Exposure-Response Plots Using SAS Janette Garner, Gilead Sciences, Inc., Foster City, CA

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1 Exposure-Response Plots Using SAS Janette Garner, Gilead Sciences, Inc., Foster City, CA ABSTRACT The Food and Drug Administration (FDA) requires that a sponsor carry out an exposure-response analysis looking at PK parameters and safety and efficacy outcomes. This exposure-response analysis is used to determine if there are any concerns over the dosing levels of the drug. The FDA carries out their own analysis and generates plots of dichotomous outcomes using S-Plus. This paper shows how the same plots can be created using SAS 9.2 or later using two examples. A macro is provided that will generate the plot from a subject-level dataset that consists of the PK parameter value and the response variable (coded as 0 or 1). INTRODUCTION During the review of a new drug application (NDA) the FDA will run their own analysis of the data submitted by a sponsor. The sponsor is asked to conduct an exposure-response analysis to assess the potential impact that drug concentrations have on efficacy and safety outcomes. The FDA will also carry out its own analysis. Below is a reproduction of Figure 7 from the Clinical Pharmacology review of Zydelig, a cancer drug indicated for relapsed chronic lymphocytic leukemia (CLL) and refractory indolent mature B cell non-hodgkin s lymphoma (inhl). The following plot was produced in S-Plus. Figure 1. Reproduction of Exposure-Response Plots prepared by FDA using S-Plus The figure presents four dichotomous safety outcomes (Grade 3 events of the following: ALT/AST elevation, Diarrhea, Rash, and Infection). It was noted that subjects with greater area under the curve (AUC) reported more episodes of Grade 3 Diarrhea. This is seen by the increasing red line in the top-right panel. 1

2 Each plot consists of four main features: 1. A logistic regression curve (red) and its 95% CI (blue region) with the dichotomous safety outcome (coded as 0 or 1) as the response and the PK parameter (eg, AUC) as the predictor 2. Quartile distribution of the PK parameter (black bar across the bottom with tick marks) 3. The mean and 95% CI for the number of subjects reporting the outcome in each quartile (black box and error bars) 4. Across the bottom, n/n is presented, where N denotes the number of subjects in the quartile and n denotes the number of subjects with the outcome within that quartile. It is possible to use the SG Procedures available in SAS 9.2 or higher to generate these plots. CREATING THE GRAPH USING SAS We build the graph in six steps. 1. A shaded region of the 95% CI for the estimated probabilities 2. The logistic regression line (estimated probabilities) 3. A boxplot of the proportion of subjects with the response variable in that quartile a. Align the boxplots at the midpoints of the intervals defined in (4) below b. Use a black square for the proportion and draw upper/lower bounds at the 95% CI for the mean 4. A line across the bottom of the graph showing the distribution of the PK parameter 5. Add the "n/n" below the boxplots (which is the value shown in the black box in (3) 6. Add a legend to describe the elements in the graph We present two examples. RESP1N is a binary variable that has equal probability to be 0 or 1. RESP2N is a binary variable that has a greater chance of being equal to 1 as the PKPARM value increases. data example(drop=i); call streaminit(123); label pkparm = "PK Parameter" resp1n = "Response Variable 1 (N)" resp2n = "Response Variable 2 (N)"; do i = 1 to 1000; pkparm = rand('normal',500,150); resp1n = rand('bernoulli',0.5); resp2n = rand('bernoulli',pkparm/1000); output; proc sort data = example; by pkparm; We call the macro twice (for the two examples) as follows: %exp_resp_plot(dsin=example, respvar=resp1n, pkparam=pkparm, xlabel=%str('pk Parameter Label'), ylabel=%str('proportion of Subjects with Response Equal to 1'), xval=%str(0 to 1000 by 100), title=%str('exposure-response Plot for Response Variable 1')); %exp_resp_plot(dsin=example, respvar=resp2n, pkparam=pkparm, xlabel=%str('pk Parameter Label'), ylabel=%str('proportion of Subjects with Response Equal to 1'), xval=%str(0 to 1000 by 100), title=%str('exposure-response Plot for Response Variable 2')); The resulting outputs are shown in Figures 2 and 3. 2

3 Figure 2. Exposure-Response Plot of Variable that has no Relationship with PK Parameter Figure 3. Exposure-Response Plot of Variable that has a Relationship with PK Parameter 3

