April 25 Exam April 27 (bring calculator with exp) Cox-Regression
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1 April 25 Exam April 27 (bring calculator with exp) Cox-Regression 15 multiple choice4 problemsCox-RegressionReview notesPractice questionsDescription of project
2 Getting Confidence Intervals PHREG PROC PHREG DATA = vet;MODEL SurvTime*death(0)= treatment/clRUN;Provides 95% CI for HR
3 Assessing Impact of Variable on Odds Ratio Analysis of Maximum Likelihood EstimatesStandard WaldParameter DF Estimate Error Chi-Square Pr > ChiSqInterceptAGEmensmokerBLACKOdds Ratio EstimatesPoint % WaldEffect Estimate Confidence LimitsAGEmensmokerBLACKIs effect of age small or large ?
4 Proportional hazards regression model If X is binary then exp (b) is relative hazard of group 1 versus group 0If X is continuous then exp (b) is relative hazard of 1 unit difference in X variable
5 Hazard of Divorce Proportional Hazards l (t)*cPreviously marriedl (t)Never married before
6 Proportional Hazard of Death from Birth Probability of dying in next year as function of age l (t)At which age would the hazard be greatest?
7 95% Confidence Intervals for the relative risk (hazard ratio) Based on transforming the 95% CI for the hazard ratioSupplied by SAS (CL option on model statement)“We have a statistically significant association between the predictor and the outcome controlling for all other covariates”Equivalent to a hypothesis test; reject Ho: RR = 1 at alpha = 0.05 (Ha: RR1)
8 Logistic Regression Versus Cox Regression Exp (b) is relative oddsCox Regression regressionExp (b) is relative hazardRelative hazard is often simply referred to as relative risk
9 Example survival analysis Veteran’s Administration lung cancer data137 Males with inoperable lung cancerRandomized to standard or new chemo therapyPrimary endpoint; time to death9 observations censored9 patients survived for length of study
10 Example - VA Lung Cancer variables SurvTime - time to death or study enddeath - 1 if died, 0 if censoredtreatment - new or standard treatment1 = new, 0 = standardcelltype - type of canceradeno, squamous, small cell ,large cellkps - general health measure (0-100)diagtime - time between diagnosis and study entryage - age at entryprior - prior treatment, 1 = yes, 0 = no
11 PROC PHREG PROC PHREG DATA = vet; MODEL SurvTime*death(0) = treatment; RUN;Fit proportional hazards model with time to death as outcome“death(0)”; observations with death variable = 0 are censoreddeath = 1 means an event occurredLook at effect of new vs. standard treatment on mortalitySame as LIFETEST
12 P-value for test of regression coefficient (hazard ratio) PROC PHREG OutputSummary of the Number of Event and Censored ValuesPercentTotal Event Censored CensoredAnalysis of Maximum Likelihood EstimatesParameter Standard HazardVariable DF Estimate Error Chi-Square Pr > ChiSq Rationewtrt bP-value for test of regression coefficient (hazard ratio)exp(b1)Relative risk of death for new vs. standard treatment
13 Complications with PH regression Similar issues arise that we saw in linear and logistic regression; assumptions may not holdIndependence of observations?Correlation can cause problems; use other methodsLinearity of terms?Can check for quadratic term, transformCorrelated predictor variables?Causes interpretation problems for individual parameter estimates
14 Complications with PH regression Unique issue; proportional hazards assumptionOne example of violation, crossing survival curvesRemedies;Stratify time scale so PH assumption holds over intervals, fit model to each intervalTransformation of time variable (example; log)Use other models
15 Question 1A journal article reports a 95%CI for the relative risk (RR) of an event (treatment versus control as (0.55, 0.97). What can be said of the p-value associated with testing Ho: RR=1?The p-value is < 0.01.The p-value is < 0.05.The p-value is > 0.05No statement can be said about the p-value.
16 Question 2If S (t) is the survival function and t is in years what is the meaning of S(3) .The probability of dying at year 3.The probability of surviving to year 3.The probability of dying by year 3The hazard of dying at year 3.
17 Question 3In logistic regression with a continuous variable age what is the meaning of b1 ?The difference in log odds between two persons 1 year apart in ageThe relative odds between two persons 1 year apart in ageThe difference in probabilities between two persons 1 year apart in age
18 Question 4If the probability of developing diabetes is 0.20 among Hispanics and 0.15 among whites, what is the relative odds (Hispanics v white) of developing diabetes.1.420.700.751.33
19 Question 5Suppose the logistic regression model: log odds = b0 + b1X1 + b2X2 +b3X1*X2 where X1 is an indicator for treatment and X2 is an indicator for male gender. The relative odds (treatment versus no treatment) for women is:b1b2.b1 + b3b1 - b3
20 Question 6The probability and odds of an event will be nearly equal if:The probability of the event is smallThe probability of the event is largeThe probability of the event is 0.50