Models for Predicting Time to Sputum Conversion Among Multi-Drug Resistant Tuberculosis Patients in Lagos, South–West Nigeria

Background: Multi-drug resistant tuberculosis (MDR-TB) develops due to problems such as irregular drug supply, poor drug quality, inappropriate prescription, and poor adherence to treatment. These factors allow the development and subsequent transmission of resistant strains of the pathogen. However, due to the chronic nature of MDR-TB, cure models allow us to investigate the covariates that are associated with the long-term effects of time-to-sputum conversion among multi-drug resistant (MDR-TB) tuberculosis individuals. Therefore, this study was designed to develop suitable cure models that can predict time to sputum conversion among MDR-TB patients. Methods: A retrospective clinic-based cohort study was conducted on 413 records of patients who were diagnosed of MDR-TB and met inclusion criteria from April 2012 to October 2016 at the Infectious Disease Hospital, Lagos. The main outcome measure (time-to-sputum conversion) was the time from the date of MDR-TB treatment to the date of specimen collection for the first of two consecutive negative smear and culture taken 30 days apart. The predictor variables of interest include: demographic (age, gender and marital status) and clinical (registration group, number of drugs resistant to at treatment initiation, HIV status, diabetes status, and adherence with medication) characteristics. Kaplan-Meier estimates of a detailed survivorship pattern among the patients were examined using Cox regression models. Mixture Cox cure models were fitted to the main outcome variable using Log-normal, Log-logistic and Weibull models as alternatives to the violation of Proportional Hazard (PH) assumption. Akaike Information Criterion (AIC) was used for models comparison based on different distributions, while the effect of predictors of time to sputum conversion was reported as Hazard Ratio (HR) at α0.05. Results: Age was 36.8 ± 12.7 years, 60.8% were male and 67.6% were married. Majority of the patients (58.4%) converted to sputum negatives. Patients who were resistant to two drugs at treatment initiation had 39% rate of conversion than those resistant to at least three drugs [HR: 1.39; CI: 0.98, 1.98]. The likelihood of sputum conversion time was shorter among non-diabetic patients compared to diabetics [HR: 0.55; CI: 0.24, 0.85]. The overall median time for sputum conversion was 5.5 (IQR: 1.5–11.5). In the cure model, resistance to more drugs at the time of initiation was significantly associated with a longer time to sputum culture conversion for Log normal Cox mixture [2.06 (1.36–3.47)]; Log-logistic Cox mixture cure [2.56(1.85–4.09)]; and Weibull Cox mixture [2.81(1.94–4.19)]. Diabetic patients had a significantly higher sputum conversion rate compared to non-diabetics; Log-normal Cox mixture [2.03(1.17–3.58)]; Log-logistic Cox mixture cure [2.11(1.25–3.82)]; and Weibull Cox mixture [2.02(1.17–3.34)]. However, Log-normal PH model gave the best fit and provided the fitness statistics [(−2LogL: 519.84); (AIC: 1053.68); (BIC: 1078.04)]. The best fitting Log-normal PH model was Y = 1.00X1+2.06X2+0.98X3+2.03X4+ε where Y is time to sputum conversion and Xs are age, number of drugs, adherence, and diabetes status. Conclusion: The models confirmed the presence of some factors related with sputum conversion time in Nigeria. The quantum of drugs resistant at treatment initiation and diabetes status would aid the clinicians in predicting the rate of sputum conversion of patients.


INTRODUCTION
Tuberculosis (TB) is second to HIV/AIDS as the greatest killer worldwide due to a single infectious agent. "Nigeria is now the 3rd highest TB country in the world and the first in African region" was among the 22 high burden countries with an annual incidence of 338 per 100,000 and prevalence of 322 per 100,000 individuals (1). According to the National TB Prevalence Survey in 2012, the report also confirmed a worrisome situation with regards to Multi-Drug Resistance Tuberculosis (MDR-TB). Consequently, "Nigeria is now the 13th highest MDR-TB country globally and 2nd highest in the Africa region" (1). In 2014, an estimated 480,000 new cases of MDR-TB occurred and about 190,000 people died of MDR-TB. Since then MDR-TB has emerged as a worldwide problem with an estimated incidence of 425,000 cases occurring annually and the worldwide prevalence estimated to be 2-to 3-times the incidence (1). Yearly, about 8 million people were infected with tuberculosis with an estimated 1.8 million casualties, despite extensive vaccination and drug treatment programmes. In Nigeria, the estimated number of patients with multi-drug resistant tuberculosis (MDR-TB) varies between 2,700 and 4,500 while the prevalence rate of MDR-TB was 2.9% among new patients and 14.5% among previously treated cases in Nigeria (2).
Several studies have consistently reported that different socioeconomic problems have influenced outcomes of patients with tuberculosis condition. However, very few of these studies, particularly in Nigeria and in Africa have studied any correlates and prognostic differentials for predicting time to sputum conversion among MDR-TB patients. The knowledge of the correlates and prognostic differentials of sputum conversion time of multi-drug resistance would provide insight into cause and timings of the relapse and factors that influence drug failure.
This would help considerably in the management of patients with tuberculosis condition and facilitate the reduction of the degree, as well as, the frequency of the ailment.
Sputum conversion (which is used to monitor program performance) is one the most important interim indicators of pulmonary tuberculosis treatment outcome, measuring efficacy and identifying the constraints. Culture-based monitoring of MDR-TB patients is used to evaluate treatment efficacy and helps to identify those who remain infectious. The internationally agreed-upon definition of culture conversion is two consecutive negative smear/culture from sputum samples collected ≥30 days apart (3). Early conversion is very important to prevent transmission of MDR-TB, reduce hospitalization time, and reduce cost related to infection control measures. There is also some evidence that delayed sputum conversion is associated with amplifications of drug resistance (4). However, due to the chronic nature of MDR-TB, cure models allow us to investigate the covariates that are associated with the long-term effects of time to sputum conversion among MDR-TB individuals (5,6). Therefore, this study investigated the survival of tuberculosis patients with the aid of suitable models by predicting the time to sputum conversion.

