5  IDA plan

5.1 Preparations

1. Statistical analysis plan: as assumed above, the analysis strategy to answer the main research question has been prespecified. It comprises of the set of independent variables to be considered in a model, the outcome variable, and the analytical strategy to build the regression model.

The aim of the analysis is to derive a parsimonious model to predict bacteremia status from age, gender, and 49 continuous laboratory variables. Logistic regression with consideration of nonlinear effects by fractional polynomials will be considered. The multivariable fractional polynomial algorithm will be employed considering first-order fractional polynomials for the continuous covariates. In a first step, optimal transformations for each covariate will be determined without variable selection. In the second step, we will apply the garrote to assign nonnegative shrinkage factors to the coefficients. The shrinkage factors will be determined by optimizing AIC in the second step. It is considered to impute missing values using multiple imputation with chained equations, and to generate a stacked data set for analysis. The number of imputations will be determined after initial data analysis. To assess internal performance of the diagnostic model, we will consider 10-fold cross-validation (CV), repeating the above-described model building steps. The folds will be built by dividing the patient cohort into 10 approximately equally-sized groups. All imputed observations of a patient will be assigned to the same fold. From the 10-fold CV, the area under the ROC, the calibration in the large and the calibration slope will be estimated and reported. The final regression model will be derived from analysing the full cohort with that strategy.

2. Data dictionary and metadata: a detailed data dictionary should be available which informs about the meaning of each variable in context of the research question, the units of measurement, the possible levels in case of categorical variables, or admissible values. More generally, metadata, also refer to information about the research study protocol and data collection processes.

A data dictionary is available.

3. Domain expertise and pivotal covariates (‘very important predictors’, VIPs)

3.1. In particular for analyses with a moderate to high number of covariates, domain expertise should guide assumptions which covariates are considered to be 'strongly related' with the outcome and hence are ‘very important predictors’ in the regression model, and which variables have a weak or unknown association with the outcome (cf. Heinze et al, Biometrical Journal 2018). Depending on context and assumptions on strength of association with the outcome variable, two to three pivotal covariates should be defined (e.g., age and sex).

Pivotal covariates:

Ratzinger et al (2014) cite 5 papers who have proposed a prediction model for bacteremia before. From these papers, the following knowledge could be extracted:

Covariates with assumed strong association with bacteremia:

• Jaimes (2004):
  • age
  • heart rate
  • temperature
  • leukocyte count
  • use of central venous catheter
  • length of hospitalization
• Bates 1997
  • Suspected or documented focal infection at onset
  • antibiotics before onset
  • any liver disease
  • Hickman catheter present
  • altered mental status within 24h
  • focal abdominal signs withing 24h
• Lee (2012)
  • age
  • presence of rigor
  • presence of chills
  • body temperature
  • blood urea nitrogen
  • blood urea nitrogen/creatinine ratio
  • thrombocytopenia
• Tudela (2010)
  • Charlson index
  • PCT
• Kuppermann (1998)
  • age
  • temperature
  • clinical score
  • WBC count
  • absolute neutrophil count
  • absolute band count

It has to be admitted that some of these selections are based on inappropriate methods, e.g., use of univariate logistic regression screening, or were derived for special settings or cohorts, e.g. use in emergency room, or use in children.

Out of the set of variables used in the models of the cited 5 papers, the following six variables also available in our data set and are considered as very important predictors (VIPs):

• age (mentioned in 3 papers)
• leukocytes (WBC) (2)
• blood urea neutrogen (BUN) (1)
• creatinine (KREA) (1)
• thrombocytes (PLT) (1)
• neutrophiles (NEU) (1)

Based on this review, we consider age and leukocytes (WBC) as pivotal covariates for the research question.

3.2. Domain expertise may also be useful to specify in advance which variables are expected to correlate with each other. This background knowledge could be summarized in a directed or undirected acyclic graph connecting the covariates with each other as also suggested by Heinze et al, 2018.

Important variable groups for modeling may be from the group of leukocytes, kidney function related parameters and parameters indicating a reaction to an acute phase.

Leukocytes

The following systematic dependencies between variables exist:

• WBC \(\approx\) BASO + EOS + NEU + LYM + MONO

In some patients, this relation may only approximately apply because they are in an acute infection phase.

Moreover, the following variables are percentages and hence sum up to 100:

• BASOR = BASO / (BASO + EOS + NEU + LYM + MONO) * 100
• EOSR = EOS / (BASO + EOS + NEU + LYM + MONO) * 100
• NEUR = NEU / (BASO + EOS + NEU + LYM + MONO) * 100
  
• MONOR = MONO / (BASO + EOS + NEU + LYM + MONO) * 100
• LYMR = LYM / (BASO + EOS + NEU + LYM + MONO) * 100
• BASOR + EOSR + NEU + MONOR + LYMR = 100

Therefore, at least one of these five variables is redundant.

