# Excess Hazard Modelling Considering Inappropriate Mortality Rates Contains functions to fit excess hazard models, with or without proportional population hazards assumption. The baseline excess hazard could be a piecewise constant function or a B-splines. When B-splines is choosen for the baseline excess hazard, the user can specify some covariates which have a time-dependent effect (using "bsplines") on the baseline excess hazard. The user can also specify if the framework corresponds to the classical excess hazard modeling, i.e. assuming that the expected mortality of studied individuals is appropriate. He can also consider two other frameworks: first, the expected mortality available in the life table is not accurate and requires taking into account an additional variable in the life table by allowing the latter acts on the general population morality with a proportional effect. This approach is presented by Touraine et al. (2020) [doi:10.1177/0962280218823234](doi:10.1177/0962280218823234). The user can also fit a model that relax the proportional expected hazards assumption considered in the latter excess hazard model. This extension was proposed by Mba et al. (2020) [doi:10.1186/s12874-020-01139-z](doi:10.1186/s12874-020-01139-z) allows non-proportional effect of the additional variable on the general population mortality; second, there is a non-comparability source of bias in terms of expected mortality of selected individuals in a non-population-based studies such as clinical trials. The related excess hazard model correcting this source of bias is presented in Goungounga et al. (2019) [doi:10.1186/s12874-019-0747-3](doi:10.1186/s12874-019-0747-3). The optimization process in these presented models uses the maximum likelihood method through the routine `optim` or an internal function of the `xhaz-package`. Finally, it is now possible to fit a rescaled excess hazard regression model using various flexible parametrisations proposed by the mexhaz R package. Moreover, the package enables the implementation of a rescaled random effects excess hazard regression model, which allows for the examination of heterogeneity between clusters (i.e., random effects at the cluster level) impacts on excess hazard, as well as the investigation of potentially inappropriate mortality rates. In other words, the latter concerns situations where the assumption of comparability between other-cause mortality rates in the cohort under study and observed mortality rates in the general population may be invalid, which could introduce bias into the estimation of excess hazard model parameters (Goungounga et al. (2023) [doi:10.1002/bimj.202100210](doi:10.1002/bimj.202100210)). package ## Details ||| |:--|:--| |Package:|xhaz| |Type:|Package| |Version:|2.0.2| |Date:|2024-04-25| |License:|GPL-3| ## Examples ```r library("numDeriv") library("survexp.fr") library("splines") data("simuData", "dataCancer", package = "xhaz") # load the data sets 'simuData' and 'dataCancer'. # Esteve et al. model: baseline excess hazard is a piecewise function # linear and proportional effects for the covariates on # baseline excess hazard. fit.estv1 <- xhaz(formula = Surv(time_year, status) ~ agec + race, data = simuData, ratetable = survexp.us, interval = c(0, NA, NA, NA, NA, NA, max(simuData$time_year)), rmap = list(age = 'age', sex = 'sex', year = 'date'), baseline = "constant", pophaz = "classic") fit.estv1 # Touraine et al. model: baseline excess hazard is a piecewise function # with a linear and proportional effects for the # covariates on the baseline excess hazard. # An additionnal cavariate (here race) missing in the life table is # considered by the model. fit.corrected1 <- xhaz(formula = Surv(time_year, status) ~ agec + race, data = simuData, ratetable = survexp.us, interval = c(0, NA, NA, NA, NA, NA, max(simuData$time_year)), rmap = list(age = 'age', sex = 'sex', year = 'date'), baseline = "constant", pophaz = "corrected", add.rmap = "race") fit.corrected1 # An additionnal cavariate (here race) missing in the life table is # considered by the model with a breakpoint at 75 years