Study Area and Period
A retrospective cohort analysis was conducted on 413 records of patients who were diagnosed of MDR-TB and met inclusion criteria from April 2012 to October 2016 at the Infectious Disease Hospital, Lagos. Four hundred and twenty-one patients were recruited for the study. The Cochran's sample size formula was used to calculate sample size for the study: n = Z 2 pq/d 2 Where n is the estimated sample size calculation Z = standard normal deviate corresponding to 2-sided level of 1% significance level = 2.33 p = prevalence of MDR-TB among cohort of treated patients = 13.1% 2 q = 1-p = 1-0.131 = 0.869 d = desired level of precision = 4% n = 2.33 2 × 0.131 × 0.869/(0.04) 2 = 386 Therefore, 7% addition of the calculated sample size was added to make up for patients who met the inclusion criteria. A total of 413 patients which represent 99.5% of the estimated sample size were recruited for the study.

Data Management And Analysis
R statistical software was used in carrying out the Kaplan-Meier Estimation and Modeling. Statistical Package for Social Sciences (IBM) version 20.0 was used to produce life tables in order to give a detailed survivorship pattern among MDR-TB patients and also to assess the effect of other socio-biological factorsusing Cox regression models. The Cox proportional hazard model was used to determine which of the explanatory variables explains differences in time to sputum conversion of patients with multidrug resistant tuberculosis. Descriptive statistical techniques were employed to examine the distribution of the patients according to some socio-economic and demographic variables of interest. Mixture Cox cure models were also fitted to the data using Log-normal, Log-logistic, and Weibull models (7,8).
The goodness of fit was assessed using the maximum likelihood technique of −2Loglikelihood statistic. Akaike Information Criterion (AIC) was used for model comparison based on different distributions (9, 10), while the effect of predictors of time to sputum conversion was reported as Hazard Ratios at α 0.05

Socio-Demographic Characteristics
A total of 413 multi-drug tuberculosis records of patients were reviewed (see Table 1).  Table 2 shows the clinical characteristics of the MDR-TB patients. A larger percentage (86.9%) of the patients was of pulmonary tuberculosis status. The distribution ratio of the registration category of the patients in respect to new and retreatment cases was 1:3. More than half of them (58.4) converted within the duration of study period while among non-converted, 11.4% extended into extensive drug resistant category. A paltry percentage (13.3%) of the patients were HIV positive and on anti-retroviral treatment (11.1%). Less than a fifth of the patients (15.5%) were cured while 7.3% died, 8.2% are lost to follow-up, 9.2% defaulted, and 5.3% relapsed.

Factors Associated With Time to Sputum Conversion Among Multi-Drug Resistant Tuberculosis Patients
Factors associated with time to sputum conversion among MDR-TB patients are as shown in Table 3. The overall median time for sputum conversion was 5.5 (IQR: 1.5-11.5) among those who converted. The median sputum conversion time of patients who resided within Lagos was 3.5 (IQR: 1.5-6.0) months compared to 5.5 (IQR: 3.0-8.5) among those who resided outside Lagos [p = 0.037]. In respect of age, the median sputum conversion time for patients who were ≤40 years was 4.5 (IQR: 2.0-11.5) compared to 5.25 (IQR: 2.33-9.5) among patients who were older than 40 years [p < 0.001]. Also, the median sputum conversion among patients who were resistant to at most two drugs at treatment initiation was 3.75 (IQR: 2.9-6.2) compared to 5.5 (4.6-9.8) among patients who were resistant to at least three drugs [p = 0.002]. The median sputum conversion time for patients who  The factors identified to be significantly associated with time to sputum conversion in bivariate analysis were harvested and subjected to multivariate analysis. The result of the multivariate Cox regression analysis for time-to-sputum conversion is shown in Table 4. The dependent variable in Table 4

Factors Associated With Time to Sputum Conversion Among MDR-TB Patients Using Mixture Cure Model
All the Cox PH mixture cure models showed that all the selected covariates had no effect on the sputum conversion time except

