analysera tid-till-försäljning har metoder från överlevnadsanalys använts. Överlevnadsfunktionen och den kumulativa hasardfunktionen har skattats med Kaplan-Meier-skattningen och Nelson-Aalen-skattningen. Därutöver har tre modeller skattats; en Cox proportionell hasardmodell och två 'Accelerated Failure Time'-modeller varav en var en Weibullmodell och en var en Loglogistiskmodell. Resultaten indikerar att tid-till-försäljning har en hög hasard efter två veckor på marknaden varefter en avtagande hasard. Resultaten indikerar att kovariat har en statistisk signifikant effekt på tid-till-försäljning. Grafiska tester indikerar att antagandet om proportionalitet för Cox proportionella hasardmodell och antagandet om den underliggande hasardfunktionen för Weibullmodellen är orimliga. Antagandet om den underliggande hasardfunktionen för loglogistiskamodellen verkar rimlig. Goodness-of-fit indikerar att Weibullmodellen och loglogistiskamodellen var mer välanpassade till datamaterialet än Cox proportionella hasardmodell. / This bachelor's thesis has investigated time-to-sale on the Uppsala municipality property market for apartments during 2021. Analysis has been performed utilising methods from survival analysis. Both the survival function and cumulative hazard function were estimated using the Kaplan-Meier estimate and the Nelson-Aalen estimate respectively. Furthermore, three models were estimated; a Cox Proportional Hazards model as well as two Accelerated Failure Time models of which one was a Weibullmodell and the other was a loglogistic model. The results indicate that time-to-sale has a high hazard after two weeks on the market followed by a decreasing hazard. The results also indicate that covariates have a statistically significant effect on time-to-sale. Graphical tests indicate that the assumption of proportionality for the Cox Proportional Hazards model and the assumption of the underlying hazard function for the Weibullmodell are unreasonable. The assumed hazardfunction of the loglogistic model was found to be reasonable. Goodness of fit indicates that the Weibull model and loglogistic model were a better fit to the data than the Cox proportional Hazardsmodel.

如何藉由DNA微陣列資料跟存活資料的資訊來找出基因表現定型一直是個重要的議題。這些研究的主要目標是從大量的基因中找出那些真正跟存活時間或其它重要的臨床結果有顯著關係的小部分。Threshold Gradient Directed Regularization (TGDR)是ㄧ種已經被應用在高維度迴歸問題中能同時處理變數選取以及模型配適的演算法。然而，TGDR採用一種梯度投影型態的演算法使得收斂速率緩慢。在本篇論文中，我們建議新的包含Newton-Raphson求解演算法類型的改良版TGDR方法。我們建議的方法有類似TGDR的特性但卻有比較快的收斂速率。文中並利用一筆附有設限存活時間的真實微陣列癌症資料來做示範。 本篇論文的第二部份是關於適用於區間設限存活資料的重複抽樣Peto-Peto檢定。這個重複抽樣Peto-Peto檢定能夠評估存活函數估計方法的檢定力，例如Turnbull的估計方法以及Kaplan-Meier的估計方法。這個檢定方法顯示出在區間設限資料時Kaplan-Meier的估計方法的檢定力要比Turnbull的估計方法的檢定力來得低。這個檢定方法將以模擬的區間設限資料以及一筆真實關於乳癌研究的區間設限資料來說明。 / Analyzing censored survival data with high-dimensional covariates arising from the microarray data has been an important issue. The main goal is to find genes that have pivotal influence with patient's survival time or other important clinical outcomes. Threshold Gradient Directed Regularization (TGDR) method has been used for simultaneous variable selection and model building in high-dimensional regression problems. However, the TGDR method adopts a gradient-projection type of method and would have slow convergence rate. In this thesis, we proposed Modified TGDR algorithms which incorporate Newton-Raphson type of search algorithm. Our proposed approaches have the similar characteristics with TGDR but faster convergence rates. A real cancer microarray data with censored survival times is used for demonstration. The second part of this thesis is about a proposed resampling based Peto-Peto test for survival functions on interval censored data. The proposed resampling based Peto-Peto test can evaluate the power of survival function estimation methods, such as Turnbull’s Procedure and Kaplan-Meier estimate. The test shows that the power based on Kaplan-Meier estimate is lower than that based on Turnbull’s estimation on interval censored data. This proposed test is demonstrated on simulated data and a real interval censored data from a breast cancer study.

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