4 SUMMARY An exposure-response plot allows for a quick evaluation of any relationship between a PK parameter and a dichotomous safety or efficacy endpoint. The FDA typically generates their own plots using S-Plus and this paper shows how the same plots can be generated using SAS 9.2 or later using a subject-level dataset that contains variables for the PK parameter and the response variable (coded as 0 or 1). REFERENCES FDA Clinical Pharmacology Review of Zydelig, Accessed 17APR2015. CONTACT INFORMATION Your comments and questions are valued and encouraged. Contact the author at: Name: Janette Garner Company: Gilead Sciences, Inc. Address: 333 Lakeside Dr City, State ZIP: Foster City, CA Work Phone: (650) janette.garner@gilead.com SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are trademarks of their respective companies. 4

5 APPENDIX A SAS CODE TO PRODUCE EXPOSURE-RESPONSE PLOT The following macro will carry out the logistic regression modeling (steps 1 and 2), as well as compute the quartiles of the PK parameter (step 3), and determine the positions and labels for the boxplot and counts (steps 4 and 5). /* Macro to quickly transpose data */ %macro transpose(inds=, prefix=, var=, suffix=, pkparam=); proc transpose data = &inds out=xpk_&var prefix=&prefix %if &inds=pk_cnt %then suffix=&suffix;; id &pkparam.grp; var &var; where &pkparam.grp ^=.; data xpk_&var; set xpk_&var; glue = 1; %mend transpose; /* Conduct the logistic regression modeling and calculate the values to display */ %macro logreg(dsin=,respvar=,pkparam=); *** Output a dataset, ESTIMATED, with the values for (1) and (2) ***; proc logistic DESCENDING data=&dsin.;* noprint; model &respvar. = &pkparam.; output out=estimated predicted=estprob l=lower95 u=upper95; *** Get the quartile group for PK Parameter and determine the cutoffs for the PK parameter for use in (3) ***; proc means data=estimated; var &pkparam.; output out=tmpquar min=minn q1=q1n median=medn q3=q3n max=maxn; proc sql; create table _tmp as select a.*, b.minn, b.q1n, b.medn, b.q3n, b.maxn from estimated as a, tmpquar as b; quit; data estimated; set _tmp; if minn <= &pkparam. <= q1n then &pkparam.grp=1; else if q1n < &pkparam. <= medn then &pkparam.grp=2; else if medn < &pkparam. <= q3n then &pkparam.grp=3; else if q3n < &pkparam. <= maxn then &pkparam.grp=4; *** Determine the values for the boxplot in (4) ***; proc freq data = estimated noprint; by &pkparam.grp; table &respvar. /binomial(level='1'); output out=pk_box(rename=(_bin_=meann L_BIN=lclmn U_BIN=uclmn)) binomial; %transpose(inds=pk_box, prefix=mean_q, var=meann, pkparam=&pkparam.); %transpose(inds=pk_box, prefix=low_q, var=lclmn, pkparam=&pkparam.); %transpose(inds=pk_box, prefix=upp_q, var=uclmn, pkparam=&pkparam.); 5

6 data pk_box_final(drop=_name_); merge xpk_meann xpk_lclmn xpk_uclmn; by glue; *** Determine the n/n values for the annotation in (5) ***; proc freq data = estimated noprint; table &respvar.*&pkparam.grp /out=pk_cnt0 sparse; proc sql; create table pk_cnt as select *, sum(count) as total from pk_cnt0 group by &pkparam.grp; quit; data pk_cnt; set pk_cnt; prop = strip(count) "/" strip(total); where &respvar. = 1; %transpose(inds=pk_cnt, prefix=mid_q, var=prop, suffix=c, pkparam=&pkparam.); *** Prepare the datasets for merging ***; proc sort data = estimated out = est_sort; by &pkparam.; where &pkparam. ^=.; data est_sort0; set est_sort; if _N_ = 1 then glue = 1; else do; glue = 2; minn =.; q1n =.; medn =.; q3n =.; maxn =.; data &respvar.; merge est_sort0 pk_box_final xpk_prop(drop=_name_); by glue; *** Determine midpts of each quartile for plotting boxplot, n/n in (4) and (5) ***; if glue = 1 then do; mid_q1 = (minn + q1n)/2; mid_q2 = (q1n + medn)/2; mid_q3 = (medn + q3n)/2; mid_q4 = (q3n + maxn)/2; *** Assign the y-axis values ***; y_nc = -3; y_pk = -8; y_pk_low = -10; y_pk_upp = -6; *** Rescale y-values to reflect percentage ***; array yvalues {12} mean_q: low_q: upp_q:; do i = 1 to 12; yvalues[i] = 100*yvalues[i]; drop i; /*** Rescale y-values ***/ array logreg {3} estprob lower95 upper95; do i = 1 to 3; logreg[i] = 100*logreg[i]; drop i; 6

