Supplementary data

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Supplementary data Methods extended

The criteria considered for model selection were the log-likelihood ratio test, based on the reduction of the objective function value provided by NONMEM® (OFV), as well as diagnostic plots and precision of parameters estimates (relative standard error, RSE). In the forward inclusion of covariates, a decrease in OFV greater than 3.84 (P<0.05) for 1 additional parameter was considered statistically significant, while an increase in OFV greater than 7.88 (P<0.005) was considered statistically significant in the backward stepwise covariate elimination (ΔOFV between any two nested models approximates a χ2 distribution).

Nonparametric bootstrapping (2000 replicates) was used to evaluate the precision of BMI and WHR final models, generating 95% confidence intervals (CI95%) for parameters estimates.

Prediction-corrected Visual predictive checks (pcVPCs), in which observed measurements were visually compared with 5^th, 50^th and 95^th prediction percentiles, were used to evaluate the predictive performance of the models.

Using the final model estimates with variability, we predicted BMI and WHR values in each individual over a ten-year period after ART initiation. We also simulated BMI and WHR values for 10’000 individuals using the bootstrap models estimates (2000 sets of parameters) to account for imprecision in the model estimates and extrapolate the model results to the population of interest. Based on these simulated values, we classified individuals according to the WHO cut- offs for pre-obesity and abdominal obesity (BMI ≥ 25 kg/m²and WHR >0.9 for men and >0.85 for women) [1, 2].

BMI and WHR model validation

Both BMI and WHR models were considered reliable based on bootstrap median values contained within the 95% CI and differing by <10% from the population estimates. Goodness of fit plots and pcVPCs showed an overall good predictive performance (Supplementary Figure 1- 6).

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Annex 1. NONMEM code for the structural BMI piecewise-linear model.

$PROBLEM BMI study

$INPUT ID DAT2=DROP TIME TART DV SEX ETHNICITY NADIRCAT DIAB CIG AGE0 WHR0

$DATA data.csv TRANSLATE=(TIME/8766)

$SUBROUTINES ADVAN13 TOL=9

$MODEL COMP=(EFFECT)

$PK

TVBASE = THETA(1)

BASE = TVBASE * EXP(ETA(1)) TVSLOPE1 = THETA(2)

SLOPE1 = TVSLOPE1 + ETA(2) TVSLOPE2 = THETA(3)

SLOPE3 = TVSLOPE3 + ETA(4)

;; piecewise linear model

IF(TART.LE.1.5) SLOPE = SLOPE1

IF(TART.GT.1.5.AND.TART.LE.3) SLOPE = SLOPE2 IF(TART.GT.3) SLOPE = SLOPE3

A_0 (1)= BASE ;; compartment initiation

$DES

DADT(1) = SLOPE ; linear

$ERROR

IPRED = LOG( A(1) ) Y = IPRED + ERR(1) IRES = DV-IPRED IWRES = IRES/IPRED

$THETA (23.5) ; BASE

(-5, 0.0741,5) ; SL<1.5y (-5, 0.275,5) ; SL1.5-3y (-5, 0.02,5) ; SL>3y

$OMEGA

0.0212 ; ETA_BASE 0.0828 ; ETA_SL<1.5y 0.1 ; ETA_SL1.5-3y 0.1 ; ETA_SL>3y

$SIGMA 0.00188

$EST METHOD=1 INTERACTION MAXEVAL=9900

$COV 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

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Annex 2. NONMEM code for the final covariate BMI piecewise-linear model.

$PROBLEM BMI study

$INPUT ID DAT2=DROP TIME TART DV SEX ETHNICITY NADIRCAT DIAB CIG AGE0 WHR0

$SUBROUTINE ADVAN13 TOL=9

$PK

;;; SLOPE1NADIRCAT-DEFINITION START

IF(NADIRCAT.EQ.1) SLOPE1NADIRCAT = ( 1 + THETA(13)) IF(NADIRCAT.EQ.3) SLOPE1NADIRCAT = 1

IF(NADIRCAT.EQ.2) SLOPE1NADIRCAT = ( 1 + THETA(14))

;;; SLOPE1NADIRCAT-DEFINITION END

;;; SLOPE1-RELATION START SLOPE1COV=SLOPE1NADIRCAT

;;; SLOPE1-RELATION END

;;; BASENADIRCAT-DEFINITION START

IF(NADIRCAT.EQ.1) BASENADIRCAT = ( 1 + THETA(12)) IF(NADIRCAT.EQ.3) BASENADIRCAT = 1

IF(NADIRCAT.EQ.2) BASENADIRCAT = ( 1 + THETA(12))

