I am using the `glmer` function (`lme4` package) to get estimations in a Poisson regression model (generalized linear model).
I wanted to compare the estimations for the fixed effects with those obtained with the `glm` function.
I was surprised to see big differences !
 I know that `glmer` includes random effect; but that does not suffice to explain theses differences.
 
Could someone explain to me what I missed in my approach ?

**EDIT and ANSWER :**
Put an `offset` term in both `glm`and `glmer`

        library(surrosurv)
        library(survival)
        library(lme4)
    
         data(colon)
         colon1 = subset(colon, etype == 1)
        # Poissonization
    
       don_pois = poissonize(colon1, interval.width = 365.25, factors = c ('surg', 'rx'), compress = FALSE)
       names(don_pois)[3] = 'trt'; names(don_pois)[4] = 'trialref'
        
    
        fitpoi_glmer   <- glmer(
                        formula = event ~ -1 + interval + ( 1 | trialref ),
                        data = don_pois,
                        family = poisson(link = "log")
                         )
        
        
        fitpoi_glm <- glm(
          formula = event ~ -1+ interval + offset(log(time)), 
          data = don_pois, 
          family = poisson(link = "log")
        )
        
    
        summary(fitpoi_glmer)$coefficients 
        summary(fitpoi_glm)$coefficients

    # Survival graphics
    
       fixed.coef.glmer = summary(fitpoi_glmer)$coefficients[,'Estimate']
         risks0 = exp(fixed.coef.glmer[grep("(?!.*:)interval.*", names(fixed.coef.glmer), perl = T)]) * 365.25
         surv0 <- c(1,exp(-cumsum(risks0)))
         x = seq(0, max(colon1$time), length.out = length(surv0))
         plot(x, surv0, type ='l', col = 'blue', lwd = 2)
      
         
         risks3 = exp(coef(fitpoi_glm)[grep("(?!.*:)interval.*", names(coef(fitpoi_glm)), perl = T)]) * 365.25
         surv3 <- c(1,exp(-cumsum(risks3)))
         lines(x, surv3, type ='l', col = 'pink', lwd = 2)
         
         # Comparison with survfit
         lines(survfit(Surv(time, status)~1, data = colon1 ), lty = 2, conf.int= FALSE)