DISCUSSION
This study provides important information for understanding the development of suitable models that could predict time-tosputum conversion among MDR-TB patients. The findings can support activities being implemented to decrease the burden of tuberculosis. An overwhelming majority of the patients were male. This is in agreement with the findings of Hovhannesyan and Breeze (11) that there are fewer females than males in cases of multi-drug resistant TB condition. Nigerian women are extremely sensitive about the stigma associated with TB disease and negative social consequences have been shown to be more of importance to women (12)(13)(14)(15)(16). This differential could be attributed to biological and epidemiological characteristics, as well as, socio-economic and cultural barriers in access to health care (17). Moreover, studies have shown that women with pulmonary TB are diagnosed on average 2 weeks later than men due to a delay from the health care provider, and in a study on cough patients it was found that men more often than women were asked for sputum specimen (18,19). According to this finding, there is an increasing risk of TB drug adverse events when age increases. Sylvere (19) reported that about two-third of the male population were MDR-TB patients. In previous reports, the occurrence of any major side effects has been associated with age, especially amongst the elderly (13). The frequency of adverse reactions has shown to increase in a progressive and direct form in relationship to age. Overall, vulnerability to adverse reactions are more probable at older ages (20)(21)(22)(23). This is usually due to high hepatotoxic level caused by significant reduction in clearance rate of metabolized drug agents by the cytochrome P450 enzyme, changes in the hepatic blood flow distribution, as well as, other factors affecting liver function (24). By and large, favorable outcomes can be achieved in co-infected patients using a communitybased treatment model when both MDR-TB and HIV disease are treated concurrently and treatment is initiated promptly.
In this study, patients who resided within Lagos had twelve percent decreased rate of time-to-sputum conversion than those who resided outside Lagos. This variation could be attributed to the proximity to the health care facility for patients who reside within Lagos (25). Also, patients who were resistant to one or two drugs at treatment initiation had approximately fortypercent (39%) rate of sputum conversion than those who were resistant to at least three drugs. This finding was consistent with a previous study of Oladimeji et al. (2) on Intensive-Phase Treatment Outcomes among Hospitalized MDR-TB from a Nationwide Cohort in Nigeria. Besides, non-diabetic patients had 55% rate of sputum conversion than diabetic patients while patients who adhered with medication had about twenty-percent (19%) rate of sputum conversion than non-adherence. These results were true reflection of better monitoring mechanism of patients with prognostic factors of MDR-TB in this facility.
Moreover, the quantum of drugs resistant to treatment initiation and diabetes status emerged as significant risk factors, even after controlling for other variables. The results suggested that patients who had fewer numbers of drugs and diabetic status significantly predicted the sputum conversion time for the converted patients. The reasons for this require further investigation. One explanation might be due to misclassification in proper case definition of the MDR-TB patients since the study was purely based on analytical retrospective study. This is consistent with other MDR-TB programs showing that later cohort's outcomes are likely to be different than earlier cohort outcomes (22).
This research provides an Expectation-maximization (EM) algorithm to fit the mixture cure model to the grouped relative survival data. It can fit both a parametric and a semiparametric mixture cure model. This algorithm utilizes the standard statistical software (R software) to achieve the M-step and is easier to implement than the Newton-Raphson. The EM algorithm is usually stable than the Newton-Raphson method (26) and the convergence of the EM algorithm is generally fast for the grouped survival data. The estimate of the mixture cure model was fitted by making parametric assumptions visà-vis; Log-normal, Log-logistic, and Weibull PH Cox mixture cure. The resulting model showed no significant effects on the treatment initiation period among the patients. However, among the entire model, the Log normal PH cure model has the best fitted data as it yielded the lowest goodness of fits criteria.
From some developed models, various studies have proposed and assessed parametric and semi-parametric mixture cure models such as Default time from tuberculosis treatment in the Southern Republic of Benin Using Mixture Cure Model for Survival Analysis (19). This cohort assessed the cured fraction, the conditional probability of default (CPD) from treatment course and identified the risk factors predicting its timing. With Cox proportional hazards (PH), predictors of default time were HIV/AIDS, TB history, and Age. However, with logistic Cox PH mixture cure model, HIV/AIDS, and Age significantly increased the probability of default, whereas TB history significantly reduced default probability from previous TB infection. This study findings suggests that time to sputum conversion model could enhance the compliance of patients with anti-TB treatment where Age,

CONCLUSION
In conclusion, despite high rate of drug resistance in the studied population, most patients with multi-drug resistant TB achieved sputum conversion within 13 weeks of starting treatment. Factors negatively associated with culture conversion at 2 months can be easily identified either before diagnosis or early in the course of MDR-TB treatment. This may help in better care of individual patients by identifying them early and treating them vigorously. Mixture cure models allow both the cured proportion and the remaining uncured individuals to be modeled simultaneously with incidence and latency portions, respectively. The great advantage of the mixture model is related to the simple interpretations, especially for medical researchers, where we have the proportion of cured and non-cured individuals given directly in the survival function expression.