Table 4.
Explanation of Basis Functions Identified in the Final Multivariate Adaptive Regression Splines Model
| Basis Function | Function | Coefficient in Model | Interpretation and No. of Patients Basis Function Applies to |
|---|---|---|---|
| BF0 | Constant/intercept | 0.652 | Baseline probability of sputum conversion |
| BF1 | max (0, INH Cmax – 4.6) | 0.24 | Where INH Cmax >4.6 mg/L (n = 26), the probability of culture conversion was increased as an additive effect (+0.24 * BF1). However, at or below 4.6 mg/L, the effect of BF1 became zero. |
| BF2 | max (0, 4.6 – INH Cmax) | 0.17 | The mirror image of BF1, basis function 2 (BF2), had a lower bound of 0 and was only retained when INH Cmax <4.6 mg/L (n = 74). As the value of INH Cmax decreased, the value of the function included increased as an additive effect (+0.17 * BF2). There were also some interactions with BF3, BF6 (ie, HIV-1 status and RIF Cmax/ MIC. |
| BF3 | max(subset = HIV infected) * BF2 | Nil | Basis function 3 was a dummy variable for HIV-infected patients and solely existed to interact with BF2 and only applied to HIV-1–infected patients with INH Cmax <4.6 mg/L (n = 46). |
| BF4 | max (0, CD4 – 190) * BF3 | –0.001 | BF4 retained its function only in HIV-infected patients with CD4 lymphocyte count >190 (n = 40). For these patients, probability of culture conversion was reduced by a small factor (–0.001 * BF4) as CD4+ lymphocyte count increased from 190 upwards. This function was modified by an interaction with BF2 where the effect size increased as INH Cmax decreased from 4.6 to 0 mg/L. |
| BF5 | max(subset = smear grade 3+) | –0.33 | In those with an initial sputum smear grade of 3+, the average probability of culture conversion was decreased (–0.33 * BF5) (n = 24). |
| BF6 | max (0, 28.00 – RIF Cmax /MIC) * BF2 | –0.016 | For patients with RIF Cmax/MIC <28 (n = 12), probability of culture conversion decreased as per negative coefficient (–0.016) as RIF Cmax/MIC decreased from 28 to 0 (–0.016 * BF6). This function was modified by an interaction with BF2, where the negative effect increased as INH Cmax increased from 0 to 4.6 mg/L. |
Abbreviations: BF, basis function; Cmax, maximum concentration; HIV, human immunodeficiency virus; INH, isoniazid; MIC, minimum inhibitory concentration; RIF, rifampicin.