fit.corrected2 <- xhaz(formula = Surv(time_year, status) ~ agec + race, data = simuData, ratetable = survexp.us, interval = c(0, NA, NA, NA, NA, 6), rmap = list(age = 'age', sex = 'sex', year = 'date'), baseline = "constant", pophaz = "corrected", add.rmap = "race", add.rmap.cut = list(breakpoint = TRUE, cut = 75)) fit.corrected2 data("breast") #load the data sets 'breast'. # Flexible mexhaz model: baseline excess hazard with cubic B-splines # assumption on the life table available : # other cause mortality in the cohort is comparable to the mortality # observed in the general population with the same characteristics. # The life table to be used is survexp.us. Note that SEX is coded 2 instead of female in survexp.us. breast$sexe <- "female" fit.haz <- exphaz( formula = Surv(temps, statut) ~ 1, data = breast, ratetable = survexp.us, only_ehazard = FALSE, rmap = list(age = 'age', sex = 'sexe', year = 'date')) breast$expected <- fit.haz$ehazard breast$expectedCum <- fit.haz$ehazardInt mod.bs <- mexhazLT(formula = Surv(temps, statut) ~ agecr + armt, data = breast, ratetable = survexp.us, degree = 3, knots=quantile(breast[breast$statut==1,]$temps, probs=c(1:2/3)), expected = "expected",expectedCum = "expectedCum", base = "exp.bs", pophaz = "classic") mod.bs # Flexible mexhaz model: baseline excess hazard with cubic B-splines # assumption on the life table available : # other cause mortality in the cohort is different to the mortality # observed in the general population with the same characteristics. mod.bs2 <- mexhazLT(formula = Surv(temps, statut) ~ agecr + armt, data = breast, degree = 3, knots=quantile(breast[breast$statut==1,]$temps, probs=c(1:2/3)), expected = "expected",expectedCum = "expectedCum", base = "exp.bs", pophaz = "rescaled") mod.bs2 # Flexible mexhaz model with a random effects at cluster level: # baseline excess hazard with cubic B-splines # assumption on the life table used : # other cause mortality in the cohort is different to the mortality # observed in the general population with the same characteristics. mod.bs3 <- mexhazLT(formula = Surv(temps, statut) ~ agecr + armt, data = breast, degree = 3, knots=quantile(breast[breast$statut==1,]$temps, probs=c(1:2/3)), expected = "expected",expectedCum = "expectedCum", base = "exp.bs", pophaz = "rescaled", random = "hosp") mod.bs3 ``` ## References Goungounga JA, Touraine C, Graff\'eo N, Giorgi R; CENSUR working survival group. Correcting for misclassification and selection effects in estimating net survival in clinical trials. BMC Med Res Methodol. 2019 May 16;19(1):104. doi: 10.1186/s12874-019-0747-3. PMID: 31096911; PMCID: PMC6524224. ([PubMed](https://pubmed.ncbi.nlm.nih.gov/31096911/)) Touraine C, Graff\'eo N, Giorgi R; CENSUR working survival group. More accurate cancer-related excess mortality through correcting background mortality for extra variables. Stat Methods Med Res. 2020 Jan;29(1):122-136. doi: 10.1177/0962280218823234. Epub 2019 Jan 23. PMID: 30674229. ([PubMed](https://pubmed.ncbi.nlm.nih.gov/30674229/)) Mba RD, Goungounga JA, Graff\'eo N, Giorgi R; CENSUR working survival group. Correcting inaccurate background mortality in excess hazard models through breakpoints. BMC Med Res Methodol. 2020 Oct 29;20(1):268. doi: 10.1186/s12874-020-01139-z. PMID: 33121436; PMCID: PMC7596976. ([PubMed](https://pubmed.ncbi.nlm.nih.gov/33121436/)) Goungounga, JA, Graff\'eo N, Charvat H, Giorgi R. “Correcting for heterogeneity and non-comparability bias in multicenter clinical trials with a rescaled random-effect excess hazard model.” Biometrical journal. Biometrische Zeitschrift vol. 65,4 (2023): e2100210. doi:10.1002/bimj.202100210.PMID: 36890623; ([PubMed](https://pubmed.ncbi.nlm.nih.gov/36890623/)) ## Author(s) Maintainer : Juste Goungounga juste.goungounga@ehesp.fr ([ORCID](https://orcid.org/0000-0002-9039-2639)) Authors: * Hadrien Charvat ([ORCID](https://orcid.org/0000-0003-3624-1394)) * Darlin Mba ([ORCID](https://orcid.org/0000-0001-9768-0230)) * Nathalie Graffeo ([ORCID](https://orcid.org/0000-0001-7227-7525)) * Roch Giorgi ([ORCID](https://orcid.org/0000-0001-6135-3078))