;;; BASENADIRCAT-DEFINITION END

;;; BASEETHNICITY-DEFINITION START

IF(ETHNICITY.EQ.2) BASEETHNICITY = ( 1 + THETA(10)) IF(ETHNICITY.EQ.0) BASEETHNICITY = 1

IF(ETHNICITY.EQ.1) BASEETHNICITY = 1 IF(ETHNICITY.EQ.3) BASEETHNICITY = 1

IF(ETHNICITY.EQ.4) BASEETHNICITY = ( 1 + THETA(11))

;;; BASEETHNICITY-DEFINITION END

;;; BASEDIAB-DEFINITION START

IF(DIAB.EQ.1) BASEDIAB = ( 1 + THETA(9)) IF(DIAB.EQ.0) BASEDIAB = 1

;;; BASEDIAB-DEFINITION END

;;; BASECIG-DEFINITION START

IF(CIG.NE.1) BASECIG = ( 1 + THETA(8)) IF(CIG.EQ.1) BASECIG = 1

;;; BASECIG-DEFINITION END

;;; BASEWHR0-DEFINITION START

BASEWHR0= ( 1 + THETA(7)*((WHR0 - 0.89)/0.89))

;;; BASEWHR0-DEFINITION END

;;; BASEAGE0-DEFINITION START

BASEAGE0= ( 1 + THETA(6)*((AGE0 - 40.00)/40.00))

;;; BASEAGE0-DEFINITION END 68

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;;; BASE-RELATION START

BASECOV=BASEAGE0*BASECIG*BASEDIAB*BASEETHNICITY*BASENADIRCAT*BASEWH R0

;;; BASE-RELATION END TVBASE = THETA(1)

TVBASE = BASECOV*TVBASE BASE = TVBASE * EXP(ETA(1))

TVSLOPE1 = THETA(2)

TVSLOPE1 = SLOPE1COV*TVSLOPE1 SLOPE1 = TVSLOPE1 + ETA(2)

TVSLOPE2 = THETA(3)

SLOPE3 = TVSLOPE3 + ETA(4) IF(TART.LE.1.5) SLOPE = SLOPE1

A_0 (1)= BASE

$DES

$ERROR

IPRED = LOG( A(1) ) W=THETA(5)

Y = IPRED + W*ERR(1) IRES = DV-IPRED IWRES = IRES/IPRED

$THETA

23.4007 ; BASE

(-5,0.269194,5) ; SL<1.5y (-5,0.165037,5) ; SL1.5-3y (-5,0.10202,5) ; SL>3y 0.0331525 ; W

$THETA (-10.00,0.0852687,1000000) ; BASEAGE0

$THETA (-10.00,0.0852687,1000000) ; BASEWHR0

$THETA ( -1.00,0.034914,1000000) ; BASECIG

$THETA ( -1.00,0.176069,1000000) ; BASEDIAB

$THETA ( -1.00,0.0733542,1000000) ; BASEETHNICITYAFRICAN ( -1.00,-0.0796919,1000000) ; BASEETHNICITYASIAN

$THETA ( -1.00,-0.0611332,1000000) ; BASENADIR<200 117

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$THETA (-1000000,5.4111,1000000) ; SL1NADIR<100 (-1000000,0.937967,1000000) ; SL1NADIR100-200

$OMEGA 0.0192042 ; ETA_BASE 0.72461 ; ETA_SL<1.5y

0.600887 ; ETA_SL1.5-3y 0.110867 ; ETA_SL>3y

$SIGMA 1 FIX

$ESTIMATION METHOD=1 INTERACTION MAXEVAL=9900

$COV 163 164 165 166 167 168 169 170 171 172 173

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Annex 3. NONMEM code for the structural WHR piecewise-linear model.

