ATTACH YOUR SAS CODE WITH YOUR ANSWERS.

Transcription

1 BSTA 6652 Survival Analysis Winter, 2017 Problem Set 5 Reading: Klein: Chapter 12; SAS textbook: Chapter 4 ATTACH YOUR SAS CODE WITH YOUR ANSWERS. The data in BMTH.txt was collected on 43 bone marrow transplant patients at the Ohio State University Bone Marrow Transplant Unit. All patients had either Hodgkin s disease (HOD) or non-hodgkin s lymphoma (NHL) and were given either an Allogeneic (Allo) transplant from an HLA match sibling donor or an Autogeneic (Auto) transplant. Also included are two possible explanatory variables, Karnofsky score at transplant and the waiting time in months from diagnosis to transplant. Of interest is to study the difference in the leukemia-free survival rate between patients given an Allo or Auto transplant, adjusting for the patient s disease state (HOD or NHL) and other covariates. The variables in this data set are as follows: GRAFT Disease Time Status Score Wait Transplant type (1=Allo, 2=Auto) Disease state (1=NHL, 2=HOD) Survival time in days Status of patient (0 =alive, 1 = dead or relapse) Karnofsky score at transplant Waiting time in months from diagnosis to transplant The data set BMTH.txt is posted online. (a) Create a SAS dataset including all these variables and a new variable for the combination of GRAFT and Disease. Write your SAS code here. data transplant; input graft disease time status score wait; if graft = 1 and disease = 1 then type = 1; if graft = 2 and disease = 1 then type = 2; if graft = 1 and disease = 2 then type = 3; if graft = 2 and disease = 2 then type = 4; cards; ; (b) Fit the Accelerated Failure Time (AFT) model including all covariates under the assumption of Lognormal survival times. Write the fitted AFT model and your SAS code.

2 /* (b): lognormal AFT model with all covariates */ model time*status(0) = score wait type /dist=lognormal; Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Type III Analysis of Effects Effect Wald DF Chi-Square Pr > ChiSq score <.0001 wait type The LIFEREG Procedure The fitted model is Analysis of Maximum Likelihood Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept score <.0001 wait type type type type Scale log( time) = Score Wait Allo * NHL Auto * NHL Allo * HOD w where Allo, Auto, NHL, HOD are indicator functions of Allo, Auto, NHL, HOD, separately; w follows N(0,1). (c) Fit the Accelerated Failure Time (AFT) model including all covariates under the assumption of Log-logistic survival times. Write the fitted AFT model and your SAS code. /* (c): loglogistic AFT model with all covariates */ model time*status(0) = score wait type /dist=llogistic;

3 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Algorithm converged. Type III Analysis of Effects Effect Wald DF Chi-Square Pr > ChiSq score <.0001 wait type The LIFEREG Procedure Analysis of Maximum Likelihood Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept score <.0001 wait type type type type Scale The fitted model is log( time) = Score Wait Allo * NHL Auto * NHL Allo * HOD w where Allo, Auto, NHL, HOD are indicator functions of Allo, Auto, NHL, HOD, separately; and w follows logistic(0,1). (d) Fit the Accelerated Failure Time (AFT) model including all covariates under the assumption of Weibull survival times. Write the fitted AFT model and SAS code. /* (d): Weibull AFT model with all covariates */

4 Fit Statistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Algorithm converged. Type III Analysis of Effects Effect Wald DF Chi-Square Pr > ChiSq score <.0001 wait type The LIFEREG Procedure Analysis of Maximum Likelihood Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept score <.0001 wait type type type type Scale Weibull Shape The fitted model is log( time) = Score +.019Wait Allo * NHL Auto * NHL Allo * HOD w where Allo, Auto, NHL, HOD are indicator functions of Allo, Auto, NHL, HOD, separately; and w follows extremevalue(0,1). (a) Which model is the best initial model among the three models in parts (a), (b), and (c)? Defend your answer. Conduct a model selection (at 5% level) and fit the final model. i. Write the fitted final model. ii. Interpret the final model: how each variable is associated with the survivorship.

5 Based on the AIC, Weibull AFT model is the best. According to the SAS output of Type III Analysis of Effects in part (d), all variables are significant at 10% level, so the reduced model is the same as the full model in part (d). Interpretation: The effect of Karnofsky score at transplant: When controlling other variables, as the score increases by 1, the risk of death or relapse is exp(-.0572/1.0644)=.9477 times smaller. The larger the score is, the smaller the risk is. The effect of waiting time: When controlling other variables, as a patient waits for one more month, the risk of death or relapse is exp(-.019/1.0644)=.9823 times smaller. The longer the waiting is, the smaller the risk is. The effect of type: When controlling other variables, compared to the Auto-HOD patients, the risk of death or relapse for the Allo-NHL patients is (=exp( /1.0644)) times smaller; the risk for the Auto-NHL patients is times smaller; and the risk for the Allo-HOD patients is 6.86 times larger. Overall, the ranks of risk associated with these types are: Allo-HOD > Auto-HOD > Auto-NHL > Allo-NHL. (b) Check the goodness of fit of the reduced model by i. Probability plot and residual analysis ii. Compare it to the Generalized Gamma AFT model Does the reduced model fit the data adequately? i) Residual analysis ii) probplot; output out=a cdf=f; data b; set a; e=-log(1-f); proc lifetest data=b plots=(ls) notable graphics; time e*status(0); symbol1 v=none;

6 Figure 1 From Figure 1, the points do not follow the line more or less but most of them are within the 95% confidence band Negative Log SDF e Figure 2 The residual plot does not show a straight line from the origin with slope 1, so the model fits the data poorly. iii) Compared to the Generalized Gamma (GG) AFT model: model time*status(0) = score wait type /dist=gamma; Fit Statistics

7 -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Do L-R test: Ho: Weibull AFT model vs. Ha: GG AFT model. The test statistic is -2loglikelihood(Weibull AFT model) - (-2loglikelihood(GG AFT model) = = larger than 3.841, the critical value of Chi-square distribution with 1 d.f. at 5%. Therefore, the Weibull AFT model fits significantly worse than GG AFT model. Overall, the Weibull AFT model does not fit the data. SAS Code: /* (b): lognormal AFT model with all covariates */ model time*status(0) = score wait type /dist=lognormal; /* (c): loglogistic AFT model with all covariates */ model time*status(0) = score wait type /dist=llogistic; /* (d): Weibull AFT model with all covariates */ /* (e)(f) residual analysis and compared to GG AFT model */ probplot; output out=a cdf=f; data b; set a; e=-log(1-f); proc lifetest data=b plots=(ls) notable graphics; time e*status(0); symbol1 v=none; model time*status(0) = score wait type /dist=gamma;