Software requirements

SAS V9.4 or higher.

Installation

Below download times should only take a few seconds.

1. Download and uncompress simdata.zip to obtain simdata.csv. This provides simulated participant level data to fit a ToP model similar to the manuscript.
2. Download ToPModel.sas. This provides SAS code to fit the ToP model to simdata.csv and generate efficacy point estimates and bootstrapped two-sided 90% confidence intervals.

Instructions to run code

1. Open ToPModel.sas in SAS V9.4 or higher.
2. Set macro variables on lines 1-2 as described in ToPModel.sas.
3. Run code. Run time will highly dependent on the number of bootstrap samples defined.

Variables in simdata.csv:

• id = participant ID

• z = 1 if received treatment, else 0

• start, stop = daily at-risk intervals relative to time since dose

• ev = 1 if participant had an event between [start, stop] days after dose, else 0

• conc = daily serum mAb concentration (μg/mL) predicted from pop-PK

• wtg = prevalence-adjusted IC50 (ng/mL)

• wtg_nab = prevalence-adjusted nAb titre, calculated as (conc*1000)/wtg

• wtglnab = log10(wtgnab+1)

Results

In the below example NBOOT is set to 10. This take approximately 20 seconds to run.

%let DPATH = <SET TO LOCAL FILE PATH WHERE SIMDATA.CSV IS SAVED.>;
%let NBOOT = <SET TO NUMBER OF BOOTSTRAP REPLICATES. CAN BE SET TO SMALLER NUMBER (E.G. 10) FOR QUICK RUN TIME.>;
goptions device=png;
ods graphics on / reset=all noborder width=10in height=6in;
proc datasets kill nolist mt=data lib=work;
run;
quit;

*Read in simulated TTE data;
proc import datafile="&DPATH.simdata.csv" out=simdata dbms=csv replace;
proc sort;
    by z id start;
run;

*Fit ToP Cox Model on full data to get efficacy point estimates;
ods exclude hazardratios;
proc phreg data = simdata covout outest=mat;
    model (start, stop)*ev(0) = z z*wtg_lnab / rl ties=efron;
    hazardratio z / at(wtg_lnab = 0.001 to %sysevalf(%sysfunc(ceil(%sysfunc(log10(1e5+1))*1000))/1000) by 0.001);
    ods output hazardratios = hrfull;
run;

data efffull;
    set hrfull;
    *Derive efficacy as 1 - HR;
    eff = 100*(1 - hazardratio);
    *Get covariate value HR assessed at;
    wtg_lnab = input(scan(scan(description,3,'='),1,' '),best.);
    *Backmap to nAbs;
    nab = (10**wtg_lnab)-1;
    keep eff: nab;
proc sort;
    by nab;
run;

*Bootstrapped confidence interval;
proc sql noprint;
    select count(distinct id) into :n trimmed from simdata;
quit;
ods select none;
*Resample with replacement with each size equivalence to the total sample size from the original data;
proc surveyselect data=simdata out=bootsamp method=urs reps=&NBOOT seed=7442 sampsize=&n outhits;
    cluster z id;
run;
*Fit model and derive efficacy (similar to above) for each replicate;
proc phreg data = bootsamp;
    by replicate;
    model (start, stop)*ev(0) = z z*wtg_lnab / rl ties=efron;
    hazardratio z / at(wtg_lnab = 0.001 to %sysevalf(%sysfunc(ceil(%sysfunc(log10(1e5+1))*1000))/1000) by 0.001) alpha=0.1;
    ods output hazardratios = hrboot;
run;
data effboot;
    set hrboot;
    eff = 100*(1 - hazardratio);
    wtg_lnab = input(scan(scan(description,3,'='),1,' '),best.);
    nab = (10**wtg_lnab)-1;
    keep replicate eff: nab;
proc sort;
    by nab;
run;
*Calculate the two-side 90 percent CI using the quantile approach;
proc univariate data=effboot;
    by nab;
    var eff;
    output out=booteff(rename=(eff5 = eff_l eff95=eff_u)) pctlpre=eff pctlpts=5, 95;
run;
ods select all;

*Combine point estimates from full data with bootstrapped CIs;
data ToPCox;
    merge efffull(in=a) booteff;
    by nab;
    if a;
run;

*Plot threshold curve;
proc sgplot data=ToPCox noautolegend noborder nowall;
    series y=eff x=nab / lineattrs=(color=cx830051);
    band lower=eff_l upper=eff_u x=nab / transparency=.8 fillattrs=(color=cx830051);
    xaxis type=log logbase=10 values=(1e1 1e2 1e3 1e4 1e5) label='Prevalence-adjusted nAb titre';
    yaxis values=(0 to 100 by 10) label='Efficacy (%)';
run;