$PROBLEM WHR study

$INPUT ID DAT1=DROP TIME TART DV BMI0 SEX ETHNICITY NADIRCAT AGE0

$PK

TVBASE = THETA(1)

BASE = TVBASE * EXP(ETA(1)) TVSLOPE1 = THETA(2)

SLOPE3 = TVSLOPE3 + ETA(4) IF(TART.LE.2.5) SLOPE = SLOPE1

A_0 (1)= BASE

$DES

$ERROR

$THETA 0.893 ; BASE

(-5,0.00503,5) ; SL<2.5y (-5,0.00465,5) ; SL2.5-4y (-5,0.00338,5) ; SL>4y

$OMEGA BLOCK(4) 0.01 ; ETA_BASE

0.001 0.01 ; ETA_SL<2.5y

0.001 0.001 0.01; ETA_SL<2.5-4y 0 0.001 0.001 0.01 ; ETA_SL>4y

$SIGMA 0.00161

$COV 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221

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Annex 4. NONMEM code for the final covariate WHR piecewise-linear model.

$PROBLEM WHR study

$INPUT ID DAT1=DROP TIME TART DV BMI0 SEX ETHNICITY NADIRCAT AGE0

$PK

;;; SLOPE3ETHNICITY-DEFINITION START

IF(ETHNICITY.EQ.2) SLOPE3ETHNICITY = ( 1 + THETA(9)) IF(ETHNICITY.EQ.1) SLOPE3ETHNICITY = 1

IF(ETHNICITY.EQ.3) SLOPE3ETHNICITY = ( 1 + THETA(9)) IF(ETHNICITY.EQ.4) SLOPE3ETHNICITY = 1

;;; SLOPE3ETHNICITY-DEFINITION END

;;; SLOPE3-RELATION START SLOPE3COV=SLOPE3ETHNICITY

;;; SLOPE1NADIRCAT-DEFINITION START

IF(NADIRCAT.EQ.1) SLOPE1NADIRCAT = ( 1 + THETA(8)) IF(NADIRCAT.NE.1) SLOPE1NADIRCAT = 1

;;; SLOPE1NADIRCAT-DEFINITION END

;;; SLOPE1-RELATION START SLOPE1COV=SLOPE1NADIRCAT

;;; BASESEX-DEFINITION START

IF(SEX.EQ.1) BASESEX = ( 1 + THETA(7)) IF(SEX.EQ.2) BASESEX = 1

;;; BASESEX-DEFINITION END

;;; BASEBMI0-DEFINITION START

BASEBMI0= ( 1 + THETA(6)*((BMI0 - 23.24)/23.24))

;;; BASEBMI0-DEFINITION END

;;; BASEAGE0-DEFINITION START

BASEAGE0= ( 1 + THETA(5)*((AGE0 - 40.00)/40.00))

;;; BASEAGE0-DEFINITION END

;;; BASE-RELATION START

BASECOV=BASEAGE0*BASEBMI0*BASESEX

;;; BASE-RELATION END TVBASE = THETA(1)

TVBASE = BASECOV*TVBASE BASE = TVBASE * EXP(ETA(1)) 222

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TVSLOPE1 = THETA(2)

TVSLOPE2 = THETA(3)

SLOPE2 = TVSLOPE2 + ETA(3)

TVSLOPE3 = THETA(4)

IF(TART.LE.2.5) SLOPE = SLOPE1

A_0 (1)= BASE

$DES

$ERROR

$THETA

0.904287 ; BASE

(-5,0.00363326,5) ; SL<2.5y (-5,0.00426525,5) ; SL2.5-4y (-5,0.00651279,5) ; SL>4y

$THETA (-1000000,0.0881125,1000000) ; BASEAGE0

$THETA (-1000000,0.160276,1000000) ; BASEBMI0

$THETA (-1000000,-0.0667023,1000000) ; BASEMale

$THETA (-1000000,1.69968,1000000) ; SLOPE1NADIR<100

$THETA (-1000000,-0.560659,1000000) ; SLOPE3AFRICAN/HISP

$OMEGA BLOCK(4) 0.01 ; ETA_BASE

0.001 0.01 ; ETA_SL<2.5y

0.001 0.001 0.01; ETA_SL<2.5-4y 0 0.001 0.001 0.01 ; ETA_SL>4y

$SIGMA 0.00156128

$COV 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319

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References

1. WHO. World Health Organisation obesity and overweight Key facts Available at:

http://www.who.int/en/news-room/fact-sheets/detail/obesity-and-overweight. Accessed 5 May 2018.

2. WHO. Waist circumference and waist–hip ratio: Report of a WHO expert consultation.

Available at: http://apps.who.int/iris/bitstream/handle/10665/44583/9789241501491_eng.pdf.

Accessed 1 May 2018.

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