Acute phase reaction

An acute phase reaction may be indicated by FIB, CRP, and the liver parameters ASAT, ALAT and GGT; hence some correlation between these variables is expected.

Kidney function indicators

Potassium level (K), blood urea nitrogen (BUN) and serum creatinine (Scr, KREA) are variables that are related to kidney function. Kidney function is usually expressed as estimated glomerular filtration rate (eGFR). Using the CKD-EPI-formula, eGFR can be computed as follows, with sex-specific constants \(\kappa\) (kappa) and \(\alpha\) (alpha):

\(eGFR = 141 \times min(Scr/\kappa, 1)^\alpha \times max(Scr/\kappa, 1)^{-1.209} \times 0.993^{age}\)

where for males \(\kappa = 0.9, \alpha = -0.411\), and for females \(\kappa = 0.7, \alpha = -0.329\).

kappa <- rep(0.7, nrow(a_bact))
kappa[a_bact$SEX==1] <- 0.9
alpha <- rep(-0.329, nrow(a_bact))
alpha[a_bact$SEX==1] <- -0.411

a_bact$eGFR <- 141 * apply(cbind(a_bact$CREA/kappa, 1),1,min)**alpha * apply(cbind(a_bact$CREA/kappa, 1),1,max)**(-1.209) * 0.993**a_bact$AGE * 1.018**(a_bact$SEX==2)

a_bact$BUN_CREA <- a_bact$BUN / a_bact$CREA

b_bact <- Hmisc::upData(a_bact ,
               labels = c(eGFR = 'estimated glomerular filtration rate', 
                          BUN_CREA = 'BUN/Scr ratio'),
               units = c(eGFR = 'mL/min/1.73 m^2',
                         BUN_CREA = 'unitless'))

Input object size:   5456368 bytes;  56 variables    14691 observations
New object size:    5456400 bytes;  56 variables    14691 observations

Some correlation between these kidney function indicators (eGFR, potassium, BUN) can be expected. eGFR is a widely accepted and interpretable summary of kidney function. BUN should be in the range 6-20 (8-23 for adults older than 60 years). An ideal ratio of BUN to Scr is between 10 and 20. Ratios higher than 20 may be associated with high protein diet but also with impaired eGFR (lower than 60).

We define groups of variables: demographical, structural, key predictors, leukocyte-related, leukocyte-ratio-related, kidney-related, acute-phase related:

demog_vars <-c("AGE", "SEX")
structural_vars <- c("WBC", "AGE", "SEX")
key_predictors <- c("WBC", "AGE", "BUN","CREA","NEU","PLT")
leuko_related_vars <-c("WBC", "NEU", "EOS", "BASO", "LYM", "MONO")
leuko_ratio_vars <- c("NEUR", "EOSR", "BASOR", "LYMR", "MONOR")
kidney_related_vars <- c("BUN", "POTASS", "CREA", "eGFR", "BUN_CREA")
acute_related_vars <- c("FIB", "CRP", "ASAT", "ALAT", "GGT")
outcome_vars <-c("BloodCulture", "BC")
remaining_vars <- names(a_bact)[is.na(match(names(a_bact),c("ID", demog_vars, structural_vars, key_predictors,leuko_related_vars,leuko_ratio_vars, kidney_related_vars,acute_related_vars, outcome_vars)))]

bact_variables <- list(demog_vars=demog_vars, structural_vars=structural_vars, key_predictors=key_predictors, leuko_related_vars=leuko_related_vars, leuko_ratio_vars=leuko_ratio_vars, kidney_related_vars=kidney_related_vars, acute_related_vars=acute_related_vars,
                       remaining_vars=remaining_vars, outcome_vars=outcome_vars)

3.3. Missing value mechanisms: if not already specified in meta data, domain experts should also be consulted to explain possible reasons for the occurrence of missing values for each variable, which may be categorized as systematic or unsystematic.

A certain proportion of missing values is expected because of the lab test request which is often specific to the underlying condition. No specific expectations can be made.

5.2 IDA domains

5.3 Sources

Data is available in this repository (subfolder data).

To download the data set, click the link to data set

5.4 References

Ratzinger, F., Dedeyan, M., Rammerstorfer, M., Perkmann, T., Burgmann, H., Makristathis, A., Dorffner, G., Lötsch, F., Blacky, A., Ramharter, M., 2014. A Risk Prediction Model for Screening Bacteremic Patients: A Cross Sectional Study. PLOS ONE 9, e106765. doi:10.1371/journal.pone.0106765

save(list=c("b_bact", "bact_variables", "demog_vars", "structural_vars","key_predictors","leuko_related_vars","leuko_ratio_vars","kidney_related_vars", "acute_related_vars","remaining_vars"), file = here::here("data", "bact_env_b.rda"))