Chapter 12 Knowing when to worry Hazard Functions

Chapter 12 Knowing when to worry: Hazard Functions and Survival Analysis in Marketing 危險函數及存活分析 林家如 張惠盈 國立中興大學行銷研究所 8 June 2006 Hazard Functioin and Survival Analysis 1

報告流程 a. b. c. d. e. f. g. h. 專有名詞介紹 存活分析之基本概念 顧客維持( Customer Retention) 危險 (Hazards) 由“危險”推導“存活” (From Hazard to Survival) 比例危險 (Proportional Hazards) 課程回顧 SAS操作示範 8 June 2006 Hazard Functioin and Survival Analysis 2

專有名詞介紹 a. n n Customer Tenure 顧客資歷 Customer Lifetime 顧客生命 n Median customer lifetime n Customer half-life 顧客生命之中位數 n Average customer lifetime 平均顧客生命 Customer Retention 顧客維持 Retention Curve 維持曲線 Hazard 危險 Censoring 設限 8 June 2006 Hazard Functioin and Survival Analysis 3

4. 平均顧客資歷 Average Tenure n Average tenure =Average remaining lifetime =Truncated Mean lifetime n 無法計算「真正」的平均生命，除非所有的顧 客均離開。因此特定時間內的平均生命，統計 學家稱為截距式平均生命 8 June 2006 Hazard Functioin and Survival Analysis 9

n 平均顧客資歷: 特定期間內，位於維持曲線下方的面積 10 1/10 8 June 2006 20 20/10 Hazard Functioin and Survival Analysis 10

危險 Hazards d. 屬無母數(non-parametric)之統計方法 可延伸出更有用之存活曲線 1. 2. 3. 危險機率 Hazard Probability 危險函數 Hazard Function 設限 Censoring 8 June 2006 Hazard Functioin and Survival Analysis 13

Example: 圖示+計算 1 2 3 4 5 n白圈圈: 顧客已經離開，確實tenure已知 n黑圈圈: 顧客尚存活，確實tenure未知 ， 必須設限 8 June 2006 Hazard Functioin and Survival Analysis 6 7 19

Custo Censore Teun mer d re Time 0 Time 1 Time 2 Time 3 Time 4 Time 5 1 Y 5 Active Active 2 N 4 Active Stopped Censored 3 N 3 Active Stopped Censored 4 Y 3 Active Censored 5 N 2 Active Stopped Censored 6 Y 1 Active Censored 7 N 1 Active Stopped Censored Time 0 Time 1 Time 2 Time 3 Time 4 Time 5 Active 7 6 4 3 1 1 Stopped 0 1 1 0 Censored 0 0 2 3 5 6 Hazard 8 June 2006 0/(0+7 1/(1+6 1/(1+4 1/(1+3 1/(1+1 0/(0+1 )=0% )=14% )=20% )=25% )=50% )=0% Hazard Functioin and Survival Analysis 20

被強制驅離的顧客，應標示Censored而不是Stopped 8 June 2006 Hazard Functioin and Survival Analysis 22

From Hazard to Survival 由“危險”推導“存活” 1. 2. 維持曲線 由危險函數推導更為精準的存活曲線 8 June 2006 Hazard Functioin and Survival Analysis 23

存活曲線(Survival Curve) 較平滑 較精準 逐漸下降 8 June 2006 Hazard Functioin and Survival Analysis 27

比例危險 Proportional Hazards p p 範例 分層(Stratification) Cox比例危險回歸 比例危險的限制 8 June 2006 Hazard Functioin and Survival Analysis 28

存活分析之應用 p p 處理不同型態的離開(Attrition) 顧客何時回來 預測 隨時間改變的危險 8 June 2006 Hazard Functioin and Survival Analysis 42

n Tenure=1，並在 2003年停止的顧客風險人口 n 在 2002年 12月31日與2002年 12月30日之間開始的顧 客，可能有一天的資歷，並在 2003年停止 Tenure=1 12/30 8 June 2006 12/31 Hazard Functioin and Survival Analysis 57

n Tenure=365，並在 2003年停止的顧客風險人口 2002/1/1 8 June 2006 2002/12/31 Hazard Functioin and Survival Analysis Tenure=365 58

SAS操作示範 p p 客戶資料說明 操作示範 8 June 2006 Hazard Functioin and Survival Analysis 63

客戶資料說明 n Variables n n n n CUSTOMER_ID：行動電話號碼 RATE_PLAN：費率(高、中、低) MONTHLY_FEE：每月電話費 MARKET：地點 CHANNEL：通路 START_DATE：起租日 CANCEL_DATE：終止日 CANCEL_TYPE：N活躍、V自願離去、I被迫離去 8 June 2006 Hazard Functioin and Survival Analysis 64

操作示範 n 新建立Library時，勾選Enable at startup 8 June 2006 Hazard Functioin and Survival Analysis 65

n Input Data Source 8 June 2006 Hazard Functioin and Survival Analysis 66

n Open Input Data Source Node 選擇 RAW 8 June 2006 選擇整 筆資料 Hazard Functioin and Survival Analysis 67

n 增加SAS Code Node 8 June 2006 Hazard Functioin and Survival Analysis 68

n n Program>Score 輸入設限指令 n n 尚存活的顧客tenure=20061231 -起租日，標注設限 其他：終止日-起始日，不設限 8 June 2006 Hazard Functioin and Survival Analysis 69

n Export增加score選項 8 June 2006 Hazard Functioin and Survival Analysis 70

n 增加Score Node n n 執行SAS Code進行設限 增加tenure, censored二個變數 8 June 2006 Hazard Functioin and Survival Analysis 71

n Data>對應到資料 8 June 2006 Hazard Functioin and Survival Analysis 72

n Setting>Apply training data score code to score data set 8 June 2006 Hazard Functioin and Survival Analysis 73

n 執行score node，新增的兩個變數已經加入 8 June 2006 Hazard Functioin and Survival Analysis 74

n n n 再新增一個SAS CODE 對應到Score的資料 Program>run(執行SAS Process) n n n proc lifetest data=emdata. sd_k 8 xbw outsurv=lifetest method=act intervals= 0 to 1000 by 1 plots=(s, h); time tenure*censored(1); run; 8 June 2006 Hazard Functioin and Survival Analysis 75

n Survival Curve 8 June 2006 Hazard Functioin and Survival Analysis 76

n Hazards Curve 8 June 2006 Hazard Functioin and Survival Analysis 77

The end Thank you for your listening 8 June 2006 Hazard Functioin and Survival Analysis 78