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Correcting first-year mortality estimates for loss to follow up in antiretroviral treatment programmes in sub-Saharan Africa.

% mortality in patients retained in care:  MNL
Estimate at one year
95% CI lower bound
95% CI upper bound
% mortality in patients lost to follow-up:  ML
Estimate at one year
95% CI lower bound
95% CI upper bound
Proportion of patients lost to follow-up:  r (= NL / NR * 100)
Number of eligible patients for determining the proportion lost to follow-up
Number of patients lost to follow-up
R Code
M_nltfu <- as.numeric(par1) #estimated mortality % at 1 year from a Kaplan Meier M_nltfu_lb <- as.numeric(par2) # 95%CI lower bound M_nltfu_ub <- as.numeric(par3) # 95%CI upper bound M_ltfu <- as.numeric(par6) #estimated mortality % at 1 year from a Kaplan Meier M_ltfu_lb <- as.numeric(par7) # 95%CI lower bound M_ltfu_ub <- as.numeric(par8) # 95%CI upper bound N_ltfu <- as.numeric(par4) # N potential LTFU n_ltfu <- as.numeric(par5) # N true LTFU S_nltfu <- (100-M_nltfu)/100 # estimated survival at 1 year from a Kaplan Meier S_nltfu_lb <- (100-M_nltfu_ub)/100 # 95%CI lower bound S_nltfu_ub <- (100-M_nltfu_lb)/100 # 95%CI upper bound S_ltfu <- (100-M_ltfu)/100 # estimated survival at 1 year from a Kaplan Meier S_ltfu_lb <- (100-M_ltfu_ub)/100 # 95%CI lower bound S_ltfu_ub <- (100-M_ltfu_lb)/100 # 95%CI upper bound display_error <- '' if(is.na(M_nltfu_lb)) { display_error = 'Please, enter 95%CI lower bound' } else { if (M_nltfu_lb < 0.01) display_error = 'Please, enter a higher 95%CI lower bound' if (M_nltfu_lb > M_nltfu) display_error = 'Please, enter a 95%CI lower bound which is lower than the Estimate at one year' } if(is.na(M_nltfu_ub)) { display_error = 'Please, enter 95%CI upper bound' } else { if (M_nltfu_ub > 99) display_error = 'Please, enter a lower 95%CI upper bound' if (M_nltfu_ub < M_nltfu) display_error = 'Please, enter a 95%CI upper bound which is higher than the Estimate at one year' } if(is.na(M_nltfu)) { display_error = 'Please, enter Estimate at one year' } else { if (M_nltfu < 0.01) display_error = 'Please, enter a higher Estimate at one year' if (M_nltfu > 99) display_error = 'Please, enter a smaller Estimate at one year' } if(is.na(M_ltfu_lb)) { display_error = 'Please, enter 95%CI lower bound' } else { if (M_ltfu_lb < 0.01) display_error = 'Please, enter a higher 95%CI lower bound' if (M_ltfu_lb > M_ltfu) display_error = 'Please, enter a 95%CI lower bound which is lower than the Estimate at one year' } if(is.na(M_ltfu_ub)) { display_error = 'Please, enter 95%CI upper bound' } else { if (M_ltfu_ub > 99) display_error = 'Please, enter a lower 95%CI upper bound' if (M_ltfu_ub < M_ltfu) display_error = 'Please, enter a 95%CI upper bound which is higher than the Estimate at one year' } if(is.na(M_ltfu)) { display_error = 'Please, enter Estimate at one year' } else { if (M_ltfu < 0.01) display_error = 'Please, enter a higher Estimate at one year' if (M_ltfu > 99) display_error = 'Please, enter a smaller Estimate at one year' } if(is.na(N_ltfu)) { display_error = 'Please, enter the Number of eligible patients for determining the proportion lost to follow-up' } else { if (N_ltfu < 1) display_error = 'Please, enter a higher Number of eligible patients for determining the proportion lost to follow-up' } if(is.na(n_ltfu)) { display_error = 'Please, enter the Number of patients lost to follow-up' } else { if (n_ltfu > N_ltfu) display_error = 'Please, enter a lower Number of patients lost to follow-up' } load(file='createtable') table.element <- function(mytable,x,colspan=1,header=FALSE,align='left',bg='white'){ if (colspan>1){ mytable <- paste(mytable,'<td bgcolor=',bg,' align=',align,' colspan=',colspan,sep='') } else mytable <- paste(mytable,'<td bgcolor=',bg,' align=',align,'',sep='') if (header) mytable <- paste(mytable,' bgcolor=#CCCCCC>',sep='') else mytable <- paste(mytable,' bgcolor=#FFFFFF>',sep='') mytable <- paste(mytable,x,'</td>',sep='') } if (display_error != '') { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Error',1,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,display_error,1,FALSE,align='center') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable0.tab') } else { n_rep<-10^5 set.seed(12345) seu_S_nltfu<-(log(-log(S_nltfu))-log(-log(S_nltfu_ub)))/1.96 sel_S_nltfu<-(log(-log(S_nltfu_lb))-log(-log(S_nltfu)))/1.96 se_S_nltfu<-mean(c(seu_S_nltfu,sel_S_nltfu)) m_S_nltfu<-log(-log(S_nltfu)) dev_S_nltfu<-rnorm(n_rep, mean = m_S_nltfu, sd = se_S_nltfu) dev_S_nltfu<-exp(-exp(dev_S_nltfu)) seu_S_ltfu<-(log(-log(S_ltfu))-log(-log(S_ltfu_ub)))/1.96 sel_S_ltfu<-(log(-log(S_ltfu_lb))-log(-log(S_ltfu)))/1.96 se_S_ltfu<-mean(c(seu_S_ltfu,sel_S_ltfu)) m_S_ltfu<-log(-log(S_ltfu)) dev_S_ltfu<-rnorm(n_rep, mean = m_S_ltfu, sd = se_S_ltfu) dev_S_ltfu<-exp(-exp(dev_S_ltfu)) dev_R_ltfu<-rbinom(n_rep, N_ltfu, n_ltfu/N_ltfu)/N_ltfu dev_M_corr<-(1-dev_R_ltfu)*(1-dev_S_nltfu)+dev_R_ltfu*(1-dev_S_ltfu) M_corr<-median(dev_M_corr)*100 M_corr_ci<-quantile(dev_M_corr,c(0.025,0.975))*100 M_corr M_corr_ci } if (display_error == '') { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Kaplan-Meier Estimate for Mortality of Patients Not Lost to Follow-Up (%)',3,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Estimate',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Lower limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Upper limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,round(M_nltfu,2),align='center') a<-table.element(a,round(M_nltfu_lb,2),align='center') a<-table.element(a,round(M_nltfu_ub,2),align='center') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Kaplan-Meier Estimate for Mortality of Patients Lost to Follow-Up (%)',3,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Estimate',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Lower limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Upper limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,round(M_ltfu,2),align='center') a<-table.element(a,round(M_ltfu_lb,2),align='center') a<-table.element(a,round(M_ltfu_ub,2),align='center') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable0.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Loss to Follow-up in Programme',2,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number at risk (eligible)',1,TRUE,bg='#DADADA') a<-table.element(a,'Number lost to follow',1,TRUE,bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,N_ltfu,align='center') a<-table.element(a,n_ltfu,align='center') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'<b>Estimate of Overall Mortality (%) for Programme</b>',3,TRUE,align='center',bg='#D2D1F1') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Estimate',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Lower limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.element(a,'Upper limit of 95% CI',1,TRUE,align='center',bg='#DADADA') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,round(M_corr,1),align='center') a<-table.element(a,round(M_corr_ci[1],1),align='center') a<-table.element(a,round(M_corr_ci[2],1),align='center') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable2.tab') }
© Patrick Wessa

Cite this software as:

Martin WG Brinkhof, Ben D Spycher, 2010, Correcting Mortality Estimates for Loss to Follow-up in sub-Saharan African ART Programmes (v1.0) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_mortality_mc.wasp/

The R code is based on :

Egger M, Spycher BD, et al. under review (source updated ASAP).

To cite Wessa.net in publications use:
Wessa, P. (2025), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL http://www.wessa.net/

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Algorithms & Software : Patrick Wessa, PhD
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