Table 3 Results of multivariable parametric Gompertz distribution cluster-level shared frailty survival regression model among under-five children in Malawi,

Age of mother

 20–29

2.1557*

0.8251

1.0181

4.5645

 30–39

3.7526*

1.7551

1.5004

9.3853

 40–49

11.4197*

6.3899

3.8139

34.1936

Birth Order

 3–4

0.7407

0.1900

0.4481

1.2244

 4 or more

0.4917*

0.1863

0.2339

1.0334

 Household size

0.8558

0.0441

0.7736

0.9468

 Sex of household head

0.7650

0.1851

0.4761

1.2291

Antenatal visits

 Less than 4 ANC visits

3.0074*

0.6427

1.9782

4.5720

Socioeconomic status (Poverty)

 Middle

1.0783

0.2558

0.6774

1.7166

 Rich

0.6547*

0 .135577

0 .4362

0.9824

Use of mosquito nets

0.3189*

0.0633

0.2161

0.4706

Early breast feeding at birth

0.2074*

0.0391

0.1432

0.3002

Place of Birth

 Public hospital

0.6755

0.2305

0.3461

1.3184

 Private hospital

0.8918

0.3510

0.4123

1.9289

Birth weight

 Hight birthweight

0.6719

0.1686

0.4109

1.0986

Place of residence

 Residence

0.5300*

0.1726

0.2800

1.0033

Sex of child

 Male

0.6658*

0.1217

0.4653

0.9525

Education level of mother

 Primary

0.9088

0.2644

0.5138

1.6073

 Secondary

1.1236

0.3977

0.5615

2.2484

 Tertiary

1.03E-12

6.80E-07

0.0000

Occupation

 Mother

1.8247

0.4044

1.1818

2.8172

 Father

0.6392

0.2113

0.3344

1.2218

Water and sanitation

 Portable water

0.8138

0.2004

0.5022

1.3187

 Improved toilet

1.0969

0.1997

0.7677

1.5673

Region

 Central

0.6333

0.1634

0.3819

1.0500

 Southern

0.8655

0.1965

0.5547

1.3506

 Intercept

0.3907

0.2534

0.1096

1.3928

 Gamma

 − 0.1062*

0.0086

 − 0.1231

 − 0.0894

 Frailty theta

 − 13.389

435.670

 − 867.5

840.6

 Frailty Kendall’s tau (theta)

0.000*

0.001

–

 Log likelihood

 − 349.113

 Chi-square

199.49*