7 *** Create macro variables to determine the min and max x-values to plot ***; data _null_; set &respvar.; if _n_ = 1; call symputx('minx',minn); call symputx('maxx',maxn); %mend logreg; proc template; define style listingsf; parent = Styles.Listing; style GraphFonts from GraphFonts "Fonts used in graph styles" / 'GraphDataFont' = ("<sans-serif>, <MTsans-serif>",7pt) 'GraphValueFont' = ("<sans-serif>, <MTsans-serif>",7pt) 'GraphLabelFont' = ("<sans-serif>, <MTsans-serif>",7pt, bold); %macro exp_resp_plot(dsin=,respvar=,pkparam=,xlabel=,ylabel=,xval=,title=); *** Run the logistic regression ***; %global minx maxx; %logreg(dsin=&dsin.,respvar=&respvar.,pkparam=&pkparam.); *** Generate the Exposure-Response Plot ***; ods graphics on / reset=all width=5in height=4in imagemap=on border=off; ods noproctitle; ods listing style=listingsf sge=off image_dpi=300; proc sgplot data = &respvar. noautoleg title &title.; band x=&pkparam lower=lower95 upper=upper95 / fillattrs=(color=cxa9e2ff); /* Item 1 */ series x=&pkparam y=estprob / lineattrs=(color=red) name='logreg' legendlabel='logistic regression'; /* Item 2 */ scatter x=mid_q1 y=mean_q1 / yerrorlower=low_q1 yerrorupper=upp_q1 markerattrs=(symbol=squarefilled) name='obsprop' legendlabel='observed Proportion (95% CI)'; /* Item 3a */ scatter x=mid_q2 y=mean_q2 / yerrorlower=low_q2 yerrorupper=upp_q2 markerattrs=(symbol=squarefilled); /* Item 3b */ scatter x=mid_q3 y=mean_q3 / yerrorlower=low_q3 yerrorupper=upp_q3 markerattrs=(symbol=squarefilled); /* Item 3c */ scatter x=mid_q4 y=mean_q4 / yerrorlower=low_q4 yerrorupper=upp_q4 markerattrs=(symbol=squarefilled); /* Item 3d */ vector x=maxn y=y_pk / xorigin=minn yorigin=y_pk noarrowheads; /* Item 4a */ vector x=minn y=y_pk_upp / xorigin=minn yorigin=y_pk_low noarrowheads; /* Item 4b */ vector x=q1n y=y_pk_upp / xorigin=q1n yorigin=y_pk_low noarrowheads; /* Item 4c */ vector x=medn y=y_pk_upp / xorigin=medn yorigin=y_pk_low noarrowheads; /* Item 4d */ vector x=q3n y=y_pk_upp / xorigin=q3n yorigin=y_pk_low noarrowheads; /* Item 4e */ vector x=maxn y=y_pk_upp / xorigin=maxn yorigin=y_pk_low noarrowheads; /* Item 4f */ /* Item 4a is the main bar, 4b-f are vertical ticks at Min, Q1, Median, Q3, and Max */ scatter x=mid_q1 y=y_nc / markerchar=mid_q1c; /* Item 5a */ scatter x=mid_q2 y=y_nc / markerchar=mid_q2c; /* Item 5b */ scatter x=mid_q3 y=y_nc / markerchar=mid_q3c; /* Item 5c */ scatter x=mid_q4 y=y_nc / markerchar=mid_q4c; /* Item 5d */ 7

8 xaxis min=&minx max=&maxx values=(&xval) valueshint offsetmin=0.01 offsetmax=0.01 label=&xlabel; yaxis min=-10 max=100 values=(0 to 100 by 20) valueshint label=&ylabel; *** Show the legend specified in (6) ***; keylegend 'logreg' 'obsprop' / across=1 location=inside position=topleft; /* Item 6*/ ods listing close; %mend exp_resp_plot; 8